multiplying mixed numbers problem solving

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Multiplying Mixed Numbers Worksheets

Count on our printable multiplying mixed numbers worksheets for all the practice you need to perfect your skills in multiplying a mixed number with another mixed number, or multiplying three mixed numbers or completing the fraction multiplication equations. Without even realizing it, your grade 5, grade 6, and grade 7 learners will be well on their way to multiplying any number of mixed fractions with ease. It is well known that repeated exposure propels one to fluency, and these multiplying mixed numbers worksheets are sure to give you plenty of it. The process remains the same, but the difficulty level increases. Evaluation becomes easy with our answer keys. Our free multiplying mixed numbers worksheet is the first step to structured practice.

Multiplying Mixed Numbers by Mixed Numbers

Make lightning-fast progress with these multiplying mixed fractions worksheet pdfs. Change the mixed numbers to improper fractions, cross-cancel to reduce them to the lowest terms, multiply the numerators together and the denominators together and convert them to mixed numbers, if improper fractions.

• Download the set

Finding the Product of Three Mixed Numbers

Revisiting concepts often takes the hassle out and helps 5th grade, 6th grade, and 7th grade learners spring into action in finding the product of three mixed numbers. The addition of a third term doesn't deter them.

Completing the Fraction Multiplication Equation

Convert mixed fractions into improper fractions. Rearrange the equation, making the missing multiplier or multiplicand the subject, and flip the fraction when you put it on the other side of the equation and simplify it.

Related Worksheets

» Multiplying Fractions on Number Lines

» Multiplying Fractions by Whole Numbers

» Multiplying Fractions Word Problems

» Multiplying Fractions with Cross Cancelling

» Fraction Division

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Multiplying mixed numbers

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Fractions worksheets: Multiplying mixed numbers by mixed numbers

Below are six versions of our grade 5 math worksheet on multiplying mixed numbers together. These worksheets are pdf files .

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Multiplying Mixed Fractions

("Mixed Fractions" are also called "Mixed Numbers")

To multiply Mixed Fractions :

• convert to Improper Fractions
• Multiply the Fractions
• convert the result back to Mixed Fractions

Example: What is 1 3 8 × 3 ?

Think of Pizzas.

First, convert the mixed fraction (1 3 8 ) to an improper fraction ( 11 8 ):

Now multiply that by 3:

And, lastly, convert to a mixed fraction (only because the original fraction was in that form):

And this is what it looks like in one line:

1 3 8 × 3 = 11 8 × 3 1 = 33 8 = 4 1 8

Another Example: What is 1 1 2 × 2 1 5 ?

Do the steps from above:

Step, by step it is:

Convert Mixed to Improper Fractions:

1 1 2 = 2 2 + 1 2 = 3 2

2 1 5 = 10 5 + 1 5 = 11 5

Multiply the fractions (multiply the top numbers, multiply bottom numbers):

3 2 × 11 5 = 3 × 11 2 × 5 = 33 10

Convert to a mixed number

33 10 = 3 3 10

If you are clever you can do it all in one line like this:

1 1 2 × 2 1 5 = 3 2 × 11 5 = 33 10 = 3 3 10

One More Example: What is 3 1 4 × 3 1 3 ?

3 1 4 = 13 4

3 1 3 = 10 3

13 4 × 10 3 = 130 12

Convert to a mixed number:

130 12 = 10 10 12

And simplify :

10 10 12 = 10 5 6

Here it is in one line:

3 1 4 × 3 1 3 = 13 4 × 10 3 = 130 12 = 10 10 12 = 10 5 6

This One Has Negatives: What is −1 5 9 × −2 1 7 ?

1 5 9 = 9 9 + 5 9 = 14 9 2 1 7 = 14 7 + 1 7 = 15 7

Then multiply the Improper Fractions (note that negative times negative gives positive ) :

−14 9 × −15 7 = −14 × −15 9 × 7 = 210 63  

We can simplify now. Here we use two steps, first by 7 (21 and 63 are both multiples of 7), then again by 3. But it could be done in one step by dividing by 21:

210 63 = 30 9 = 10 3

Finally convert to a Mixed Fraction (because that was the style of the question):

10 3 = (9+1) 3 = 9 3 + 1 3 = 3 1 3

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How to Multiply Mixed Numbers

Last Updated: May 11, 2023 Fact Checked

This article was co-authored by Mario Banuelos, PhD . Mario Banuelos is an Assistant Professor of Mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at both the high school and collegiate levels. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 467,429 times.

A mixed number is a whole number next to a fraction, such as 3 ½. Multiplying two mixed numbers can be tricky, because you have to convert them to improper fractions first. If you want to know how to multiply mixed numbers, you can learn how to do it just by following a few easy steps.

Practice Problems

• Multiply the whole number by the denominator of the fraction . [2] X Research source If you are converting the number 4 1 / 2 to an improper fraction, you would first multiply the whole number 4 by the denominator of the fraction which is 2. So, 4 x 2 = 8
• Add this number to the numerator of the fraction. So adding 8 to the numerator 1, we get 8 + 1 = 9.
• Place this new number over the original denominator of the fraction. [3] X Research source The new number is 9, so you can place it over 2, the original denominator. The mixed number 4 1 / 2 converts to the improper fraction 9 / 2 .

• Multiply the whole number by the denominator of the fraction . If you are converting the number 6 2 / 5 to an improper fraction, you would first multiply the whole number 6 by the denominator of the fraction which is 5. So, 6 x 5 = 30
• Add this number to the numerator of the fraction. So adding 30 to the numerator 2, we get 30 + 2 = 32.
• Place this new number over the original denominator of the fraction. The new number is 32, so you can place it over 5, the original denominator. The mixed number 6 2 / 5 converts to the improper fraction 32 / 5 .

• To multiply 9 / 2 and 32 / 5 , you should multiply the numerators, 9 and 32. So 9 x 32 = 288.
• Next, multiply the denominators, 2 and 5, to get 10.
• Place the new numerator over the new denominator to get 288 / 10 .

• 2 is the greatest common factor of both 288 and 10. Divide 288 by 2 to get 144, and divide 10 by 2 to get 5. 288 / 10 is reduced to 144 / 5 .

• First, divide the top number by the bottom number. Do long division to divide 5 into 144. 5 goes 28 times into 144. This means that the quotient is 28. The remainder, or the number that is left over, is 4.
• Make your quotient the new whole number. Take your remainder and place it over the original denominator to finish converting the improper fraction into a mixed number. The quotient is 28, the remainder is 4, and the original denominator was 5, so 144 / 5 expressed as a mixed fraction is 28 4 / 5 .

• ↑ https://www.cuemath.com/numbers/improper-fractions/
• ↑ https://www.mathsisfun.com/improper-fractions.html
• ↑ https://www.calculatorsoup.com/calculators/math/mixed-number-to-improper-fraction.php
• ↑ https://www.cuemath.com/numbers/multiplying-fractions/
• ↑ https://www.mathsisfun.com/greatest-common-factor.html
• ↑ https://www.cuemath.com/numbers/improper-fraction-to-mixed-number/

Community Q&A

• When multiplying mixed numbers, do not multiply the whole numbers together and then multiply the fractions together. This will lead you to get the wrong answer. Thanks Helpful 1 Not Helpful 0
• When you're cross-multiplying mixed numbers, you can multiply the numerator of the first number with the denominator of the second, and the denominator of the first number with the numerator of the second. Thanks Helpful 0 Not Helpful 1

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About This Article

To multiply mixed numbers, start by converting each mixed number to an improper fraction. Then, multiply the improper fractions together. Reduce your answer to the lowest terms using the greatest common factor. Finally, convert your answer back to a mixed number. To learn how to find the greatest common factor to reduce your fraction, keep reading the article! Did this summary help you? Yes No

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Multiplying Mixed Numbers Mastery - Lesson Plan

Join us on a mathematical journey as we explore the world of multiplying mixed numbers. this interactive lesson will guide students through different tasks, including multiplying mixed numbers by whole numbers and fractions. students will also learn how to convert between mixed numbers and improper fractions. with engaging activities and opportunities for practice, students will gain a solid understanding of this important math concept..

Know more about Multiplying Mixed Numbers Mastery - Lesson Plan

This lesson covers key terms such as mixed number, improper fraction, whole number, thirds, fourths, one and one-third, etc.

This lesson emphasizes strategies for converting mixed numbers into improper fractions and vice versa. It also encourages students to see the relationship between factors and the final product in relation to the whole number part and the fractional part.

Students can expect a warm-up activity to recall fraction of a fraction concepts, followed by tasks that involve multiplying mixed numbers by whole numbers, fractions, and other mixed numbers. The class also includes opportunities for reflection and assessment.

Your one stop solution for all grade learning needs.

Multiplying Mixed Numbers — Rules & Problems - Expii

Multiplying mixed numbers — rules & problems, explanations (4).

Multiplying Mixed Numbers

Just like any other real numbers , we can multiply two mixed numbers together. The procedure is quite different from adding or subtracting them.

The steps for mixed number multiplication are as follows:

• Convert the mixed numbers to improper fractions
• Multiply the fractions
• Convert back to a mixed number

Image by Caroline Kulczycky

Let's do one more example.

What is 1912⋅2513?

Related Lessons

Convert them to improper fractions.

To multiply mixed numbers, we need a few steps. The most important thing to remember is that we cannot multiply these numbers as written. The first step is to convert the mixed numbers to improper fractions .

Then we can multiply the fractions together. Finally, we want our final answer as a mixed number. This is because the original problem was written with mixed numbers. So, we convert the result back to a mixed number .

So, let's try it together! We're going to multiply 512 by 267.

Step 1: Convert each term into an improper fraction.

What is 512 as an improper fraction?

(Video) How to Multiply Mixed Numbers

Mahalo has a good video on mixed number multiplication.

The process for mixed number multiplication is as follows:

• Convert the mixed numbers into improper fractions.
• Multiply the fractions.
• Convert back to a mixed number.

The example she looks at is 135×312.

Start by converting. 135=85312=72

Now, multiply. 85×72=45×71=285

We crossed out the 8 and 2 because there was a common factor of 2 to cancel out .

Finally, convert back. 285=535

If you like things more compact, here are all the steps on one line.

135×312=85×72=285

Introduction

A mixed number is a combination of an integer and a fraction. The integer is called the integer part . The fraction is called the fraction part . Hence they are sometimes called mixed fractions . Some examples are

456,723,318

We usually write the mixed number so that the fraction is a proper fraction. These mixed fractions are equivalent to

4+56,7+23,3+18

respectively. The difference is we don't write the plus sign anymore.

We can add or subtract two mixed numbers . The next question that arises is, can we multiply mixed numbers? The answer is a resounding yes, but it takes a bit of work.

Before multiplying, we must convert both mixed numbers to improper fractions . Then we multiply the improper fractions together directly. In some cases we will need to reduce the fraction to lowest terms . Finally, we can convert back to a mixed number. This procedure assumes we know how to multiply regular fractions. You should review that first if you need to.

Since our problem was given with mixed numbers, we aim to have our final answer be a mixed number too.

Multiplying two mixed numbers might be harder than adding or subtracting them. However, multiplication lets us avoid one painful step. We don't have to worry about common denominators. You might remember adding and subtracting fractions with unlike denominators . For those problems you had to find the greatest common denominator. It's the same for adding or subtracting mixed numbers. No need to worry about that when multiplying them together!

Let's work some examples.

First Example

We're going to multiply

The first step is to convert the mixed numbers to improper fractions. To calculate the new numerators, we use order of operations .

115=5×1+15=65 113=3×1+13=43

Now we multiply these fractions. Multiplying the numerators and denominators together gives

This is an improper fraction. That's a good sign because we want to convert back to a mixed number. First, however, we ask if we can reduce this fraction. We look for common factors of the numerator and denominator. That leads to the conclusion that 3 is a common factor. Let's get rid of it:

2415=8×35×3=8×35×3=85

And finally, let's turn this back into a mixed number.

In summary, we've shown that

115×113=135

Second Example

Let's work out another example. This time we're going to multiply

The fractions are slightly different, but the procedure is the same. Let's convert the mixed numbers to improper fractions. One of these fractions is repeated from the first example.

513=5×3+13=163 113=1×3+13=43

Now, let's multiply these two fractions together. Multiply the numerators. Then multiply the denominators.

In the last example we reduced the fraction. Can we do that again here? It turns out the answer to this question is no. The numerator and denominator are relatively prime. That means they share no common prime factors. In other words, the greatest common factor is 1. More thoroughly, we write the prime factorization for each number.

64=2×2×2×2×2×2=26 9=3×3=32

So we see 64 and 9 share no common factors besides 1. That means we can't reduce the fraction 649. All that's left is to convert back to a mixed number.

In summary, we've shown

513×113=719

Third Example

We're going to mix it up a bit now (no pun intended). Let's throw in a negative sign. We're going to multiply

Once again we convert from mixed number back to improper fraction. We can just carry around the negative sign in front. It won't mess with anything else.

−335=−3×5+35=−185 225=2×5+25=125

Now let's multiply the fractions. The negative sign in front will act as multiplying by −1.

−185×125=−21625

This fraction does not need to be reduced. The numerator and denominator don't share factors besides 1. If you want, you can check this with the prime factorizations of 216 and 25. Anyway,

−21625=−81625

Just like in the other examples, we wrote our final answer as a mixed number.

A Word Problem

To wrap things up we're going to do a word problem.

Question Statement: Filip works part-time at a factory. He works three shifts in a week. Each shift is 512 hours long. How many hours does he work in a week? Write your answer as a mixed number.

The wording of the problem suggests we'll need multiplication . Each shift is 512 hours long, and there are three shifts. This is the multiplication problem

Only the first number is a mixed number. The second number is an integer. So we convert 512 to an improper fraction:

512=5×2+12=112

We will also write the 3 as 31. This will make multiplying easier. Then

512×3=112×31

Now multiply the numerators and denominators:

Finally, let's turn this back into a mixed number:

Hence our final answer is 1612 hours.

The Most Common Mistake

Let's conclude by discussing the most common mistake students make. Don't multiply the integer parts and the fraction parts. This doesn't work because of the invisible plus sign present in any mixed number. In other words, doing this violates the order of operations.

Moving Forward

In this explanation we skipped over one of the big operations. What about division? Well, we can divide ordinary fractions . This includes those improper fractions.

As a result we're also able to divide mixed numbers . The procedure is similar to multiplying mixed numbers.

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How to Solve Word Problems Involving Multiplying Mixed Numbers?

In this step-by-step guide, you will learn how to solve word problems involving multiplying mixed numbers.

A step-by-step guide to word problems involving multiplying mixed numbers

Mixed numbers have a whole number and a fraction.

To multiply mixed numbers, follow these steps: Step 1: Write down the mixed number as an improper fraction. Step 2: Multiply the numerators. Step 3: Multiply the denominators. Step 4: Simplify the product if possible.

Word Problem Involving Multiplying Mixed Numbers – Example 1

Daniel and Kevin made ladders. Daniel’s ladder is \(7\) feet tall. Kevin’s ladder is \(2 \frac{3}{5}\) times as tall as Daniel’s. How tall is Kevin’s ladder?

Since the Kevin’s ladder is \(2 \frac{3}{5}\) times as tall as Daniel’s, multiply \(2 \frac{3}{5}\) in \(7\). \(2 \frac{3}{5}×7=\)?, \(2 \frac{3}{5}=\frac{(2×5)+3}{5}=\frac{13}{5}\) Write \(7\) as an improper fraction. \(\frac{7}{1}\) Multiply the numerators and the denominators. \(\frac{13}{5}×\frac{7}{1}=\frac{91}{5}\) Simplify and write as a mixed number. \(\frac{91}{5}=18 \frac{1}{5}\)

Word Problem Involving Multiplying Mixed Numbers – Example 2

An office is \(16 \frac{2}{3}\) yards wide. Its length is \(4 \frac{1}{4}\) times as long as it is wide. How long is the length of the office?

Since the length is \(4 \frac{1}{4}\) times as long as \(16 \frac{2}{3}\), multiply \(4 \frac{1}{4}\) in \(16 \frac{2}{3}\). \(4 \frac{1}{4}×16 \frac{2}{3}=\)?, \(4 \frac{1}{4}=\frac{(4×4)+1}{4}=\frac{17}{4}, 16 \frac{2}{3}=\frac{(16×3)+2}{3}=\frac{50}{3}\) Multiply the numerators and the denominators. \(\frac{17}{4}×\frac{50}{3}=\frac{850}{12}\) Simplify and write as a mixed number. \(\frac{850}{12}=70 \frac{10}{12}=70 \frac{5}{6}\)

by: Effortless Math Team about 1 year ago (category: Articles )

Effortless Math Team

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2.2.1: Multiplying Fractions and Mixed Numbers

• Last updated
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• Page ID 61459

• The NROC Project

Learning Objectives

• Multiply two or more fractions.
• Multiply a fraction by a whole number.
• Multiply two or more mixed numbers.
• Solve application problems that require multiplication of fractions or mixed numbers.

Introduction

Just as you add, subtract, multiply, and divide when working with whole numbers, you also use these operations when working with fractions. There are many times when it is necessary to multiply fractions and mixed numbers . For example, this recipe will make 4 crumb piecrusts:

5 cups graham crackers

8 tablespoons sugar

\(\ 1 \frac{1}{2}\) cups melted butter

\(\ \frac{1}{4}\) teaspoon vanilla

Suppose you only want to make 2 crumb piecrusts. You can multiply all the ingredients by \(\ \frac{1}{2}\), since only half of the number of piecrusts are needed. After learning how to multiply a fraction by another fraction, a whole number or a mixed number, you should be able to calculate the ingredients needed for 2 piecrusts.

Multiplying Fractions

When you multiply a fraction by a fraction, you are finding a “fraction of a fraction.” Suppose you have \(\ \frac{3}{4}\) of a candy bar and you want to find \(\ \frac{1}{2}\) of the \(\ \frac{3}{4}\):

By dividing each fourth in half, you can divide the candy bar into eighths.

Then, choose half of those to get \(\ \frac{3}{8}\).

In both of the above cases, to find the answer, you can multiply the numerators together and the denominators together.

Multiplying Two Fractions

\(\ \frac{a}{b} \cdot \frac{c}{d}=\frac{a \cdot c}{b \cdot d}=\frac{\text { product of the numerators }}{\text { product of the denominators }}\)

\(\ \frac{3}{4} \cdot \frac{1}{2}=\frac{3 \cdot 1}{4 \cdot 2}=\frac{3}{8}\)

Multiplying More Than Two Fractions

\(\ \frac{a}{b} \cdot \frac{c}{d} \cdot \frac{e}{f}=\frac{a \cdot c \cdot e}{b \cdot d \cdot f}\)

\(\ \frac{1}{3} \cdot \frac{2}{4} \cdot \frac{3}{5}=\frac{1 \cdot 2 \cdot 3}{3 \cdot 4 \cdot 5}=\frac{6}{60}\)

\(\ \frac{8}{15}\)

If the resulting product needs to be simplified to lowest terms, divide the numerator and denominator by common factors.

\(\ \frac{2}{3} \cdot \frac{1}{4}=\frac{1}{6}\)

You can also simplify the problem before multiplying, by dividing common factors.

You do not have to use the “simplify first” shortcut, but it could make your work easier because it keeps the numbers in the numerator and denominator smaller while you are working with them.

\(\ \frac{3}{4} \cdot \frac{1}{3}\) Multiply. Simplify the answer.

• \(\ \frac{3}{12}\)
• \(\ \frac{4}{7}\)
• \(\ \frac{1}{4}\)
• \(\ \frac{36}{144}\)
• Incorrect. \(\ \frac{3}{12}\) is an equivalent fraction to the correct answer \(\ \frac{1}{4}\), but it is not in lowest terms. You must divide numerator and denominator by the common factor 3. The correct answer is \(\ \frac{1}{4}\).
• Incorrect. You may have added numerators (3+1) and added denominators (4+3) instead of multiplying. The correct answer is \(\ \frac{1}{4}\).
• Correct. One way to find this answer is to multiply numerators and denominators, \(\ \frac{3 \cdot 1}{4 \cdot 3}=\frac{3}{12}\), then simplify: \(\ \frac{3 \div 3}{12 \div 3}=\frac{1}{4}\).
• Incorrect. You probably found a common denominator, multiplied correctly, but then forgot to simplify. Finding a common denominator is not necessary and makes the multiplication harder because you are working with greater than necessary numbers. The correct answer is \(\ \frac{1}{4}\).

Multiplying a Fraction by a Whole Number

When working with both fractions and whole numbers, it is useful to write the whole number as an improper fraction (a fraction where the numerator is greater than or equal to the denominator). All whole numbers can be written with a "1" in the denominator. For example: \(\ 2=\frac{2}{1}\), \(\ 5=\frac{5}{1}\), and \(\ 100=\frac{100}{1}\). Remember that the denominator tells how many parts there are in one whole, and the numerator tells how many parts you have.

Multiplying a Fraction and a Whole Number

\(\ a \cdot \frac{b}{c}=\frac{a}{1} \cdot \frac{b}{c}\)

\(\ 4 \cdot \frac{2}{3}=\frac{4}{1} \cdot \frac{2}{3}=\frac{8}{3}\)

Often when multiplying a whole number and a fraction, the resulting product will be an improper fraction. It is often desirable to write improper fractions as a mixed number for the final answer. You can simplify the fraction before or after rewriting it as a mixed number. See the examples below.

\(\ 7 \cdot \frac{3}{5}=4 \frac{1}{5}\)

\(\ 4 \cdot \frac{3}{4}=3\)

\(\ 3 \cdot \frac{5}{6}\) Multiply. Simplify the answer and write it as a mixed number.

• \(\ 1 \frac{1}{7}\)
• \(\ 2 \frac{1}{2}\)
• \(\ \frac{5}{2}\)
• \(\ \frac{8}{6}\)
• Incorrect. You may have added the numerators and added the denominators to get \(\ \frac{8}{7}\), which is the mixed number \(\ 1 \frac{1}{7}\). Make sure you multiply numerators and multiply denominators. Multiplying the two numbers gives you \(\ \frac{15}{6}\), and since \(\ 15 \div 6=2 \mathrm{R} 3\), the mixed number is \(\ 2 \frac{3}{6}\). The fractional part simplifies to \(\ \frac{1}{2}\). The correct answer is \(\ 2 \frac{1}{2}\).
• Correct. Multiplying the two numbers gives \(\ \frac{15}{6}\), and since \(\ 15 \div 6=2 \mathrm{R} 3\), the mixed number is \(\ 2 \frac{3}{6}\). The fractional part simplifies to \(\ \frac{1}{2}\).
• Incorrect. Multiplying the numerators and multiplying the denominators results in the improper fraction \(\ \frac{5}{2}\), but you need to express this as a mixed number. The correct answer is \(\ 2 \frac{1}{2}\).
• Incorrect. You may have added numerators and placed it over the denominator of 6. Make sure you multiply numerators and multiply denominators. Multiplying the two numbers gives \(\ \frac{15}{6}\), and since \(\ 15 \div 6=2 \mathrm{R} 3\), the mixed number is \(\ 2 \frac{3}{6}\). The fractional part simplifies to \(\ \frac{1}{2}\). The correct answer is \(\ 2 \frac{1}{2}\).

Multiplying Mixed Numbers

If you want to multiply two mixed numbers, or a fraction and a mixed number, you can again rewrite any mixed number as an improper fraction.

So, to multiply two mixed numbers, rewrite each as an improper fraction and then multiply as usual. Multiply numerators and multiply denominators and simplify. And, as before, when simplifying, if the answer comes out as an improper fraction, then convert the answer to a mixed number.

\(\ 2 \frac{1}{5} \cdot 4 \frac{1}{2}=9 \frac{9}{10}\)

\(\ \frac{1}{2} \cdot 3 \frac{1}{3}=1 \frac{2}{3}\)

As you saw earlier, sometimes it’s helpful to look for common factors in the numerator and denominator before you simplify the products.

\(\ 1 \frac{3}{5} \cdot 2 \frac{1}{4}=3 \frac{3}{5}\)

In the last example, the same answer would be found if you multiplied numerators and multiplied denominators without removing the common factor. However, you would get \(\ \frac{72}{20}\), and then you would need to simplify more to get your final answer.

\(\ 1 \frac{3}{5} \cdot 3 \frac{1}{3}\)

• \(\ \frac{80}{15}\)
• \(\ 5 \frac{5}{15}\)
• \(\ 4 \frac{14}{15}\)
• \(\ 5 \frac{1}{3}\)
• Incorrect. You probably wrote both mixed numbers as improper fractions correctly. You probably also correctly multiplied numerators and denominators. However, this improper fraction still needs to be rewritten as a mixed number and simplified. Dividing \(\ 80 \div 15=5\) with a remainder of 5 or \(\ 5 \frac{5}{15}\), then simplifying the fractional part, the correct answer is \(\ 5 \frac{1}{3}\).
• Incorrect. You probably wrote both mixed numbers as improper fractions correctly. You probably also correctly multiplied numerators and denominators, and wrote the answer as a mixed number. However, the mixed number is not in lowest terms. \(\ \frac{5}{15}\) can be simplified to \(\ \frac{1}{3}\) by dividing numerator and denominator by the common factor 5. The correct answer is \(\ 5 \frac{1}{3}\).
• Incorrect. This is the result of adding the two numbers. To multiply, rewrite each mixed number as an improper fraction: \(\ 1 \frac{3}{5}=\frac{8}{5}\) and \(\ 3 \frac{1}{3}=\frac{10}{3}\). Next, multiply numerators and multiply denominators: \(\ \frac{8}{5} \cdot \frac{10}{3}=\frac{80}{15}\). Then, write the resulting improper fraction as a mixed number: \(\ \frac{80}{15}=5 \frac{5}{15}\). Finally, simplify the fractional part by dividing both numerator and denominator by the common factor, 5. The correct answer is \(\ 5 \frac{1}{3}\).
• Correct. First, rewrite each mixed number as an improper fraction: \(\ 1 \frac{3}{5}=\frac{8}{5}\) and \(\ 3 \frac{1}{3}=\frac{10}{3}\). Next, multiply numerators and multiply denominators: \(\ \frac{8}{5} \cdot \frac{10}{3}=\frac{80}{15}\). Then write as a mixed fraction \(\ \frac{80}{15}=5 \frac{5}{15}\). Finally, simplify the fractional part by dividing both numerator and denominator by the common factor 5.

Solving Problems by Multiplying Fractions and Mixed Numbers

Now that you know how to multiply a fraction by another fraction, by a whole number, or by a mixed number, you can use this knowledge to solve problems that involve multiplication and fractional amounts. For example, you can now calculate the ingredients needed for the 2 crumb piecrusts.

The ingredients needed for 2 pie crusts are:

\(\ 2 \frac{1}{2}\) cups graham crackers

4 tablespoons sugar

\(\ \frac{3}{4}\) cup melted butter

\(\ \frac{1}{8}\) teaspoon vanilla

Often, a problem indicates that multiplication by a fraction is needed by using phrases like “half of,” “a third of,” or "\(\ \frac{3}{4}\) of."

The cost of a vacation is \(\ \$ 4,500\) and you are required to pay \(\ \frac{1}{5}\) of that amount when you reserve the trip. How much will you have to pay when you reserve the trip?

You will need to pay \(\ \$ 900\) when you reserve the trip.

Hours spent:

sleeping: 8 hours

attending school: 4 hours

eating: 2 hours

Neil bought a dozen (12) eggs. He used \(\ \frac{1}{3}\) of the eggs for breakfast. How many eggs are left?

• Correct. \(\ \frac{1}{3}\) of 12 is \(\ 4\left(\frac{1}{3} \cdot \frac{12}{1}=\frac{12}{3}=4\right)\), so he used 4 of the eggs. Because \(\ 12-4=8\), there are 8 eggs left.
• Incorrect. \(\ \frac{1}{3}\) of 12 is 4, but that gives how many eggs Neil used, not how many he had left. You need to subtract 4 from 12 to find the number of remaining eggs. The correct answer is 8.
• Incorrect. You may have incorrectly found \(\ \frac{1}{3}\) of 12 to be \(\ \text { 3. } \frac{1}{3}\) of 12 is 4, and then 12-4 is 8. The correct answer is 8.
• Incorrect. You need to find \(\ \frac{1}{3}\) of 12, which is 4. Then subtract 4 from 12 to get 8 remaining eggs.

You multiply two fractions by multiplying the numerators and multiplying the denominators. Often the resulting product will not be in lowest terms, so you must also simplify. If one or both fractions are whole numbers or mixed numbers, first rewrite each as an improper fraction. Then multiply as usual, and simplify.

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Multiplying Mixed Numbers – Definition With Examples

Created: December 29, 2023

Last updated: January 6, 2024

At Brighterly , we believe that mastering the skill of multiplying mixed numbers can open up a whole new world of problem-solving and real-life applications. Learning to multiply mixed numbers might appear challenging initially, but with a little perseverance and our step-by-step guidance, it becomes an enjoyable and effortless math skill for children to acquire. In this article, we will deconstruct the process of multiplying mixed numbers, making it simpler and more accessible for young learners. So, let’s embark on this exciting journey through the realm of mixed numbers and uncover the various techniques of multiplication.

What Are Mixed Numbers

Mixed numbers are numbers that have both a whole number part and a fractional part. They are commonly used to represent quantities that are not whole numbers, such as lengths, weights, or volumes. For example, 2 1/2 (two and one-half) is a mixed number because it contains a whole number (2) and a fraction (1/2).

Mixed numbers are a useful way to represent and compare quantities that are not exactly whole numbers. They help us understand the world around us better and make it easier to solve real-life problems involving fractions.

How to Multiply Mixed Numbers?

When it comes to multiplying mixed numbers, there are a few simple steps to follow:

• Convert the mixed numbers to improper fractions.
• Multiply the improper fractions.
• Simplify the result, if necessary.
• Convert the result back to a mixed number, if desired.

In the following sections, we will explore each of these steps in more detail and provide examples to help solidify your understanding.

Mixed Number To Improper Fraction Worksheet PDF

Mixed Number To Improper Fraction Worksheet

Mixed Numbers To Improper Fractions Worksheet PDF

Mixed Numbers To Improper Fractions Worksheet

To strengthen your comprehension of the concept of Mixed Numbers, we recommend checking out the collection of math worksheets available at Brighterly. These worksheets are intended to support your learning and practice of this topic.

Multiplying Two or More Mixed Numbers

To multiply two or more mixed numbers, first convert them to improper fractions. An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). To convert a mixed number to an improper fraction, use the following formula:

Improper Fraction = (Whole Number × Denominator) + Numerator / Denominator

Once you have converted the mixed numbers to improper fractions, simply multiply the numerators and multiply the denominators. Finally, simplify the resulting fraction, if possible.

Multiplying a Mixed Number with Fraction

When multiplying a mixed number with a fraction, the process is very similar to multiplying two mixed numbers. First, convert the mixed number to an improper fraction. Then, multiply the improper fraction and the given fraction. As always, simplify the result if necessary.

Multiplying a Mixed Number by a Whole Number

Multiplying a mixed number by a whole number is a straightforward process. First, convert the mixed number to an improper fraction. Next, multiply the numerator of the improper fraction by the whole number, keeping the denominator unchanged. Finally, simplify the result and convert it back to a mixed number, if desired.

Practice Questions on Multiplying Fractions with Mixed Numbers

• Multiply 2 1/2 by 3 3/4.
• Multiply 4 1/3 by 1/2.
• Multiply 5 by 1 2/3.

Mixed Numbers Into Improper Fractions Worksheet

Mixed Number And Improper Fractions Worksheet

The journey to mastering mixed numbers multiplication may seem daunting at first, but with the right mindset and consistent practice, it becomes an indispensable and manageable math skill. By following the straightforward steps provided in this Brighterly article, you can effortlessly multiply mixed numbers and apply this valuable knowledge to a myriad of real-life situations.

At Brighterly, our goal is to empower children to tackle complex mathematical concepts with confidence and enthusiasm. As they learn to multiply mixed numbers, they will not only develop a solid foundation in mathematics but also gain the ability to think critically and creatively when faced with real-world challenges. So, let’s continue learning and growing together on this exciting mathematical adventure!

Frequently Asked Questions on Multiplying Fractions with Mixed Numbers

How do i multiply mixed numbers with different denominators.

• Convert the mixed numbers to improper fractions, find a common denominator, and then multiply the numerators and denominators.

Can I multiply mixed numbers without converting them to improper fractions?

• While it’s possible to multiply mixed numbers using the distributive property, converting them to improper fractions simplifies the process and is the recommended method.

How do I know if my result is in simplest form?

• After multiplying the fractions, check if the numerator and denominator have any common factors. If they do, divide both by the greatest common factor to simplify the fraction.

What if my result is an improper fraction? Should I convert it back to a mixed number?

• Yes, it’s usually a good idea to convert the result back to a mixed number, especially if the context of the problem involves mixed numbers or whole numbers.

Can I use the same process for dividing mixed numbers?

• Yes, but you will need to multiply by the reciprocal of the second mixed number (or fraction) instead of directly multiplying. The overall process remains similar.

To learn more about multiplying mixed numbers and other related topics, consider visiting the following resources:

• Mathplanet – Multiplying Fractions
• Math-Aids – Multiplying Mixed Numbers Worksheets
• BBC Bitesize – Multiplying Fractions and Mixed Numbers

Remember, practice makes perfect. By regularly working on problems involving multiplying mixed numbers, children will become more comfortable with this concept and gain confidence in their math skills. Happy learning!

I am a seasoned math tutor with over seven years of experience in the field. Holding a Master’s Degree in Education, I take great joy in nurturing young math enthusiasts, regardless of their age, grade, and skill level. Beyond teaching, I am passionate about spending time with my family, reading, and watching movies. My background also includes knowledge in child psychology, which aids in delivering personalized and effective teaching strategies.

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Surface Area of Pyramid – Formula, Definition With Examples

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Mathematics 6 Quarter 1 – Module 7: Multiplying Decimals and Mixed Decimals

This module was designed and written with you in mind. It is here to help you master the skills in multiplying decimals. The scope of this module allows you to use it in many different learning situations. The language used recognizes your diverse vocabulary level. The lessons are arranged to follow the standard sequence of your course. But the order in which you read them can be changed to match with the textbook you are now using.

The module is divided into three lessons, namely:

• Lesson 1 – Multiplying Decimals with Factors Up to 2 Decimal Places
• Lesson 2 – Multiplying Mixed Decimals with Factors Up to 2 Decimal Places
• Lesson 3 – Multiplying Decimals and Mixed Decimals with Factors Up to 2 Decimal Places

After going through this module, you are expected to:

1. multiply decimals with factors up to 2 decimal places; (M6NS-Ie-111.3)

2. multiply mixed decimals with factors up to 2 decimal places; (M6NS-Ie-111.3)

3. multiply decimals and mixed decimals with factors up to 2 decimal places; (M6NS-Ie-111.3)

4. solve routine and non-routine problems involving multiplication of decimals and mixed decimals including money using appropriate problem-solving strategies; (M6NS-Ie-113.2) and

5. solve multi-step problems involving multiplication and addition or subtraction of decimals, mixed decimals and whole numbers including money using appropriate problem-solving strategies and tools. (M6NS-If-113.3)

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