How to Multiply Mixed Numbers? (+FREE Worksheet!)

How to Multiply Mixed Numbers? (+FREE Worksheet!)

Fractions greater than \(1\) are usually represented as mixed numbers. In this case, the mixed number consists of an integer part and a standard fraction less than \(1\). The integer part is the same as the quotient part and the numerator of the fraction is the remainder of the division and the denominator of the fraction will also be the divisor. You can multiply Mixed numbers in a few simple steps. To learn this join us.

Related Topics

Step by step guide to multiply mixed numbers

In the Multiplication of mixed numbers, their improper fractions can be used instead, and if necessary, the result can be converted back to the form of mixed numbers.

Here’s how to multiply mixed numbers:

  • Step 1: Convert all mixed numbers into improper fractions (improper fraction is a fraction in which the top number is bigger than bottom number): To convert a mixed number to a fraction, you must first multiply the mixed number by the denominator, then add the result to the numerator. Put the resulting number in the case of a new numerator and keep the denominator of the same fraction as the previous one. This way you have converted a mixed number into a fraction. \(a \ \frac{c}{ \color{ blue }{b} }= a \ \color{blue}{+} \ \frac{c}{\color{ blue }{b}}=\frac{a \color{ blue }{b} \ \color{blue}{+} \ c}{ \color{ blue }{b} }\)
  • Step 2: multiply these two improper fractions: To multiply fractions, we multiply the first fraction by the second fraction
  • Step 3: Convert the answer to a mixed number: To convert a fraction larger than one to a mixed number, you must divide the numerator by the denominator. After division, the obtained quotient is the same integer in the mixed number and the remainder of the division is the numerator of the fraction. The denominator is also the denominator of the initial fraction in the mixed number.

Multiplying Mixed Numbers – Example 1:

Multiply mixed numbers. \(2 \ \frac{1}{4} \ \times \ 3 \ \frac{1}{2}=\)

Solution:

Converting mixed numbers to fractions, \(2 \ \frac{1}{4}=\frac{9}{4}\) and \(3 \ \frac{1}{2}=\frac{7}{2}\).
\(\frac{9}{4} \ \times \ \frac{7}{2}\),

Applying the fractions rule for multiplication, \(\frac{9}{4} \ \times \ \frac{7}{2}=\) \(\frac{9 \ \times \ 7}{4 \ \times \ 2}=\frac{63}{8}=7 \ \frac{7}{8}\)

Multiplying Mixed Numbers – Example 2:

Multiply mixed numbers. \(5 \ \frac{2}{3} \ \times \ 3 \ \frac{3}{4}=\)

Solution:

Converting mixed numbers to fractions, \(5 \ \frac{2}{3}=\frac{17}{3}\) and \(3 \ \frac{3}{4}=\frac{15}{4}\).
\(\frac{17}{3} \ \times \ \frac{15}{4}\),

Applying the fractions rule for multiplication, \(\frac{17}{3} \ \times \ \frac{15}{4}=\) \(\frac{17 \ \times \ 15}{3 \ \times \ 4}=\frac{255}{12}=\frac {255÷ 3} {12÷ 3} =\frac {85} {4}= 21 \ \frac{1}{4}\)

Multiplying Mixed Numbers – Example 3:

Multiply mixed numbers. \(3 \ \frac{2}{3} \ \times \ 2 \ \frac{1}{2}=\)

Solution:

Converting mixed numbers to fractions, \(3 \ \frac{2}{3}=\frac{11}{3}\) and \(2 \ \frac{1}{2}=\frac{5}{2}\).
\(\frac{11}{3}×\frac{5}{2} \),

Applying the fractions rule for multiplication, \(\frac{11}{3}×\frac{5}{2} =\) \(\frac{11×5}{3×2}=\frac{55}{6}=9 \ \frac{1}{6}\)

Multiplying Mixed Numbers – Example 4:

Multiply mixed numbers. \(4 \ \frac{3}{5} \ \times \ 2 \ \frac{1}{3}=\)

Solution:

Converting mixed numbers to fractions, \(4 \ \frac{3}{5}=\frac{23}{5}\) and \(2 \ \frac{1}{3}=\frac{7}{3}\).
\(\frac{23}{5} \ \times \ \frac{7}{3}\),

Applying the fractions rule for multiplication, \(\frac{23}{5} \ \times \ \frac{7}{3}=\) \(\frac{23×7}{5×3}=\frac{161}{15}=10 \ \frac{11}{15}\)

Exercises for Multiplying Mixed Numbers

Find each product.

  1. \(\color{blue}{1\frac{2}{3} \times 1\frac{1}{4}}\)
  2. \(\color{blue}{1\frac{3}{5} \times 1\frac{2}{3}}\)
  3. \(\color{blue}{1\frac{2}{3} \times 3\frac{2}{7}}\)
  4. \(\color{blue}{4\frac{1}{8} \times 1\frac{2}{5}}\)
  5. \(\color{blue}{2\frac{2}{5} \times 3\frac{1}{5}}\)
  6. \(\color{blue}{1\frac{1}{3} \times 1\frac{2}{3}}\)

ِِDownload Multiplying and Dividing Mixed Numbers Worksheet

  1. \(\color{blue}{2\frac{1}{12}}\)
  2. \(\color{blue}{2\frac{2}{3}}\)
  3. \(\color{blue}{5\frac{10}{21}}\)
  4. \(\color{blue}{5\frac{31}{40}}\)
  5. \(\color{blue}{7\frac{17}{25}}\)
  6. \(\color{blue}{2\frac{2}{9}}\)

Related to "How to Multiply Mixed Numbers? (+FREE Worksheet!)"

Top 5 GED Math Study Guides
Top 5 GED Math Study Guides
A Comprehensive Collection of FREE PSAT Math Practice Tests
A Comprehensive Collection of FREE PSAT Math Practice Tests
What’s A Good ACT Score?
What’s A Good ACT Score?
TASC Testing Accommodation and Support for Disabilities
TASC Testing Accommodation and Support for Disabilities
The History of Math Development in the USA
The History of Math Development in the USA
Use of Technology in Math Class That Works
Use of Technology in Math Class That Works
Improving Your Math in College: What You Should Do
Improving Your Math in College: What You Should Do
Top Proven Strategies To Increase Your SAT Math Score
Top Proven Strategies To Increase Your SAT Math Score
Top Math YouTube Channels For High School Students
Top Math YouTube Channels For High School Students
What Kind of Math is on the GRE?
What Kind of Math is on the GRE?

Leave a Reply

30% OFF

SAVE $9.34

Cyber Monday DEAL!

It was $16.99 now it is $7.65

X
55% OFF!

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…