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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Course: 5th grade   >   Unit 6

  • Multiplying mixed numbers

Multiply mixed numbers

  • (Choice A)   12 ‍   A 12 ‍  
  • (Choice B)   8 1 3 ‍   B 8 1 3 ‍  
  • (Choice C)   10 ‍   C 10 ‍  
  • (Choice D)   6 2 3 ‍   D 6 2 3 ‍  

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2.2.1: Multiplying Fractions and Mixed Numbers

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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 \(\ \frac{3}{4}\):

Screen Shot 2021-04-21 at 10.57.59 PM.png

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

Screen Shot 2021-04-21 at 10.58.45 PM.png

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

Screen Shot 2021-04-21 at 10.59.37 PM.png

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.

SplashLearn

Multiplying Mixed Numbers – Definition, Examples, FAQs

What are mixed numbers, multiplying a mixed number by a fraction, multiplying two mixed numbers, solved examples on multiplying mixed numbers, practice problems on multiplying mixed numbers, frequently asked questions on multiplying mixed numbers.

A mixed number is a whole number and a proper fraction represented together.  It generally represents a number between any two whole numbers. 

Look at the given image, it represents a fraction that is greater than 1 but less than 2. It is thus a mixed number. 

Visual representation of a mixed number

Some other examples of mixed numbers are: 

Examples of mixed numbers

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Parts of a mixed number

A mixed number is formed by combining three parts: a whole number, a numerator , and a denominator . The numerator and denominator are part of the proper fraction that makes the mixed number .

Parts of a mixed number

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Converting Mixed Numbers to Improper Fractions

  • Multiply the whole number by the denominator of the fraction.
  • Add the answer obtained from Step 1 to the numerator of the fraction. 
  • Write an answer obtained from Step 2 over the denominator.

Let us suppose we have to convert $2\frac{2}{3}$ into an improper fraction.

Step 1 : Multiply 3 and 2, we get $3 \times 2 = 6$.

Step 2 : Add 6 and 2, we get $6 + 2 = 8$

Step 3: The fraction obtained is $\frac{8}{3}$. 

Multiplying a Mixed Number by a Whole Number

Step 1: Convert the mixed number into an improper fraction.

Step 2: Rewrite the whole number as a fraction with the denominator 1.

Step 3: Multiply two fractions by multiplying the numerators and denominators separately.

Step 4: Convert it into simplified form if required.

Suppose we have to multiply 3 and $2\frac{1}{2}$.

$2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{5}{2}$

$3\times\frac{5}{2}=\frac{3}{1}\times\frac{5}{2}=\frac{15}{2}=7\frac{1}{2}$

Step 2: Multiply the numerators of the fraction and multiply the denominators of the fraction.

Step 3: Convert it into simplified form if required.

Suppose we have to multiply $\frac{2}{5}$ and $3\frac{1}{2}$.

$3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{7}{2}$

$\frac{2}{5}\times\frac{7}{2}=\frac{14}{10}=\frac{7}{5}=1\frac{2}{5}$

Step 1: Convert the mixed numbers into improper fractions.

Step 2: Multiply the two fractions by multiplying the numerators and denominators separately.

For example: Multiply $4\frac{1}{2}$ and $3\frac{1}{3}$.

$4\frac{1}{2}=\frac{4\times2+1}{2}=\frac{9}{2}$

$3\frac{1}{3}=\frac{3\times3+1}{3}=\frac{10}{3}$

$4\frac{1}{2}\times3\frac{1}{3}=\frac{9}{2}\times\frac{10}{3}=\frac{90}{6}=15$ 

In this article, we learnt about multiplying mixed numbers. Mixed numbers are also known as mixed fractions. To read more such informative articles on other concepts, do visit our website. We, at SplashLearn , are on a mission to make learning fun and interactive for all students.

1. Multiply $5\frac{3}{7}$ by the multiplicative inverse of $7\frac{3}{5}$ . 

Solution: $5\frac{3}{7}=\frac{5\times7+3}{7}=\frac{38}{7}$

$7\frac{3}{5}=\frac{7\times5+3}{5}=\frac{38}{5}$

Multiplicative inverse of $\frac{38}{5}$ is $\frac{5}{38}$ .

Product $= \frac{38}{7}\times\frac{5}{38}=\frac{5}{7}$

2. Emma walks 5 2 3 miles in a day. How much distance will she cover in 9 days?

Solution: Distance traveled by Emma in 1 day $= 5\frac{2}{3}$ miles $=\frac{17}{3}$ miles.

Distance traveled by Emma in 9 days $= 9\times\frac{17}{3}= 51$ miles 

3. Multiply $6\frac{2}{5}\times\frac{3}{4}$ .

Solution: $6\frac{2}{5}=\frac{6\times5+2}{5}=\frac{32}{5}$

$\frac{32}{5}\times \frac{3}{4}=\frac{32\times3}{5\times4}=\frac{96}{20}=\frac{24}{5}=4\frac{4}{5}$

Multiplying Mixed Numbers - Definition With Examples

Attend this quiz & Test your knowledge.

Which of these is the first step to multiply mixed numbers?

On multiplying $10\frac{1}{6}$ by $2\frac{2}{11}$, we get ____., the value of $4\frac{2}{9}\times1\frac{1}{7}$ is:.

Are same denominators required when multiplying two or more mixed numbers?

No. We don’t need the same denominators to multiply two or more mixed numbers. We can even multiply unlike fractions.

What is another name for mixed numbers?

The other name for mixed numbers is mixed fractions.

Is the product of a mixed number with another mixed number always a mixed number?

No. A mixed number is always greater than 1. So, the product of 2 numbers greater than 1 will always be greater than 1, i.e., a mixed/whole number.

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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

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.

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Finding the Product of Three Mixed Numbers

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

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.

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» Multiplying Fractions on Number Lines

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» Multiplying Fractions with Cross Cancelling

» Fraction Division

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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 Numbers Into Improper Fractions Worksheet

Mixed Number And 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!

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Word Problems on Multiplication of Mixed Fractions | Multiplying Mixed Numbers Word Problems

Students will learn how to solve problems on multiplication of mixed fractions by referring to this page. We have covered various models of Mixed Fractions Multiplication Word Problems that range from easy ones to difficult ones. Try to answer all the questions on mixed fractions multiplication on your own and then verify with our solutions provided to test your skills on the concept. Practice as much as you can and enhance your problem-solving ability and speed of attempting the questions too.

  • Word Problems on Division of Mixed Fractions
  • Word Problems on Subtraction of Mixed Fractions
  • Word Problems on Addition of Mixed Fractions

Mixed Numbers Multiplication Word Problems

Example 1. Sai spent 8 hours selling vegetables in the market. Murali sells for 1\(\frac {1}{ 4} \)  times as many hours as Sai. How many hours did Murali sell vegetables in the market? Solution: Time is taken by Sai for selling the vegetables= 8 hours Murali sells vegetables =1 \(\frac {1}{ 4} \) × 8 =\(\frac {5}{ 4} \) × 8 =\(\frac {5}{ 4} \)× \(\frac {8}{ 1} \) =\(\frac {40}{ 4} \) =10 Therefore, Murali spent 10 hours selling vegetables in the market.

Example 2. On Doctor’s advice, Rajesh decided to walk every day. He walks \(\frac {4}{ 7} \) kilometers every day. How many kilometers did he walk in a week? Solution: Rajesh walk every day= \(\frac {4}{ 7} \) No. of kilometers Rajesh walk in a week=7 × \(\frac {4}{ 7} \) =4 km Therefore, Rajesh walks 4 km a week.

Example 3. The heaviest weight in the family of Sarath is 90 kg. Sarath’s weight is \(\frac {1}{ 3} \) of the heaviest weight. Find the weight of Sarath? Solution: The heaviest weight in the family = 90 kg Sarath weight= \(\frac {1}{ 3} \)× 90 =30 kg Hence, Sarath’s weight is 30 kg.

Example 4. Supriya is interested in singing and dancing. Supriya practices 28 hours a week with them. She takes \(\frac {1}{ 3} \) of the time for singing and \(\frac {1}{ 4} \) of the time for dancing. How many hours does she take for dancing? Solution: Total no. of hours Supriya practice every week= 28 Supriya takes time for singing=\(\frac {1}{ 3} \) Supriya takes time for dancing=\(\frac {1}{ 4} \) No. of hours she spends in dancing=\(\frac {1}{ 4} \)× 28 =7 Therefore, Supriya takes 7 hours for dancing.

Example 5. In an office, there are 2000 employees. Male employees are \(\frac {1}{ 4} \). Find the Female employees in the office? Solution: Total no. of employees in the office=2000 No. of male employees=\(\frac {1}{ 4} \) No. of female employees=1-\(\frac {1}{ 4} \)=\(\frac {3}{4} \) \(\frac {3}{ 4} \)× 2000=1500. Therefore, the total no. of female employees in the office is 1500.

Example 6. Games are conducted for the students in class X. \(\frac {3}{ 8} \) of the total no of students are in class X. \(\frac {1}{ 5} \) of the students in class X participate in games. What fraction of all the students participate in the games? Solution: No. of students in the class X= \(\frac {3}{ 8} \) No. of students participate in the games=\(\frac {1}{ 5} \) Fraction of all students participate in the games=\(\frac {3}{ 8} \) × \(\frac {1}{5} \)=\(\frac {3}{40} \) Therefore, the fraction of all the students participating in the exam is \(\frac {3}{40} \) .

Example 7. Jagadish planted a mango tree and guava tree in the garden. The guava tree is 3 \(\frac {1}{ 5} \) feet tall. The mango tree is 1 \(\frac {1}{ 3} \) as tall as the guava tree. How tall is the mango tree? Solution: The height of the guava tree=3 \(\frac {1}{5} \) The height of the mango tree =1\(\frac {1}{ 3} \) × 3 \(\frac {1}{ 5} \) =\(\frac {4}{ 3} \) × \(\frac {16}{ 5} \) =\(\frac {4 × 16}{ 3× 5} \) =\(\frac {64}{15} \) =4 \(\frac {4}{15} \) Therefore, the height of the mango tree is 4 \(\frac {4}{15} \).

Example 8. The cake needs 3 \(\frac {1}{2} \) cups of flour. Janci is baking 2 \(\frac {1}{ 2} \) cakes. How many cups of flour will she need? Solution: No. of cups of flour required for cake=3 \(\frac {1}{ 2} \) No. of cakes baking= 2 \(\frac {1}{ 2} \) No. of cups of flour required=2 \(\frac {1}{ 2} \) × 3 \(\frac {1}{ 2} \) =\(\frac {5}{ 2} \)× \(\frac {7}{ 2} \) =\(\frac {35}{ 4} \) =8 \(\frac {3}{ 4} \) Therefore, 8 \(\frac {3}{ 4} \) cups of flour required for baking 2 \(\frac {1}{ 2} \) cakes.

Example 9. Sirisha uses \(\frac {2}{5} \) liters of petrol in her Scooty for 1 km. Find how many liters of petrol Sirisha use to drive 1 \(\frac {3}{8} \) km? Solution: No. of liters of petrol for 1 km=\(\frac {2} {5} \) No. of liters of petrol used for 1 \(\frac {3}{ 8} \) km= 1 \(\frac {3}{ 8} \)  × \(\frac {2} {5} \) =\(\frac {11} {8} \)× \(\frac {2} {5} \) =\(\frac {22} {40} \) =\(\frac {11} {10} \) Therefore, Sirisha uses \(\frac {11} {10} \) lt of petrol for 1 \(\frac {3} {8} \) km.

Example 10. A restaurant makes sweet lime juice on Friday and uses 3 \(\frac {1} {8} \) kg of sweet limes. As Saturday is a busy day, the restaurant plans to make 8 \(\frac {1} {9} \) as much as sweet lime juice. How many kg of Sweet lime juice is required? Solution: No. of kg of sweet limes used= 3 \(\frac {1} {8} \) No. of kg of sweet limes used to make 8 \(\frac {1} {9} \) lt=3 \(\frac {1} {8} \) ×  8 \(\frac {1} {9} \) =\(\frac {25} {8} \) ×  \(\frac {73} {9} \) =\(\frac {25 ×  73} {8 × 9} \) =\(\frac {1825} {72} \) =25 \(\frac {25} {72} \) Therefore, Restaurant uses 25 \(\frac {25} {72} \) kg of sweet limes.

Example 11. Rakesh can ride a bike 3 \(\frac {2} {5} \) km in 1 hour. If he plans to ride a bike for 4 \(\frac {1} {7} \) hours, how much distance he can travel? Solution: No. of km Rakesh can ride a bike= 3 \(\frac {2} {5} \) km No. of km Rakesh can ride a bike in 4 \(\frac {1} {7} \)hours=4 \(\frac {1} {7} \)  × 3 \(\frac {2} {5} \) =\(\frac {29} {7} \) × \(\frac {17} {5} \) =\(\frac {29 × 17} {7 ×  5} \) =\(\frac {493} {35} \) =14 \(\frac {3} {35} \) Therefore, Rakesh can ride a bike in 14 3/35 km.

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Word Problems - Fractions (multiplication) (with mixed numbers)

WORD PROBLEMS Fractions (multiplication) (with mixed numbers) pic

Description:  This packet helps students practice solving word problems that require multiplication with mixed numbers. Each page has a set of 7 problems. Each page also has a speed and accuracy guide to help students see how fast and how accurately they should be doing these problems. After doing all 14 problems, students should be more comfortable doing these problems and have a clear understanding of how to solve them. 

Gabe is barely 2$\dfrac{3}{5}$ years old. He has spent $\dfrac{1}{3}$ of his life sleeping or crying. How much of his short life has Gabe spent either sleeping or crying in years?

Emily needs enough fabric for 3$\dfrac{1}{2}$ hats, since she has half a hat done already. If each hat requires 1$\dfrac{2}{7}$ feet of fabric, how much fabric will she need to make the 3$\dfrac{1}{2}$ hats? 

Practice problems require knowledge of how to add, subtract, and multiply whole numbers.

multiplying mixed number fractions problem solving

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Multiplying fractions word problems

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multiplying mixed number fractions problem solving

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  1. solving multi step problems with fractions and mixed numbers worksheet

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  2. How To Simplify Expressions With Fractions And Whole Numbers

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  3. Multiplying Fractions and Mixed Numbers Anchor Chart Poster and Guided Notes

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  4. Multiplying Fractions with Whole Numbers 4th Grade Math Worksheets

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VIDEO

  1. Multiplying Fractions and Mixed Numbers

  2. Multiplying Fractions and Mixed Numbers

  3. Multiplying Mixed Numbers by @MathTeacherGon

  4. How to Multiply FRACTIONS? @MathTeacherGon

  5. Multiplying Fractions (Six Example Problems)

  6. Multiplying Fractions and Mixed Numbers, Example 1

COMMENTS

  1. Multiplying mixed numbers (video)

    By converting mixed numbers into improper fractions, you can multiply the two numbers together in a straightforward way. Once you have the product as an improper fraction, you can convert it back into a mixed number. Created by Sal Khan and Monterey Institute for Technology and Education. Questions Tips & Thanks Sort by: Top Voted Arbaaz Ibrahim

  2. Mixed Numbers Calculator

    Calculator Use Do math calculations with mixed numbers (mixed fractions) performing operations on fractions, whole numbers, integers, mixed numbers, mixed fractions and improper fractions. The Mixed Numbers Calculator can add, subtract, multiply and divide mixed numbers and fractions. Mixed Numbers Calculator (also referred to as Mixed Fractions):

  3. Fractions Worksheets

    Multiplying Mixed Numbers Worksheets This fraction worksheet is great for practicing Multiplying Mixed Numbers Problems. The problems may be selected for two different degrees of difficulty. The easiest will keep the denominators 2, 3, 4, 5, & 10 and the numerators between 1 and 9.

  4. Multiplying Mixed Numbers

    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 = 33 10 If you are clever you can do it all in one line like this:

  5. Solving Problems by Multiplying and Dividing Fractions and Mixed Numbers

    Solving Problems by Multiplying and Dividing Fractions and Mixed Numbers Fraction Word Problems With Interactive Exercises Example 1: If it takes 5/6 yards of fabric to make a dress, then how many yards will it take to make 8 dresses? Analysis: To solve this problem, we will convert the whole number to an improper fraction.

  6. Multiply mixed numbers (practice)

    Math Multiply fractions Multiplying mixed numbers Multiply mixed numbers Google Classroom Multiply. 1 2 3 × 6 Choose 1 answer: 12 A 12 8 1 3 B 8 1 3 10 C 10 6 2 3 D 6 2 3 Stuck? Review related articles/videos or use a hint. Report a problem Do 4 problems

  7. Grade 5 Fractions Worksheets: Multiplying mixed numbers

    Worksheets Math Grade 5 Fractions: multiply / divide Multiplying mixed numbers Multiplying mixed numbers 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.

  8. Multiplying Mixed Numbers and Fractions

    Welcome to Multiplying Mixed Numbers and Fractions with Mr. J! Need help with how to multiply a mixed number by a fraction? You're in the right place!Whether...

  9. 2.2.1: Multiplying Fractions and Mixed Numbers

    41 2 = 9 2. Change 41 2 to an improper fraction. 2 ⋅ 4 + 1 = 9, and the denominator is 2. 11 5 ⋅ 9 2. Rewrite the multiplication problem, using the improper fractions. 11 ⋅ 9 5 ⋅ 2 = 99 10. Multiply numerators and multiply denominators. 99 10 = 9 9 10. Write as a mixed number. 99 ÷ 10 = 9 with a remainder of 9.

  10. Multiplying Fractions with Mixed Numbers: Steps, Examples

    To multiply fractions and mixed numbers, the first step is to convert the mixed number into an improper fraction. After that, you proceed with the regular multiplication of two fractions. A fraction represents parts of a whole.

  11. How to Multiplying Mixed Numbers

    Step 1: Convert the mixed number into an improper fraction. Step 2: Rewrite the whole number as a fraction with the denominator 1. Step 3: Multiply two fractions by multiplying the numerators and denominators separately. Step 4: Convert it into simplified form if required. Suppose we have to multiply 3 and 2 1 2. 2 1 2 = 2 × 2 + 1 2 = 5 2

  12. Free Math Help on Multiplying Mixed Numbers

    Example 1: Nina's garden is 4 and 2/3 feet long and 1 and 1/8 feet wide.What is the area of the garden? Analysis: We will multiply these mixed numbers in order to solve this problem. Solution: First we will convert each mixed number to an improper fraction.Then we can multiply. Step 1: Step 2: Answer: The area of Nina's garden is 5 and 1/4 sq ft.

  13. Multiplying Mixed Numbers Worksheets

    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

  14. Mixed Problems Worksheets

    This fractions mixed problems worksheet is great for working on adding, subtracting, multiplying, and dividing two fractions on the same worksheet. You may select between three different degrees of difficulty and randomize or keep in order the operations for the problems. The worksheet will produce 12 problems per worksheet.

  15. Multiplying Fractions and Mixed Numbers

    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 An expression in which a whole number is combined with a proper fraction. For example 5 2 3 is a mixed number. .For example, this recipe will make 4 crumb piecrusts:

  16. How to Multiplying Mixed Numbers ⭐ Definition, Fractions, Examples

    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.

  17. IXL

    Improve your math knowledge with free questions in "Multiply fractions and mixed numbers: word problems" and thousands of other math skills.

  18. Multiplying Fractions Practice Questions

    The Corbettmaths Practice Questions on Multiplying Fractions. Welcome; Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths ... multiplication. Practice Questions. Previous: Increasing/Decreasing by a Fraction Practice Questions. Next: Conversion Graphs Practice Questions. GCSE Revision Cards. 5-a ...

  19. Word Problems on Multiplication of Mixed Fractions

    Practice as much as you can and enhance your problem-solving ability and speed of attempting the questions too. Do Check: Word Problems on Division of Mixed Fractions; Word Problems on Subtraction of Mixed Fractions; Word Problems on Addition of Mixed Fractions; Mixed Numbers Multiplication Word Problems. Example 1.

  20. Mixed Fractions Problem Solving

    Each task contains a brief description of the mixed fractions problem and it is down to the learner to form a solution while explaining their reasoning. Sheet one contains brief, more direct questions while sheet 2 builds more context into the task. Here are examples from each sheet: Show that 3 ⅓ - ⅘ = 2 8/15.

  21. Word Problems

    Description: This packet helps students practice solving word problems that require multiplication with mixed numbers. Each page has a set of 7 problems. Each page also has a speed and accuracy guide to help students see how fast and how accurately they should be doing these problems.

  22. Mixed fraction multiplication problems

    Fraction multiplication worksheets: mixed problems. Below are six versions of our grade 6 math worksheet with various multiplication problems involving proper fractions, improper fractions and mixed numbers. These worksheets are pdf files. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4 Worksheet #5 Worksheet #6. 5 More.

  23. Working with Fractions

    Multiplying Mixed Numbers and Fractions. Representing multiplication as groups of a number can help students construct meaning and understanding as they move towards ownership of the algorithm of multiplying mixed numbers and fractions. This video offers some ideas for using the Polypad below as part of this process.

  24. Multiplying fractions word problems

    Multiplying fractions word problems Including estimating These grade 5 word problems involve the multiplication of common fractions by other fractions or whole numbers. Some problems ask students between what numbers does the answer lie? Answers are simplified where possible. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4