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fraction operations unit

Fraction Operations Unit 6th Grade CCSS

$ 14.00

An 11 day CCSS-Aligned Fraction Operations Unit including: a review of adding fractions, subtracting fractions, and multiplying fractions, and breaking down division of fractions by whole numbers, dividing whole numbers by fractions, and dividing fractions by fractions.

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This Fraction Operations Unit 6th Grade CCSS  includes: a review of adding fractions, subtracting fractions, and multiplying fractions, and breaking down division of fractions by whole numbers, dividing whole numbers by fractions, and dividing fractions by fractions.

Students will practice with both skill-based problems, real-world application questions, and error analysis to support higher level thinking skills.  You can reach your students and teach the standards without all of the prep and stress of creating materials!

This fraction operations unit is easy-to-implement and scaffolded to support student success.

Standards:   6.NS.1 and 6.NS.4;  Texas Teacher?  Grab the TEKS-Aligned Positive Rational Numbers Unit.  Please don’t purchase both as there is overlapping content.

Learning Focus:

  • review concepts of factors and multiples
  • add, subtract, multiply and divide fractions
  • understand and apply fraction operations to real-world situations

What is included in the 6th grade ccss Fraction Operations Unit?

1. Unit Overviews

  • Streamline planning with unit overviews that include essential questions, big ideas, vertical alignment, vocabulary, and common misconceptions.
  • A pacing guide and tips for teaching each topic are included to help you be more efficient in your planning.

2. Student Handouts

  • Student-friendly guided notes are scaffolded to support student learning.
  • Available as a PDF and the student handouts/homework/study guides have been converted to Google Slides™ for your convenience.

3. Independent Practice

  • Daily homework is aligned directly to the student handouts and is versatile for both in class or at home practice.

4. Assessments

  • 1-2 quizzes, a unit study guide, and a unit test allow you to easily assess and meet the needs of your students.
  • The Unit Test is available as an editable PPT, so that you can modify and adjust questions as needed.

5. Answer Keys

  • All answer keys are included.

***Please download a preview to see sample pages and more information.***

How to use this resource:

  • Use as a whole group, guided notes setting
  • Use in a small group, math workshop setting
  • Chunk each student handout to incorporate whole group instruction, small group practice, and independent practice.
  • Incorporate our  Fraction Operations Activity Bundle  for hands-on activities as additional and engaging practice opportunities.

Time to Complete:

  • Each student handout is designed for a single class period. However, feel free to review the problems and select specific ones to meet your student needs. There are multiple problems to practice the same concepts, so you can adjust as needed.

Is this resource editable?

  • The unit test is editable with Microsoft PPT. The remainder of the file is a PDF and not editable.

Looking for more 6th Grade Math Material? Join our All Access Membership Community! You can reach your students without the “I still have to prep for tomorrow” stress, the constant overwhelm of teaching multiple preps, and the hamster wheel demands of creating your own teaching materials.

  • Grade Level Curriculum
  • Supplemental Digital Components
  • Complete and Comprehensive Student Video Library 

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Licensing: This file is a license for ONE teacher and their students. Please purchase the appropriate number of licenses if you plan to use this resource with your team. Thank you!

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Maneuvering the Middle ® Terms of Use: Products by Maneuvering the Middle®, LLC may be used by the purchaser for their classroom use only. This is a single classroom license only. All rights reserved. Resources may only be posted online in an LMS such as Google Classroom, Canvas, or Schoology. Students should be the only ones able to access the resources.  It is a copyright violation to upload the files to school/district servers or shared Google Drives. See more information on our terms of use here . 

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This file is a license for one teacher and their students. Please purchase the appropriate number of licenses if you plan to use this resource with your team. Thank you!

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Maneuvering the Middle® Terms of Use

Products by Maneuvering the Middle, LLC may be used by the purchaser for their classroom use only. This is a single classroom license only. All rights reserved. Resources may only be posted online if they are behind a password-protected site.

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unit fraction operations homework 2 answer key

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This resource is often paired with:.

This 6th grade Digital activity Bundle include interactive slides (drag and match, using the typing tool, using the shape tool) and exit tickets.

6th Grade Digital Math Activity Bundle

A 15-day Positive Rational Number Operations unit for 6th grade TEKS includes adding, subtracting, multiplying, and dividing decimals and fractions. | maneuveringthemiddle.com

Positive Rational Numbers Unit 6th Grade TEKS

An engaging Fraction Operations Activity Bundle for 6th-Grade with 9 hands-on and collaborative activities for middle school math students! | maneuveringthemiddle.com

Fraction Operations Activity Bundle 6th Grade

unit fraction operations homework 2 answer key

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Mathematics LibreTexts

9.5: Homework

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  • Page ID 70336

  • Julie Harland
  • MiraCosta College
  • Submit homework separately from this workbook and staple all pages together. (One staple for the entire submission of all the unit homework)
  • Start a new module on the front side of a new page and write the module number on the top center of the page.
  • Answers without supporting work will receive no credit.
  • Some solutions are given in the solutions manual.
  • You may work with classmates but do your own work.

Do each of the following steps using your C-strips.

  • State how many C-strips (each an equal part of the whole) make up one unit.
  • State which C-strip makes up one part of the whole.
  • State the fraction that the C-strip in part b represents.
  • State how many of the C-strips in part b you need to make into a train.
  • State which C-strip is the length of the train you made in part c

a. If S represents 1 unit, then which C-strip represents \(\frac{7}{11}\)?

b. If H represents 1 unit, then which C-strip represents \(\frac{2}{3}\)?

c. If P represents 1 unit, then which C-strip represents \(\frac{3}{2}\)?

d. If L represents 1 unit, then which C-strip represents 3 ?

e. If Y represents 1 unit, then which C-strip represents \(\frac{6}{5}\)?

f. If O represents 1 unit, then which C-strip represents \(\frac{1}{2}\)?

g. If B represents 1 unit, then which C-strip represents \(\frac{4}{3}\)?

Do each step using your C-strips.

  • State how many C-strips will make up the named C-strip stated in the problem.
  • Which C-strip makes up one equal part?
  • State how many of the C-strips in part b will make up one unit.
  • Form the unit by making a train from the equal parts (C-strip in part b) and state which C-strip has the same length as that train.

a. If O represents \(\frac{5}{6}\), then which C-strip is 1 unit?

b. If W represents \(\frac{1}{7}\), then which C-strip is 1 unit?

c. If D represents \(\frac{3}{2}\), then which C-strip is 1 unit?

d. If N represents \(\frac{4}{3}\), then which C-strip is 1 unit?

e. If D represents 3, then which C-strip is 1 unit?

f. If K represents \(\frac{7}{9}\), then which C-strip is 1 unit?

  • State which C-strip is one unit.
  • State which C-strip is the answer.

a. If N represents \(\frac{2}{3}\), then which C-strip represents \(\frac{1}{4}\)?

b. If D represents \(\frac{3}{4}\), then which C-strip represents \(\frac{3}{2}\)?

c. If B represents \(\frac{3}{2}\), this which C-strip represents \(\frac{4}{3}\)?

Use your fraction arrays to determine all fractions on the fraction array that are equivalent to 3/4. Do this by finding 3/4 on the array, and seeing what other numbers are the same length. Include a diagram.

Use your multiple strips to write 6 fractions equivalent to 5/6. Draw the strips.

Use your multiple strips to write 6 fractions equivalent to 3/8 Draw the strips.

Compare 3/8 and 1/3 using models. Show all of the steps, and explain the procedure as shown in this module.

Add 3/8 and 1/3 using models. Show all of the steps, and explain the procedure as shown in this module.

Do the following subtraction using models: 3/5 – 1/4. Show all of the steps, and explain the procedure as shown in this module.

Do the following multiplications using models. Show all of the steps, and explain the procedure as shown in this module.

a. 3/8 \(\cdot\) 2/5

b. 4/7 \(\cdot\) 2/3

By looking at the final drawing someone made to model a multiplication of two fractions, determine which multiplication was performed, and then state the answer.

a. 5/6 \(\cdot\) 2/3 OR 2/3 \(\cdot\) 5/6

unit fraction operations homework 2 answer key

b. 1/2 \(\cdot\) 7/8 OR 7/8 \(\cdot\) 1/2

11b.PNG

If all of the dots shown for each problem represent 1 unit, determine the multiplication problem that someone did to get the answer, and state the answer.

12a.PNG

Fill in the chart showing how to do the following multiplications using C-strips. The multiplication is in the first column. State an appropriate choice for the unit (name a C-strip, or sum of two C-strips) in the second column. Write the C-strip obtained after the first part of the multiplication (which is the second fraction as a part of the unit) in the third column. Then, do the final multiplication, and write the C-strip obtained in the fourth column. In the fifth column, write a fraction using C-strips putting the final unit obtained in the fourth column as the numerator, and the unit in the denominator. Then, in the last column, write the answer as a fraction. Do not simplify.

Perform the following division using the box and dot methods. First define the unit. Then explain and show all of the steps. Include diagrams.

a. 5 \(\div\) 1/3

b. 3/4 \(\div\) 1/3

Determine if the following statements are true or false by comparing cross products.

a. 19/23 = 57/69

b. 24/37 = 68/91

Write each fraction in simplest form using each of the two methods:

(1) prime factorization and

(2) finding GCF.

a. \(\frac{216}{420}\)

b. \(\frac{195}{286}\)

Use cross products to compare each of the following fractions. Use < or >.

a. 18/23 and 5/8

b. 11/18 and 121/250

Find 3 rational numbers, written with a common denominator, between 3/8 and 5/8.

Find 3 rational numbers, written with a common denominator, between 1/2 and 4/7.

a. 21 of John's students have cats at home. This represents 7/10 of John's students. How many students are in John's class? Solve the problem using models. Explain how the model works.

b. At an elementary school, 38 teachers drive alone to work. This represents 2/3 of the teachers. How many teachers work at the school? Solve the problem using models. Explain how the model works.

Write in words how to read each of the following decimals.

Multiply the following decimals mentally then do it again by showing the same steps as shown in this module..

a. (0.3)(0.8)

b. (1.2)(0.4)

c. (1.22)(2.3)

d. (3.2)(2.41)

For each fraction, determine if it can be written as an equivalent fraction with a power of ten in the denominator. If a fraction cannot be written as a terminal decimal, explain why not. Otherwise, show ALL of the steps to write it as a terminal decimal.

a. \(\frac{11}{16}\)

b. \(\frac{3}{125}\)

c. \(\frac{1}{12}\)

d. \(\frac{9}{40}\)

e. \(\frac{21}{56}\)

Rewrite each of the following decimals as simplified fractions. For repeating decimals, use the techniques shown in this module. Then, check your answer using a calculator by dividing the numerator by the denominator to see if the result matches the original problem.

a. \(0.\bar{7}\)

b. \(0.\overline{72}\)

c. \(0.\overline{235}\)

d. \(0.2\bar{5}\)

e. \(0.3\overline{42}\)

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Numbers & Operations - Part 3: Fraction Operations Unit

Topics Include: Equal Parts Equivalent Fractions Finding Common Denominators Adding Fractions Subtracting Fractions Adding Mixed Numbers Subtracting Mixed Numbers Multi-Step Word Problems Multiplying Fractions Multiplying Fractions and Whole Numbers Multiplying with Mixed Numbers Interpreting Multiplication of Fractions Area of Fractional Side Length Rectangles Dividing Unit Fractions by Whole Numbers Dividing Whole Numbers by Unit Fractions Fraction Division

  • Numbers & Operations - Part 3: Fraction Operations Feb. 4, 2020, 7:21 a.m.
  • Numbers & Operations - Part 3 Unit Plan Feb. 4, 2020, 7:35 a.m.
  • Numbers & Operations - Part 3: Fraction Operations CW-HW Sept. 29, 2023, 12:27 p.m.
  • Virtual Lab: Fraction Maker Answer Key Teacher Login Required Nov. 19, 2019, 7:19 p.m.
  • Virtual Lab: Fraction Maker Nov. 19, 2019, 7:19 p.m.
  • Numbers & Operations - Part 3 Quizzes-Requizzes Teacher Login Required Feb. 4, 2020, 7:32 a.m.
  • Numbers & Operations - Part 3 Test-Retest Teacher Login Required Feb. 4, 2020, 7:34 a.m.

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A fraction represents a part of a whole or a part of a group. It consists of a numerator and a denominator , separated by a horizontal line. The numerator represents the number of parts we have, while the denominator represents the total number of parts that make up a whole.

Types of Fractions

There are different types of fractions:

  • Proper Fractions: When the numerator is less than the denominator , e.g., 1/2, 3/4.
  • Improper Fractions: When the numerator is greater than or equal to the denominator , e.g., 5/3, 7/4.
  • Mixed Numbers: A combination of a whole number and a fraction, e.g., 2 1/3, 3 2/5.
  • Equivalent Fractions: Fractions that represent the same part of a whole, e.g., 1/2 and 2/4 are equivalent.

Operations with Fractions

We can perform various operations with fractions:

  • Addition and Subtraction : When adding or subtracting fractions, we need to have a common denominator .
  • Multiplication : To multiply fractions, we simply multiply the numerators and denominators together.
  • Division : To divide fractions, we multiply by the reciprocal of the divisor .

Here are some examples of fractions:

  • 1/2 - One-half of a whole.
  • 3/4 - Three-fourths of a whole.
  • 2 1/3 - Two and one-third, a mixed number.
  • 5/6 + 1/3 = 9/6 - Adding fractions with a common denominator .
  • 2/3 * 4/5 = 8/15 - Multiplying fractions.
  • 3/4 ÷ 2/5 = 15/8 - Dividing fractions by multiplying by the reciprocal.

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Chapter 1: Algebra Review

1.2 Fractions (Review)

Working with fractions is a very important foundational skill in algebra. This section will briefly review reducing, multiplying, dividing, adding, and subtracting fractions. As this is a review, concepts will not be explained in as much detail as they are in other lessons. Final answers of questions working with fractions tend to always be reduced. Reducing fractions is simply done by dividing both the numerator and denominator by the same number.

Example 1.2.1

Reduce [latex]\dfrac{36}{84}.[/latex]

[latex]\begin{array}{rl} \dfrac{36}{84}&\text{Both the numerator and the denominator are divisible by 4.} \\ \\ \dfrac{36\div 4}{84\div 4}=\dfrac{9}{21}&\text{Both the numerator and the denominator are divisible by 3.} \\ \\ \dfrac{9\div 3}{21 \div 3}=\dfrac{3}{7}&\text{Solution} \end{array}[/latex]

The previous example could have been done in one step by dividing both the numerator and the denominator by 12. Another solution could have been to divide by 2 twice and then by 3 once (in any order). It is not important which method is used as long as the fraction is reduced as much as possible.

The easiest operation to complete with fractions is multiplication. Fractions can be multiplied straight across, meaning all numerators and all denominators are multiplied together.

Example 1.2.2

Multiply [latex]\dfrac{6}{7}\cdot \dfrac{3}{5}.[/latex]

[latex]\begin{array}{rl} \dfrac{6}{7}\cdot \dfrac{3}{5} & \text{Multiply numerators and denominators, respectively.} \\ \\ \dfrac{18}{35} & \text{Solution} \end{array}[/latex]

Before multiplying, fractions can be reduced. It is possible to reduce vertically within a single fraction, or diagonally within several fractions, as long as one number from the numerator and one number from the denominator are used.

Example 1.2.3

Dividing fractions is very similar to multiplying, with one extra step. Dividing fractions necessitates first taking the reciprocal of the second fraction. Once this is done, multiply the fractions together. This multiplication problem solves just like the previous problem.

Example 1.2.4

Divide [latex]\dfrac{21}{16}\div \dfrac{28}{6}.[/latex]

[latex]\begin{array}{rl} \dfrac{21}{16}\div \dfrac{28}{6}&\text{Take the reciprocal of the second fraction and multiply it by the first.} \\ \\ \dfrac{\cancel{21}\text{ }3}{\cancel{16}\text{ }8}\cdot \dfrac{\cancel{6}\text{ }3}{\cancel{28}\text{ }4} & \text{Reduce 21 and 28 by dividing by 7, and reduce 6 and 16 by dividing by 2.} \\ \\ \dfrac{3\cdot 3}{8\cdot 4} & \text{Multiply numerators and denominators across.} \\ \\ \dfrac{9}{32} & \text{Solution} \end{array}[/latex]

To add and subtract fractions, it is necessary to first find the least common denominator (LCD). There are several ways to find the LCD. One way is to break the denominators into primes, write out the primes that make up the first denominator, and only add primes that are needed to make the other denominators.

Example 1.2.5

Find the LCD of 8 and 12.

Break 8 and 12 into primes:

[latex]\begin{array}{rrl} 8 &= &2 \times 2 \times 2 \\ 12 &= &2 \times 2 \times 3 \end{array}[/latex]

The LCD will contain all the primes needed to make each number above.

[latex]\text{LCD}=\rlap{\overbrace{2\times 2\times 2}^8}2\times \underbrace{2\times 2\times 3}_{12}=4[/latex]

Adding and subtracting fractions is identical in process. If both fractions already have a common denominator, simply add or subtract the numerators and keep the denominator.

Example 1.2.6

Add [latex]\dfrac{7}{8}+\dfrac{3}{8}.[/latex]

[latex]\begin{array}{rl} \dfrac{7}{8}+\dfrac{3}{8}&\text{Same denominator, so add }7+3. \\ \\ \dfrac{10}{8}&\text{Reduce answer by dividing the numerator and denominator by 2.} \\ \\ \dfrac{5}{4} &\text{Solution} \end{array}[/latex]

While [latex]\dfrac{5}{4}[/latex] can be written as the mixed number [latex]1 \dfrac{1}{4}[/latex], algebra almost never uses mixed numbers. For this reason, always use the improper fraction, not the mixed number.

Example 1.2.7

Subtract [latex]\dfrac{13}{6}-\dfrac{9}{6}.[/latex]

[latex]\begin{array}{rl} \dfrac{13}{6}-\dfrac{9}{6} & \text{Same denominator, so subtract }13-9. \\ \\ \dfrac{4}{6} & \text{Reduce answer by dividing by 2.} \\ \\ \dfrac{2}{3} & \text{Solution} \end{array}[/latex]

If the denominators do not match, it is necessary to first identify the LCD and build up each fraction by multiplying the numerator and denominator by the same number so each denominator is built up to the LCD.

Example 1.2.8

Example 1.2.9

Subtract [latex]\dfrac{2}{3}-\dfrac{1}{6}.[/latex]

[latex]\begin{array}{rl} \dfrac{2}{3}-\dfrac{1}{6} & \text{LCD is 6.} \\ \\ \dfrac{2\cdot 2}{2\cdot 3}-\dfrac{1}{6}& \text{Multiply the first fraction by 2.} \\ \\ \dfrac{4}{6}-\dfrac{1}{6} & \text{Same denominator, so subtract }4-1. \\ \\ \dfrac{3}{6}& \text{Reduce answer by dividing by 3.} \\ \\ \dfrac{1}{2} & \text{Solution} \end{array}[/latex]

For questions 1 to 18, simplify each fraction. Leave your answer as an improper fraction.

  • [latex]\dfrac{42}{12}[/latex]
  • [latex]\dfrac{25}{20}[/latex]
  • [latex]\dfrac{35}{25}[/latex]
  • [latex]\dfrac{24}{8}[/latex]
  • [latex]\dfrac{54}{36}[/latex]
  • [latex]\dfrac{30}{24}[/latex]
  • [latex]\dfrac{45}{36}[/latex]
  • [latex]\dfrac{36}{27}[/latex]
  • [latex]\dfrac{27}{18}[/latex]
  • [latex]\dfrac{48}{18}[/latex]
  • [latex]\dfrac{40}{16}[/latex]
  • [latex]\dfrac{48}{42}[/latex]
  • [latex]\dfrac{63}{18}[/latex]
  • [latex]\dfrac{16}{12}[/latex]
  • [latex]\dfrac{80}{60}[/latex]
  • [latex]\dfrac{72}{48}[/latex]
  • [latex]\dfrac{72}{60}[/latex]
  • [latex]\dfrac{126}{108}[/latex]

For questions 19 to 36, find each product. Leave your answer as an improper fraction.

  • [latex](9)\left(\dfrac{8}{9}\right)[/latex]
  • [latex](-2)\left(-\dfrac{5}{6}\right)[/latex]
  • [latex](2)\left(-\dfrac{2}{9}\right)[/latex]
  • [latex](-2)\left(\dfrac{1}{3}\right)[/latex]
  • [latex](-2)\left(\dfrac{13}{8}\right)[/latex]
  • [latex]\left(\dfrac{3}{2}\right) \left(\dfrac{1}{2}\right)[/latex]
  • [latex]\left(-\dfrac{6}{5}\right)\left(-\dfrac{11}{8}\right)[/latex]
  • [latex]\left(-\dfrac{3}{7}\right)\left(-\dfrac{11}{8}\right)[/latex]
  • [latex](8)\left(\dfrac{1}{2}\right)[/latex]
  • [latex](-2)\left(-\dfrac{9}{7}\right)[/latex]
  • [latex]\left(\dfrac{2}{3}\right)\left(\dfrac{3}{4}\right)[/latex]
  • [latex]\left(-\dfrac{17}{9}\right)\left(-\dfrac{3}{5}\right)[/latex]
  • [latex](2)\left(\dfrac{3}{2}\right)[/latex]
  • [latex]\left(\dfrac{17}{9}\right)\left(-\dfrac{3}{5}\right)[/latex]
  • [latex]\left(\dfrac{1}{2}\right)\left (-\dfrac{7}{5}\right)[/latex]
  • [latex]\left(\dfrac{1}{2}\right)\left(\dfrac{5}{7}\right)[/latex]
  • [latex]\left(\dfrac{5}{2}\right)\left(-\dfrac{0}{5}\right)[/latex]
  • [latex]\left(\dfrac{6}{0}\right)\left(\dfrac{6}{7}\right)[/latex]

For questions 37 to 52, find each quotient. Leave your answer as an improper fraction.

  • [latex]-2 \div \dfrac {7}{4}[/latex]
  • [latex]-\dfrac{12}{7} \div -\dfrac{9}{5}[/latex]
  • [latex]-\dfrac{1}{9} \div -\dfrac{1}{2}[/latex]
  • [latex]-2 \div -\dfrac{3}{2}[/latex]
  • [latex]-\dfrac{3}{2} \div \dfrac{13}{7}[/latex]
  • [latex]\dfrac{5}{3} \div \dfrac{7}{5}[/latex]
  • [latex]-1 \div \dfrac{2}{3}[/latex]
  • [latex]\dfrac{10}{9} \div -6[/latex]
  • [latex]\dfrac{8}{9} \div \dfrac{1}{5}[/latex]
  • [latex]\dfrac{1}{6} \div -\dfrac{5}{3}[/latex]
  • [latex]-\dfrac{9}{7} \div \dfrac{1}{5}[/latex]
  • [latex]-\dfrac{13}{8} \div -\dfrac{15}{8}[/latex]
  • [latex]-\dfrac{2}{9} \div -\dfrac{3}{2}[/latex]
  • [latex]-\dfrac{4}{5} \div -\dfrac{13}{8}[/latex]
  • [latex]\dfrac{1}{10} \div \dfrac{3}{2}[/latex]
  • [latex]\dfrac{5}{3} \div \dfrac{5}{3}[/latex]

For questions 53 to 70, evaluate each expression. Leave your answer as an improper fraction.

  • [latex]\dfrac{1}{3} + \left(-\dfrac{4}{3}\right)[/latex]
  • [latex]\dfrac{1}{7} + \left(-\dfrac{11}{7}\right)[/latex]
  • [latex]\dfrac{3}{7} - \dfrac{1}{7}[/latex]
  • [latex]\dfrac{1}{3} + \dfrac{5}{3}[/latex]
  • [latex]\dfrac{11}{6} + \dfrac{7}{6}[/latex]
  • [latex](-2)+ \left(-\dfrac{15}{8}\right)[/latex]
  • [latex]\dfrac{3}{5}+ \dfrac{5}{4}[/latex]
  • [latex](-1)-\dfrac{2}{3}[/latex]
  • [latex]\dfrac{2}{5}+ \dfrac{5}{4}[/latex]
  • [latex]\dfrac{12}{7}- \dfrac{9}{7}[/latex]
  • [latex]\dfrac{9}{8}+ \left(-\dfrac{2}{7}\right)[/latex]
  • [latex](-2)+ \dfrac{5}{6}[/latex]
  • [latex]1+ \left(-\dfrac{1}{3}\right)[/latex]
  • [latex]\dfrac{1}{2}- \dfrac{11}{6}[/latex]
  • [latex]\left(-\dfrac{1}{2}\right)+ \dfrac{3}{2}[/latex]
  • [latex]\dfrac{11}{8}- \dfrac{1}{22}[/latex]
  • [latex]\dfrac{1}{5}+ \dfrac{3}{4}[/latex]
  • [latex]\dfrac{6}{5}- \dfrac{8}{5}[/latex]

Answer Key 1.2

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Texas Go Math Grade 3 Lesson 2.2 Answer Key Unit Fractions of a Whole

Refer to our Texas Go Math Grade 3 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 3 Lesson 2.2 Answer Key Unit Fractions of a Whole.

Essential Question What do the top and bottom numbers of a fraction tell? Answer: A fraction is a number that mentions part of a whole or part of a group. In a fraction, the top number tells how many equal numbers of parts are being counted. The bottom number mentions how many equal parts are in the whole or in the group.

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Texas Go Math Grade 3 Lesson 2.2 Answer Key 1

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Math Talk Mathematical Processes Explain how you knew what number to write as the bottom number of the fraction in Exercise 1. Answer: I counted the total number of equal parts in the whole. Since there are 3 equal parts, I wrote 3 as the bottom number.

Texas Go Math Grade 3 Lesson 2.2 Answer Key 5

Write the number of equal parts in the whole. Then write the fraction that names the shaded part.

Texas Go Math Grade 3 Lesson 2.2 Answer Key 6

Write a fraction to name the yellow part of each group.

Texas Go Math Grade 3 Lesson 2.2 Answer Key 9

Question 7.

Texas Go Math Grade 3 Lesson 2.2 Answer Key 11

Problem Solving

Draw a picture of the whole.

Texas Go Math Grade 3 Lesson 2.2 Answer Key 13

Use the pictures for 11—13.

Question 11. Use Diagrams The missing parts of the pictures show what Kylie and Dylan ate for lunch. What fraction of the pizza did Dylan eat? Answer: \(\frac{1}{8}\)

Texas Go Math Grade 3 Lesson 2.2 Answer Key 15

Question 12. What fraction of the cookie did Kylie eat? Write the fraction in numbers and in words. Answer: \(\frac{1}{2}\) one half

Question 13. Write Math What’s the Question? The answer is \(\frac{\hat{1}}{4}\). Answer: What fraction of the fruit bar did Dylan eat?

Texas Go Math Grade 3 Lesson 2.2 Answer Key 16

Explanation: From the given question we can tell that the square is not divided into six equal parts, so he did not shade \(\frac{1}{2}\).

Texas Go Math Grade 3 Lesson 2.2 Answer Key 17

Daily Assessment Task

Fill in the bubble for the correct answer choice.

Question 16. There are 2 red cubes, 3 yellow cubes, and 1 blue cube in a bag. What fraction of the cubes are blue? (A) \(\frac{1}{4}\) (B) \(\frac{1}{3}\) (C) \(\frac{1}{6}\) (D) \(\frac{1}{2}\) Answer: \(\frac{1}{6}\)

Texas-Go-Math-Grade-3-Lesson-2.2-Answer-Key-16

Explanation: Brandon shared a large burrito with two of his friends. The fraction of the burrito did Brandon eat is \(\frac{1}{3}\).

Question 18. Multi-Step For an art project, Tonya and Sahil each have a piece of fabric cut into equal pieces. They each used one piece, or \(\frac{1}{3}\) of their fabric. How many more pieces altogether do Tonya and Sahil have left to use? (A) 2 (B) 6 (C) 4 (D) 5 Answer: 4

Explanation: Tonya and Sahil have left to use 4 more pieces altogether.

Texas Test Prep

Texas Go Math Grade 3 Lesson 2.2 Answer Key 19

Explanation: As mary shaded part of a rectangle. The \(\frac{1}{3}\) fraction names the part she shaded.

Texas Go Math Grade 3 Lesson 2.2 Homework and Practice Answer Key

Texas Go Math Grade 3 Lesson 2.2 Answer Key 20

Explanation: The fraction that names the shaded part is 2 equal parts.

Texas Go Math Grade 3 Lesson 2.2 Answer Key 21

Explanation: The fraction that names the shaded part is 6 equal parts

Texas Go Math Grade 3 Lesson 2.2 Answer Key 22

Explanation: The fraction that names the shaded part is 8 equal parts

Texas Go Math Grade 3 Lesson 2.2 Answer Key 23

Explanation: The fraction that names the shaded part is 4 equal parts

Question 5. Toni’s fruit bar is divided into three equal pieces. Toni ate one piece. What fraction of the fruit bar did Toni eat? Draw a picture to show your answer. Answer: \(\frac{1}{3}\)

Texas-Go-Math-Grade-3-Lesson-2.2-Answer-Key-5

Explanation: Kylie ate half of the sandwich for lunch. The \(\frac{1}{2}\) fraction of the sandwich Kylie ate.

Lesson Check

Fill in the bubble completely to show your answer.

Texas Go Math Grade 3 Lesson 2.2 Answer Key 25

Explanation: The \(\frac{1}{2}\) fraction names the shaded part.

Texas Go Math Grade 3 Lesson 2.2 Answer Key 26

Explanation: Mike divided a piece of paper into 4 equal parts and shaded one of the parts. Now the \(\frac{1}{4}\) of the piece of paper did Mike shade.

Texas Go Math Grade 3 Lesson 2.2 Answer Key 27

Explanation: The \(\frac{1}{3}\) of this rectangle is option D.

Question 10. Multi-Step Two brothers each have a sandwich divided into 4 equal pieces. Each brother eats one part, or \(\frac{1}{4}\), of his sandwich. How many parts of the sandwiches are left altogether? (A) 1 part (B) 4 parts (C) 6 parts (D) 8 parts Answer: 6 parts

Explanation: Two brothers each have a sandwich divided into 4 equal pieces. They both have eight pieces in total. Each one eats one part from eight pieces. Hence there are 6 parts of the sandwiches left altogether.

Go Math Grade 3 Lesson 2.2 Homework Answers Question 11. Multi-Step Taylor has a yellow block of cheese and an orange block of cheese. He cuts each block into eight equal parts and takes one part, or \(\frac{1}{8}\), of each block. How many parts of the blocks of cheese are left altogether? (A) 6 part (B) 14 parts (C) 8 parts (D) 12 parts Answer: 14 parts

Explanation: Taylor has a yellow block of cheese and an orange block of cheese. He cuts each block into eight equal parts. The total number of cheese blocks Taylor has is 16 parts. After that one block is taken from both yellow and orange. The parts of the blocks of cheese are left altogether is 16-2=14 parts.

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Everyday Math Grade 5 Answers Unit 2 Whole Number Place Value and Operations

Everyday mathematics 5th grade answer key unit 2 whole number place value and operations, everyday mathematics grade 5 home link 2.1 answers.

Solving Place-Value Riddles Solve the number riddles. Question 1. I have 5 digits. My 5 is worth 50,000. My 8 is worth 8,000. One of my 6s is worth 60. The other is worth 10 times as much. My other digit is a 0. What number am I? Answer: The number is 58,660 Explanation: Here I have 5 digits number. My 5 is worth 50,000 ; Ten thousand place. My 8 is worth 8,000 ; Thousands place. One of my 6s worth is 60. The number is written as 66; Tens place. My other digit is 0. 0 is in ones place. By adding the above numbers we got the 5 digit number. The number is 58,660.

Question 2. I have 5 digits. My 9 is worth 9 ∗ 10,000. My 2 is worth 2 thousand. One of my 7s is worth 70. The other is worth 10 times as much. My other digit is a 6. What number am I? Answer: The number is 92,776 Explanation: Here I have 5 digits number. My 9 is worth 9 ∗ 10,000 = 90,000; Ten thousand place. My 2 is worth 2,000; Thousands place. One of my 7s worth is 70. The number is written as 77; Tens place. My other digit is 6. 6 is in ones place. By adding the above numbers we got the 5 digit number. The number is 92,776.

Question 3. I have 4 digits. My 7 is worth 7 ∗ 1,000. My 2 is worth 200. One of my 4s is worth 40. The other is worth \(\frac{1}{10}\) as much. What number am I? Answer: The number is 7,244 Explanation: I have 4 digits number. My 7 is worth 7 ∗ 1,000 = 7,000; Thousands place. My 2 is worth 200. Hundreds place. One of my 4s is worth 40. The number is written as 44; tens place. By adding the above numbers we got the 4 digit number. The number is 7,244.

Question 4. I have 6 digits. One of my 3s is worth 300,000. The other is worth \(\frac{1}{10}\) as much. My 6 is worth 600. The rest of my digits are zeros. What number am I? Answer: The number is 330,600 Explanation: I have 6 digits number. My 3s is worth 300,000; The number is written as 330,000. My 6 is worth 600; Hundreds place. The rest of my digits are zeroes. By adding the above numbers we got the 6 digit number. The number is 330,600.

Question 5. I have 5 digits. My 4s are worth 4 [10,000s] and 4 ∗ 10. One of my 3s is worth 3,000. The other is worth \(\frac{1}{10}\) as much. My other digit is a 2. What number am I? Answer: The number is 43,342 Explanation: I have 5 digits number. My 4s is worth 4[10,000s]=40,000; and 4 ∗ 10= 40. My 3s is worth 3,000. The number is written as 3,300. The other digit is 2. keep 2 in ones place. By adding the above numbers we got the 5 digit number. The number is 43,342.

Question 6. I am the largest 7-digit number you can write with the digits 3, 6, 9, 4, 0, 8, and 2. What number am I? Answer: The largest 7-digit number with the above digits is 9,864,320 Explanation: We can write the largest seven digits number with the above digits. Write the above numbers in descending order. The largest seven digit number is 9,864,320.

Practice Solve. Question 7. 4 ∗ (3 + 2) = _______ Answer: 4 ∗(3 + 2) = 20 4 ∗ (5) = 20 Explanation: In the above expression we can observe two arithmetic operations. One is multiplication and other one is addition. First we have to perform addition operation and then multiplication operation. An addition sentence is a mathematical expression that shows two or more values added together. First add three and two then we got five. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Then multiply four and five then we got 20.

Question 8. 100 – [(\(\frac{25}{5}\)) ∗ 10] = ________ Answer: 100 – [(25/5) ∗ 10] = 50 100 – [(5) ∗ 10] = 50 100 -[50] = 50 Explanation: In the above expression we can observe three arithmetic operations. One is subtraction, division, and multiplication. First we have to perform division operation and then we have to perform multiplication operation and then subtraction operation. The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing. The division is an operation inverse of multiplication. First divide 25/5 which is equal to the five. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Second multiply 5 with 10 then we got 50. Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Third Subtract the result 50 from 100 then we got 50.

Question 9. {(\(\frac{24}{6}\)) + (\(\frac{36}{6}\))} + 2 = ________ Answer: {(24/6) + (36/6)} + 2 = 12 {(4) + (6)} + 2 = 12 {10} + 2 = 12 Explanation: In the above expression we can observe two arithmetic operations. One is division, and other is addition. First we have to perform division operation and then addition operation. The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing. The division is an operation inverse of multiplication. First divide 24/6 then we got four; and also divide 36/6 which is equal to the six. An addition sentence is a mathematical expression that shows two or more values added together. After completion of division operation perform addition operation. First add four and six then we got ten. Then add ten with two which results twelve.

Question 10. (3 ∗ 5) – (2 ∗ 5) = _________ Answer: (3 ∗ 5) – (2 ∗ 5)= 5 (15) – (10) = 5 Explanation: In the above expression we can observe two arithmetic operations. One is Multiplication, and other is Subtraction. First we have to perform multiplication operation and then subtraction operation. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. First multiply these two numbers 3 and 5 then we got 15. Second multiply these two numbers 2 and 5 then we got 10. Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. The result of a subtraction is called a difference. Subtract 10 from 15 then we got 5.

Question 11. (3 ∗ 7) + (2 ∗ 5) = _______ Answer: (3 ∗ 7) + (2 ∗ 5) = 31 (21) + (10) = 31 Explanation: In the above expression we can observe two arithmetic operations. One is Multiplication, and other is addition. First we have to perform multiplication operation and then addition operation. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. First multiply these two numbers 3 and 7 then we got 21. Second multiply these two numbers 2 and 5 then we got 10. An addition sentence is a mathematical expression that shows two or more values added together. ADD the two numbers 21 and 10 then we got 31.

Question 12. (\(\frac{56}{7}\)) ∗ (\(\frac{42}{7}\)) = _________ Answer: ([56/7] ∗ ([42/7]) = 48 ([8] ∗ ([6]) = 48 Explanation: In the above expression we can observe two arithmetic operations. One is division, and other is multiplication. First we have to perform division operation and then we have to perform multiplication operation. The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing. The division is an operation inverse of multiplication. First divide 56/7 which is equal to the 8. Second divide 42/7 then we got 6. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply these two numbers 8 and 6 then we got 48.

Everyday Math Grade 5 Home Link 2.2 Answer Key

Evaluating Expressions with Exponential Notation Write each number in standard notation. Question 1. 10 6 _________ Answer: 10 1  =10 10 2  = 100 10 3  = 1,000 10 4  = 10,000 10 5 = 1,00,000 10 6  = 1,000,000 Explanation: Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 1,000,000 is written as 10 6 .

Question 2. 3 ∗ 10 6 __________ Answer: 3 ∗ 10 6 = 3,000,000 3 ∗ 1,000,000 = 3,000,000 Explanation: Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 1,000,000 is written as 10 6 . Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply 3 with 1,000,000 then we got 3,000,000.

Question 3. 10 3 __________ Answer: 10 3 = 1,000 Explanation: Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 1,000 is written as 10 3 .

Question 4. 24 ∗ 10 3 __________ Answer: 24 ∗ 10 3 = 24,000 Explanation: Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 1,000 is written as 10 3 . Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply 24 with 1,000 then we got 24,000.

Everyday Math Grade 5 Home Link 2.2 Answer Key 1

Question 9. How much will Jackie pay for shipping? $ __________ Answer: Charges to ship the box of hockey is $26. Explanation: Charges to ship a box having volume = $20 up to 10 cubic feet. Since this box has the volume = 16 Cubic feet. So charges to 10 cubic feet will be $20. Remaining volume of the box = 16 – 10 = 6 cubic feet. Now charges for rest volume = $1 x 6 =$6. Total charges= $20 +$6 = $26. Therefore charges to ship the box of hockey is $26.

Everyday Mathematics Grade 5 Home Link 2.3 Answers

Solving Problems Using Powers of 10

Use estimation to solve. Renee is in charge of the school carnival for 380 students. She has 47 boxes of prizes. Each box has 22 prizes. She wants to make sure she has enough prizes for each student to win 2 prizes. Question 1. Does Renee have enough prizes? Explain how you solved the problem. Answer: Yes Renee have enough prizes for each student to win 2 prizes. Explanation: To estimate the number of prizes Renee has, I rounded 47 boxes of prizes to 50 and 22 prizes to 20. I multiplied 50 and 20 to get 1,000. If each student wins 2 prizes, that is 380 x 2. I can round 380 students to 400 students. Multiply 400 x 2 = 800. Here Renee needs only 800 prizes. So she has enough prizes for each student to win 2 prizes.

Question 2. Does Renee have enough prizes for each student to win 3 prizes? Explain. Answer: No, Renee doesn’t have enough prizes for each student to win 3 prizes. Explanation: If each student wins 3 prizes, Renee needs 380 x 3 prizes. If i rounded 380 to 400, then 400 x 3 = 1,200 prizes. Renee only has about 1,000 prizes. So she doesn’t have enough prizes for each student to win 3 prizes.

Practice Write each number in standard notation. Question 3. 42 ∗ 10 6 _________ Answer: 42 ∗ 10 6 42 ∗ 1,000,000 42,000,000 Explanation: Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 1,000,000 is written as 10 3 . Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply these two numbers 42 ∗ 1,000,000 then we got 42,000,000.

Question 4. 8 ∗ 10 1 ___________ Answer: 8 ∗ 10 1 8 ∗ 10 80 Explanation: Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 10 is written as 10 1 . Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply these two numbers 8 ∗ 10 then we got 80.

Write each number in exponential notation. Question 5. 30,000 _________ Answer: 30,000 = 3 ∗ 10 4 Explanation: Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 10,000 is written as 10 4 . Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply these two numbers 3 ∗ 10,000 then we got 30,000.

Question 6. 70,000,000 ________ Answer: 70,000,000 = 7 ∗ 10 7 Explanation: Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 10,000,000 is written as 10 7 . Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply these two numbers 7 ∗ 10,000,000 then we got 70,000,000.

Everyday Math Grade 5 Home Link 2.4 Answer Key

U.S. Traditional Multiplication Family Note Today your child began learning a multiplication strategy called U.S. traditional multiplication. This strategy may be familiar to you, as it is the multiplication strategy that many adults learned when they were in school. Your child will be learning to use U.S. traditional multiplication with larger and larger numbers over the next week or two. U.S. traditional multiplication is often challenging for students to learn. Do not expect your child to use it easily right away. There will be plenty of opportunities for practice throughout the school year. As your child uses U.S. traditional multiplication to solve the problems below, encourage him or her to check the answers by solving the problems in another way or using an estimate.

Everyday Math Grade 5 Home Link 2.4 Answer Key 1

Practice Write each number in expanded form. Question 3. 397 _____________ Answer: The expanded form of 397 = 300 + 90 + 7 Explanation: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form. The Expanded form of 397 = 300 + 90 + 7.

Question 4. 1,268 ____________ Answer: The expanded form of 1,268 = 1 ∗ 1000 + 2 ∗ 100 + 6 ∗ 10 + 8 ∗ 1 Explanation: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form. The Expanded form of 1,268 = 1 ∗ 1000 + 2 ∗ 100 + 6 ∗ 10 + 8 ∗ 1.

Question 5. 4,082 ____________ Answer: The expanded form of 4,082 = 4000 + 80 + 2 Explanation: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form. The Expanded form of 4,082 = 4000 + 80 + 2.

Question 6. 29,141 __________ Answer: The expanded form of 29,141 = (2 ∗10 4 ) + (9 ∗ 10 3 ) +(1 ∗ 10 2 ) + (4 ∗ 10 1 ) + (1 ∗ 10 0 ) Explanation: The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form. The Expanded form of 29,141 = (2 ∗10 4 ) + (9 ∗ 10 3 ) +(1 ∗ 10 2 ) + (4 ∗ 10 1 ) + (1 ∗ 10 0 ).

Everyday Mathematics Grade 5 Home Link 2.5 Answers

Multiplication Top-It: Larger Numbers Make a set of number cards by writing the numbers 0–9on slips of paper or index cards. Make four of each number card. You can also use the 2–9 cards and the aces from a deck of regular playing cards. Explain the rules of Multiplication Top-It: Larger Numbers to someone at home.

Multiplication Top-It: Larger Numbers 1. Each player draws 4 cards. Use 3 of the cards to make a 3-digit number. Use the other card to make a 1-digit number. 2. Multiply the numbers. Compare your product to the other player’s product. The player with the larger product takes all the cards. 3. Keep playing until you run out of cards. The player with more cards wins the game. To play by yourself: Keep the cards if your product is more than 1,000. Discard the cards if your product is less than 1,000. If you have more than 20 cards at the end of the game, you win.

Everyday-Math-Grade-5-Home-Link-2.5-Answer-Key-1

Practice Write each power of 10 using exponential notation. Question 3. 100 = __________ Answer: 100 = 10 2 Explanation: It is the shortest way of expressing a large number. It is also known as the Scientific Notation. The number 100 can be written as power of 10. The exponential notation of 100 is 10 2 .

Question 4. 10,000 = __________ Answer: 10,000 = 10 4 Explanation: It is the shortest way of expressing a large number. It is also known as the Scientific Notation. The number 10,000 can be written as power of 10. The exponential notation of 10,000 is 10 4 .

Question 5. 100,000,000 = __________ Answer: 100,000,000 = 10 8 Explanation: It is the shortest way of expressing a large number. It is also known as the Scientific Notation. The number 100,000,000 can be written as power of 10. The exponential notation of 100,000,000 = 10 8 .

Question 6. 1,000 = __________ Answer: 1,000 = 10 3 Explanation: It is the shortest way of expressing a large number. It is also known as the Scientific Notation. The number 1,000 can be written as power of 10. The exponential notation of 1,000 = 10 3 .

Everyday Math Grade 5 Home Link 2.6 Answer Key

Converting Units Ask someone at home to help you find the following:

  • a 1-cup measuring cup or a coffee mug
  • a large bowl
  • a stopwatch or clock
  • a 12-inch ruler or tape measure
  • a food package with a weight given in pounds

Everyday Math Grade 5 Home Link 2.6 Answer Key 1

b. Convert your measurement to fluid ounces. _________ fluid ounces Answer: 1 cup = 8 fluid ounces. 3 cups = 24 fluid ounces. Explanation: In the above image we can observe 1 cup = 8 fluid ounces. The larger bowl takes 3 cups of water to fill the bowl. The process of adding a number to itself a certain number of times is called as multiplication. Multiply 1 x 3 = 3 cups; which is equal to 24 fluid ounces.

Question 2. a. Time or estimate how long it takes you to walk around your block in minutes. _________ minutes Answer: It takes 15 minutes to walk around my block. Explanation: To walk around my block it takes 15 minutes to complete one round.

b. Convert your measurement to seconds. _________ seconds Answer: 1 minute = 60 seconds 15 minutes = 900 seconds Explanation: It takes 15 minutes to walk around our block. we have to convert minutes into seconds. 1 minute = 60 seconds. The process of adding a number to itself a certain number of times is called as multiplication. Multiply 1 x 15 = 15 minutes; which is equal to 900 seconds.

Question 3. a. Measure the length of your bed to the nearest foot. _________ feet Answer: The length of my bed is 3 feet. Explanation: Measuring the length of my bed is 3 feet long.

b. Convert your measurement to inches. _________ inches Answer: 1 foot = 12 inches. 3 foot = 36 inches. Explanation: Measuring the length of my bed is 3 feet long. Convert the measurement into inches. The process of adding a number to itself a certain number of times is called as multiplication. Multiply 1 x 3 = 3 foot; which is equal to 36 inches.

Question 4. a. Record the weight on the food package in pounds. _________ pounds Answer: The weight on the food package is 5 pounds. Explanation: Measuring the weight on the food package is 5 pounds.

b. Convert the weight to ounces. _________ ounces Answer: 1 pound = 16 ounces. 5 pounds = 80 ounces. Explanation: The weight on the food package is 5 pounds. The process of adding a number to itself a certain number of times is called as multiplication. Multiply 1 x 5 = 5 pounds; which is equal to 80 ounces.

Everyday Math Grade 5 Home Link 2.6 Answer Key 2

Everyday Mathematics Grade 5 Home Link 2.7 Answers

Estimating and Multiplying Make an estimate for each multiplication problem. Write a number sentence to show how you estimated. Then solve ONLY the problems that have answers that are more than 1,000. Use your estimates to help you decide which problems to solve.

Everyday Mathematics Grade 5 Home Link 2.7 Answers 1

Practice Solve. Question 7. a. 7 ∗ 10,000 = ________ b. 7 ∗ 10 4 = ________ Answer: a. 7 ∗ 10,000 = 70,000 b. 7 ∗ 10 4 = 70,000 Explanation: Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations. a.  By multiplying these two numbers we got 7 ∗ 10,000 = 70,000. b. By multiplying these two numbers we got 7 ∗ 10 4 = 70,000.

Question 8. a. 2 ∗ 400 = ________ b. 2 ∗ 4 ∗ 10 2 = ________ Answer: a. 2 ∗ 400 = 800 b. 2 ∗ 4 ∗ 10 2 = 8 ∗ 10 2 = 800 Explanation: Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations. a. By multiplying these two numbers we got 2 ∗ 400 = 800. b. By multiplying these three numbers we got 2 ∗ 4 ∗ 10 2 = 8 ∗ 10 2 = 800.

Question 9. a. 6,000 ∗ 300 = ________ b. 6 ∗ 10 3 ∗ 3 ∗ 10 2 = ________ Answer: a. 6,000 ∗ 300 = 1,800,000 b. 6 ∗ 10 3 ∗ 3 ∗ 10 2 = 18 ∗ 10 5 = 1,800,000 Explanation: Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations. a. By multiplying these two numbers we got 6,000 ∗ 300 =1,800,000. b. By multiplying these four numbers we got 6 ∗ 10 3 ∗ 3 ∗ 10 2 = 18 ∗ 10 5 = 1,800,000.

Everyday Math Grade 5 Home Link 2.8 Answer Key

Choosing Multiplication Strategies

Everyday Math Grade 5 Home Link 2.8 Answer Key 1

Question 4. The distance from Chicago, Illinois, to Boston , Massachusetts, by plane is 851 miles. A pilot flew from Chicago to Boston 37 times in one year. How many miles was that? Estimate: ___________ Answer: ________ miles Answer: Estimate : 850 ∗ 40 = 34,000 The distance for Chicago to Boston = 851 miles. A pilot flew from Chicago to Boston 37 times in one year. So, 851 ∗ 37 = 31,487 miles Explanation: The distance from Chicago, Illinois, to Boston , Massachusetts, by plane is 851 miles. A pilot flew from Chicago to Boston 37 times in one year. So we have to multiply 851 miles with 37 times in one year. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. So, 851 ∗ 37 = 31,487 miles.

Question 5. It takes 246 floor tiles to cover the floor of a classroom. There are 31 same-size classrooms in the school. How many floor tiles does it take to cover all the classroom floors? Estimate: ___________ Answer: ________ miles Answer: Estimate : 250 ∗ 30 = 7,500 The floor of a classroom covers 246 floor tiles. There are 31 same-size classrooms in the school. So, 246 ∗ 31 = 7,626 Explanation: The floor of a classroom covers 246 floor tiles. There are 31 same-size classrooms in the school. So we have to multiply 246 floor tiles with 31 same size classroom in the school. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. So, 246 ∗ 31 = 7,626. Question 6. Explain to someone at home which strategy you used to solve each problem and why. Answer: Here I used U.S traditional multiplication Strategy to solve the problems.

Practice Solve. Question 7. a. 5 ∗ 300,000 = ________ b. 5 ∗ 3 ∗ 10 5 =____________ Answer: a. 5 ∗ 300,000 = 1,500,000 b. 5 ∗ 3 ∗ 10 5 = 15 ∗ 10 5 = 1,500,000 Explanation: Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations. a. By multiplying these two numbers we got 5 ∗ 300,000 = 1,500,000. b. By multiplying these three numbers we got 5 ∗ 3 ∗ 10 5 = 15 ∗ 10 5 = 1,500,000.

Question 8. a. 40 ∗ 6,000 = _________ b. 4 ∗ 10 ∗ 6 ∗ 10 3 = _________ Answer: a. 40 ∗ 6,000 = 240,000 b. 4 ∗ 10 ∗ 6 ∗ 10 3 = 24 ∗ 10 4 = 240,000 Explanation: Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations. a. By multiplying these two numbers we got 40 ∗ 6,000 = 240,000. b. By multiplying these four numbers we got 4 ∗ 10 ∗ 6 ∗ 10 3 = 24 ∗ 10 4 = 240,000.

Question 9. a. 20,000 ∗ 700 = _________ b. 2 ∗10 4   ∗ 7 ∗ 10 2 = __________ Answer: a. 20,000 ∗ 700 = 14,000,000 b. 2 ∗ 10 4 ∗ 7 ∗ 10 2 = 14 ∗ 10 6 = 14,000,000 Explanation: Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations. a. By multiplying these two numbers we got 20,000 ∗ 700 = 14,000,000. b. By multiplying these four numbers we got 2 ∗ 10 4 ∗ 7 ∗ 10 2 = 14 ∗ 10 6 = 14,000,000.

Everyday Mathematics Grade 5 Home Link 2.9 Answers

Using Multiples of 10 to Estimate Question 1. Estimate about how many meters Martin swims in June if he swims about 200 meters per day. There are 30 days in June. Show how you made your estimate. About ________ meters Answer: He swims about 200 meters per day. There are 30 days in June. So 200 ∗ 30 = 6,000 meters. About 6,000 meters. Explanation: Martin swims about 200 meters per day. There are 30 days in June. So multiply 200 meters and 30 days. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations. So 200 ∗ 30 = 6,000 meters.

Question 2. Estimate how many days it would take Martin to swim 60,000 meters. Show how you made your estimate. About ________ days Answer: Martin swim 60,000 meters. We have to calculate the days. If he swim 200 meters per day. Then 200 ∗ 300 = 60,000 meters. About 300 days. Explanation: Martin swim 60,000 meters. We have to calculate the days. If he swim 200 meters per day. Then 200 ∗ 300 = 60,000 meters. Martin takes about 300 days to swim 60,000 meters.

Everyday Mathematics Grade 5 Home Link 2.9 Answers 1

Everyday Math Grade 5 Home Link 2.10 Answer Key

Mental Division Practice Use multiplication and division facts to solve the following problems mentally. Remember: Write an equivalent name for the dividend by breaking it into smaller parts that are easier to divide. Example: 72 divided by 4

  • Write some multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
  • Write an equivalent name by breaking 72 into smaller numbers that are multiples of 4. Equivalent name for 72: 40 + 32
  • Use the equivalent name to divide mentally. Ask yourself: How many 4s are in 40? (10) How many 4s are in 32? (8) Think: How many total 4s are in 72? (10 [4s] + 8 [4s] = 18 [4s], so 72 ÷ 4 = 18)

Question 1. 57 ÷ 3 → ? Multiples of 3: __________ Equivalent name for 57: __________ 57 ÷ 3 → __________ Answer: Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 Equivalent name for 57: 30 + 27 57 ÷ 3 → 19 Explanation: 1. First write some multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 2. Then write an equivalent name by breaking 57 into smaller numbers that are multiples of 3. 3. Equivalent name for 57: 30 + 27 4. Use the equivalent name to divide mentally. First we have to check how many 3s are in 30 and how many 3s are in 27. There are (10) 3s in 30 and (9) 3s in 27. 5. Then check how many total 3s are in 57. There are 10[3s] +9[3s] = 19[3s]. So 57 ÷ 3 = 19.

Question 2. 96 ÷ 8 → ? Multiples of 8: __________ Equivalent name for 96: __________ 96 ÷ 8 → __________ Answer: Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 Equivalent name for 96: 80 + 16 96 ÷ 8 → 12 Explanation: 1. First write some multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 2. Then write an equivalent name by breaking 96 into smaller numbers that are multiples of 8. 3. Equivalent name for 96: 80 + 16 4. Use the equivalent name to divide mentally. First we have to check how many 8s are in 80 and how many 8s are in 16. There are (10) 8s in 80 and (2) 8s in 16. 5. Then check how many total 8s are in 96. There are 10[8s] +2[8s] = 12[3s]. So 96 ÷ 8 = 12.

Everyday Math Grade 5 Home Link 2.10 Answer Key 1

Everyday Mathematics Grade 5 Home Link 2.11 Answers

Everyday Mathematics Grade 5 Home Link 2.11 Answers 1

Question 1. You could have started solving the example problem by taking away 110 from 237. If this was your first step, what would have been the first partial quotient, and why? Answer: 10 is the first partial quotient, because there are 10 [11s] in 110. Explanation: The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic. In the example problem, if we are taking away 110 from 237 then 10 is the first partial quotient, because there are 10 [11s] in 110.

Everyday Mathematics Grade 5 Home Link 2.11 Answers 2

Everyday Math Grade 5 Home Link 2.12 Answer Key

Division with Multiples Here is how to use partial-quotients division with a list of multiples to solve \(\frac{2106}{19}\). First, list some multiples of 19: 100 ∗ 19 = 1,900 50 ∗ 19 = 950 20 ∗ 19 = 380 10 ∗ 19 = 190 5 ∗ 19 = 95

Everyday Math Grade 5 Home Link 2.12 Answer Key 1

Complete the list of multiples below. Then use it to help you solve \(\frac{1954}{18}\). Question 1. 100 ∗ __________ = ___________ 50 ∗ __________ = __________ 20 ∗ __________ = __________ 10 ∗ __________ = __________ 5 ∗ __________ = __________ 2 ∗ __________ = __________ Answer: 100 ∗ 18 = 1,800 50 ∗ 18 = 900 20 ∗ 18 = 360 10 ∗ 18 = 180 5 ∗ 18 = 90 2 ∗ 18 = 36 Explanation: A multiple of a number is a number that is the product of a given number and some other natural number. Multiples can be observed in a multiplication table. Multiples of 18 are 100 ∗ 18 = 1,800, 50 ∗ 18 = 900, 20 ∗ 18 = 360, 10 ∗ 18 = 180,5 ∗ 18 = 90, 2 ∗ 18 = 36

Everyday Math Grade 5 Home Link 2.12 Answer Key 2

Everyday Mathematics Grade 5 Home Link 2.13 Answers

Everyday-Math-Grade-5-Home-Link-2.13-Answer-Key-1

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Math Expressions Answer Key

Math Expressions Grade 4 Unit 6 Lesson 2 Answer Key Fractions That Add to One

Solve the questions in Math Expressions Grade 4 Homework and Remembering Answer Key Unit 6 Lesson 2 Answer Key Fractions That Add to One to attempt the exam with higher confidence. https://mathexpressionsanswerkey.com/math-expressions-grade-4-unit-6-lesson-2-answer-key/

Math Expressions Common Core Grade 4 Unit 6 Lesson 2 Answer Key Fractions That Add to One

Math Expressions Grade 4 Unit 6 Lesson 2 Homework

Name the fraction of the shape that is shaded and the fraction of the shape that is not shaded. Then, write an equation that shows how the two fractions make one whole.

Unit 6 Lesson 2 Fractions That Add To One Grade 4 Math Expressions

Write the fraction that will complete each equation.

Question 4. 1 = \(\frac{3}{3}\) = \(\frac{1}{3}\) + __________ Answer: 1 = \(\frac{3}{3}\) = \(\frac{1}{3}\) + \(\frac{2}{3}\)

Question 5. 1 = \(\frac{8}{8}\) = \(\frac{3}{8}\) + ____________ Answer: 1 = \(\frac{8}{8}\) = \(\frac{3}{8}\) + \(\frac{5}{8}\)

Question 6. 1 = \(\frac{4}{4}\) = \(\frac{2}{4}\) + ____________ Answer: 1 = \(\frac{4}{4}\) = \(\frac{2}{4}\) + \(\frac{2}{4}\)

Question 7. 1 = \(\frac{10}{10}\) = \(\frac{7}{10}\) + ____________ Answer: 1 = \(\frac{10}{10}\) = \(\frac{7}{10}\) + \(\frac{3}{10}\)

Question 8. 1 = \(\frac{6}{6}\) = \(\frac{5}{6}\) + _____________ Answer: 1 = \(\frac{6}{6}\) = \(\frac{5}{6}\) + \(\frac{1}{6}\)

Question 9. 1 = \(\frac{9}{9}\) = \(\frac{8}{9}\) + ______________ Answer: 1 = \(\frac{9}{9}\) = \(\frac{8}{9}\) + \(\frac{1}{9}\)

Question 10. 1 = \(\frac{7}{7}\) = \(\frac{4}{7}\) + ______________ Answer: 1 = \(\frac{7}{7}\) = \(\frac{4}{7}\) + \(\frac{3}{7}\)

Question 11. 1 = \(\frac{12}{12}\) = \(\frac{9}{12}\) + _____________ Answer: 1 = \(\frac{12}{12}\) = \(\frac{9}{12}\) + \(\frac{3}{12}\)

Solve. Show your work.

Question 12. Kim drank \(\frac{1}{3}\) of a carton of milk. Joan drank \(\frac{1}{4}\) of a carton of milk. Who drank more milk? Answer: Kim drank more milk.

Explanation: Quantity of a carton of milk Kim drank = \(\frac{1}{3}\) = 0.33. Quantity of a carton of milk Joan drank = \(\frac{1}{4}\) = 0.25.

Question 13. Maria read \(\frac{1}{8}\) of a story. Darren read \(\frac{1}{7}\) of the same story. Who read less of the story? Answer: Maria read less of the story.

Explanation: Quantity of a story Maria read = \(\frac{1}{8}\) = 0.125. Quantity of a story Darren read = \(\frac{1}{7}\) = 0.143.

Math Expressions Grade 4 Unit 6 Lesson 2 Remembering

Write = or ≠ to make each statement true.

Math Expressions Common Core Grade 4 Unit 6 Lesson 2 Answer Key 4

Explanation: 25 + 25 = 50.

Explanation: 17 + 3 = 20. 30 – 10 = 20.

Explanation: 9 + 8 = 17. 8 + 9 = 17.

Explanation: 31. 23 + 9 = 32.

Explanation: 3 + 1 + 12 = 4 + 12 =  16. 15.

Explanation: 40 – 22 = 18. 18.

Solve each equation.

Question 7. 8 ÷ b = 2 b = ________ Answer: b = 4.

Explanation: 8 ÷ b = 2 => b = 8 ÷ 2 => b = 4.

Question 8. j ÷ 6 = 7 j = _________ Answer: j = 42.

Explanation: j ÷ 6 = 7 => j = 7 × 6 => j = 42.

Question 9. k = 5 × 3 k = ___________ Answer: k = 15.

Explanation: k = 5 × 3 => k = 15.

Question 10. q × 10 = 90 q = _________ Answer: q = 9.

Explanation: q × 10 = 90 => q = 90 ÷ 10 => q = 9.

Question 11. 12 × r = 36 r = ___________ Answer: r = 3.

Explanation: 12 × r = 36 => r = 36 ÷ 12 => r = 3.

Question 12. a = 7 × 8 a = ___________ Answer: a = 56.

Explanation: a = 7 × 8 => a = 56.

Write each fraction as a sum of unit fractions.

Question 13. \(\frac{4}{6}\) = _________________ Answer: \(\frac{4}{6}\) = \(\frac{2}{6}\) + \(\frac{2}{6}\)

Question 14. \(\frac{6}{8}\) = _________________ Answer: \(\frac{6}{8}\) = \(\frac{2}{8}\) + \(\frac{4}{8}\)

Question 15. Stretch Your Thinking Margaret and June both made a pumpkin pie of the same size. Each cut her pie into equal pieces. Margaret’s whole pie can be represented by the fraction \(\frac{8}{8}\). June’s whole pie can be represented by the fraction \(\frac{6}{6}\). What is different about the two pies? If Margaret and June each eat 1 piece of their own pie, who will eat more? Explain how you know. Answer: Two pies are cut into different size pieces. June eats more.

Explanation; Margaret’s whole pie = \(\frac{8}{8}\). June’s whole pie = \(\frac{6}{6}\). Margaret eats 1 piece = \(\frac{1}{8}\) = 0.125. June eats 1 piece = \(\frac{1}{6}\) = 0.167.

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