How to Multiply Mixed Numbers

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A mixed number is a combination of two numbers: a whole number and a proper fraction (A proper fraction is a fraction which has a denominator which is greater than the numerator, i.e., \(\frac{2}{3}\), \(\frac{4}{7}\), \(\frac{5}{6}\) , etc.). Moreover, a mixed number can be converted into a fraction and it always lies between two whole numbers.

For ex: Let's take the mixed number \(1\frac{3}{4}\). So, this mixed number comprises of two parts, a whole number which is \(1\) and a proper fraction \(\frac{3}{4}\). Now, if we convert this mixed number into an improper fraction which is \(\frac{7}{4}\) we find that it lies between the two whole numbers \(1\) and \(2\).
Some other examples of a mixed number are \(2\frac{1}{2}\), \(3\frac{1}{3}\), \(4\frac{1}{5}\), etc.

Parts of a mixed number

A mixed number consists of three distinct parts: a whole number, a numerator and a denominator. Here, the numerator and the denominator are the parts of the proper fraction.

How to Convert Improper Fractions to Mixed Fractions

First, we need to divide the numerator of the fraction by the denominator.
Next, we need to write down the quotient as the whole number of the mixed fraction.
Now, the remainder becomes the numerator and the divisor becomes the denominator of the improper part.

Ex: Let's take the improper fraction \(\frac{5}{3}\)
Now, when we divide \(5\) by \(3\), the quotient is \(1\). Also, the remainder is \(2\) and the divisor \(3\). So, the mixed number is \(1\frac{2}{3}\).

Steps to Multiply Mixed Numbers

To multiply two mixed numbers, follow these steps.

Convert the mixed numbers into improper fractions, separately.
Now multiply these improper fractions and write the answer in the lowest terms.

Ex: Let's multiply \(4\frac{1}{3} \ \) and \(2\frac{1}{5}\)
So, the multiplication becomes \( (\frac{13}{3} \times \frac{11}{5}) = \frac{11 \times 13}{5 \times 3} = \frac{143}{15} = 9\frac{8}{15} \)

Multiply Mixed Numbers Video

Free printable Worksheets

Exercises for Multiply Mixed Numbers

1) \( 2 {2 \over 3} \ \times \ 1 {1 \over 7} = \ \)

2) \( 8 {4 \over 5} \ \times \ 4 {3 \over 10} = \ \)

3) \( 2 {4 \over 7} \ \times \ 1 {2 \over 5} = \ \)

4) \( 3 {1 \over 2} \ \times \ 2 {2 \over 3} = \ \)

5) \( 5 {5 \over 7} \ \times \ 4 {3 \over 5} = \ \)

6) \( 3 {1 \over 3} \ \times \ 1 {4 \over 7} = \ \)

7) \( 3 {2 \over 3} \ \times \ 2 {3 \over 4} = \ \)

8) \( 1 {3 \over 8} \ \times \ 1 {2 \over 7} = \ \)

9) \( 2 {1 \over 4} \ \times \ 3 {4 \over 5} = \ \)

10) \( 1 {1 \over 9} \ \times \ 2 {2 \over 6} = \ \)

Answers

1) \( 2 {2 \over 3} \ \times \ 1 {1 \over 7} = \ \)\( \ \color{red}{ {(2 \times 3 + 2) \ \times \ (1 \times 7 + 1) \over 3\times7} = {64 \over 21} \ }\)

Solution:
Step 1: Convert mixed numbers to fractions, \( 2 {2 \over 3} = {8 \over 3}\) and \( 1 {1\over 7} = {8 \over 7}\)
Step 2: Apply the fractions rule for multiplication, \({8 \over 3} \times {8 \over 7} \) = \({8 \times \ 8 \over 3\times7} = \) \({64 \over 21} \)

2) \( 8 {4 \over 5} \ \times \ 4 {3 \over 10} = \ \)\( \ \color{red}{{(8 \times 5 + 4) \ \times \ (4 \times 10 + 3) \over 5\times10} = } \) \(\color{red}{{1892 \over 50} = \ 37{21 \over 25}}\)
GCF(42,50) = 2

Solution:
Step 1: Convert mixed numbers to fractions, \( 8 {4 \over 5} = {44 \over 5}\) and \( 4 {3\over 10} = {43 \over 10}\)
Step 2: Apply the fractions rule for multiplication, \({44 \over 5} \times {43 \over 10} \) = \({1892 \over 50} \) = \(37{21 \over 25}\)

3) \( 2 {4 \over 7} \ \times \ 1 {2 \over 5} = \ \)\( \ \color{red}{{(2 \times 7 + 4) \ \times \ (1 \times 5 + 2) \over 7\times5} = } \) \(\color{red}{{126 \over 35} = \ {18 \over 5} = \ 3{3 \over 5} }\)
GCF(126,35) = 7

Solution:
Step 1: Convert mixed numbers to fractions, \( 2 {4 \over 7} = {18 \over 7}\) and \( 1 {2\over 5} = {7 \over 5}\)
Step 2: Apply the fractions rule for multiplication, \({18 \over 7} \times {2\over 5} \) = \({126 \over 35} \) = \({18 \over 5}\) = \(3{3 \over 5}\)

4) \( 3 {1 \over 2} \ \times \ 2 {2 \over 3} = \ \)\( \ \color{red}{{(3 \times 2 + 1) \ \times \ (2 \times 3 + 2) \over 2\times6} = } \) \(\color{red}{{56 \over 12} = \ {14 \over 3} = \ }\)
GCF(56,12) = 4

Solution:
Step 1: Convert mixed numbers to fractions, \( 3 {1 \over 2} = {7 \over 2}\) and \( 2 {2\over 3} = {8 \over 3}\)
Step 2: Apply the fractions rule for multiplication, \({7 \over 2} \times {8\over 3} \) = \({56 \over 6} \) = \({28 \over 3}\)

5) \( 5 {5 \over 7} \ \times \ 4 {3 \over 5} = \ \)\( \ \color{red}{{(5 \times 7 + 5) \ \times \ (4 \times 5 + 3) \over 7\times5} = } \) \(\color{red}{{920 \over 35} = \ 26{2 \over 7}}\)
GCF(920,35) = 5

Solution:
Step 1: Convert mixed numbers to fractions, \( 5 {5 \over 7} = {40 \over 7}\) and \( 4 {3 \over 5} = {23 \over 53}\)
Step 2: Apply the fractions rule for multiplication, \({40 \over 7} \times {23 \over 53} \) = \({920 \over 35} \) = \(26{2 \over 7}\)

6) \( 3 {1 \over 3} \ \times \ 1 {4 \over 7} = \ \)\( \ \color{red}{{(3 \times 3 + 1) \ \times \ (1 \times 7 + 4) \over 3\times7} = } \) \(\color{red}{{110 \over 21} = \ 5{5 \over 21}}\)

Solution:
Step 1: Convert mixed numbers to fractions, \( 3 {1 \over 3} = {10 \over 3}\) and \( 1 {4 \over 7} = {11 \over 7}\)
Step 2: Apply the fractions rule for multiplication, \({10 \over 3} \times {11 \over 7} \) = \({110 \over 21} \) = \(5{5 \over 21}\)

7) \( 3 {2 \over 3} \ \times \ 2 {3 \over 4} = \ \)\( \ \color{red}{{(3 \times 3 + 2) \ \times \ (2 \times 4 + 3) \over 3\times4} = } \) \(\color{red}{{121 \over 12} = \ 10{1 \over 12}}\)

Solution:
Step 1: Convert mixed numbers to fractions, \( 3 {2 \over 3} = {11 \over 3}\) and \(2 {3 \over 4} = {11 \over 4}\)
Step 2: Apply the fractions rule for multiplication, \({11 \over 3} \times 2 {3 \over 4} \) = \({121 \over 12} \) = \(10{1 \over 12}\)

8) \( 1 {3 \over 8} \ \times \ 1 {2 \over 7} = \ \)\( \ \color{red}{{(1 \times 8 + 3) \ \times \ (1 \times 7 + 2) \over 8\times7} = } \) \(\color{red}{{99 \over 56} = \ 1{43 \over 56}}\)

Solution:
Step 1: Convert mixed numbers to fractions, \( 1 {3 \over 8} = {11 \over 8}\) and \(1 {2 \over 7} = {9 \over 7}\)
Step 2: Apply the fractions rule for multiplication, \({11 \over 8} \times {9 \over 7} \) = \({99 \over 56} \) = \(1{43 \over 56}\)

9) \( 2 {1 \over 4} \ \times \ 3 {4 \over 5} = \ \)\( \ \color{red}{{(2 \times 4 + 1) \ \times \ (3 \times 5 + 4) \over 4\times5} = } \) \(\color{red}{{171 \over 20} = \ 8{11 \over 20}}\)

Solution:
Step 1: Convert mixed numbers to fractions, \( 2 {1 \over 4} = {9 \over 4}\) and \(3 {4 \over 5} = {19 \over 5}\)
Step 2: Apply the fractions rule for multiplication, \({9 \over 4} \times {19 \over 5} \) = \({171 \over 20} \) = \(8{11 \over 20}\)

10) \( 1 {1 \over 9} \ \times \ 2 {2 \over 6} = \ \)\( \ \color{red}{{(1 \times 9 + 1) \ \times \ (2 \times 6 + 2) \over 9\times6} = } \) \(\color{red}{{140 \over 54} = \ {70 \over 27} = \ 2{16 \over 27}}\)
GCF(140,54) = 10

Solution:
Step 1: Convert mixed numbers to fractions, \( 1 {1 \over 9} = {10 \over 9}\) and \(2 {2 \over 6} = {14 \over 6}\)
Step 2: Apply the fractions rule for multiplication, \({10 \over 9} \times {14 \over 6} \) = \({140 \over 54} \) = \({70 \over 27} = 2{16 \over 27}\)

How to Multiply Mixed Numbers