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Multiplying Mixed Fractions

A mixed fraction is also called as a mixed number, because it is a combination of a whole number and a proper fraction. In order to multiply two mixed fractions, first convert the mixed fractions into improper fractions. Then multiply the numerators together and multiply the denominators together. An improper fraction is a fraction in which the numerator is greater than the denominator.

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How to Multiply Mixed Fractions

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Below are the examples based on how to multiply mixed fractions -

Step 1: Convert mixed fractions to improper fractions.

Step 2: Multiply numerators together and multiply the denominators together.

Step 3: Again convert improper fraction to mixed fractions.

Step 4: If possible simplify the result obtained in Step 3 and write the final answer.


Example: Multiply the mixed fractions: 3$\frac{4}{5}$ and 2$\frac{3}{6}$

Solution:
Step 1: Convert given fractions to improper fractions

3$\frac{4}{5}$ = $\frac{19}{5}$

2$\frac{3}{6}$ = $\frac{15}{6}$

Step 2: Multiply the numerators and then denominators

$\frac{19}{5}$ $\times$ $\frac{15}{6}$ = $\frac{19 \times 15}{5 \times 6}$

= $\frac{285}{30}$

Step 3: Simplify $\frac{285}{30}$

$\frac{285}{30}$ = $\frac{19}{2}$ (Divided numerator and denominator by 15)

= 9$\frac{1}{2}$ (By converting in mixed number)

=> 3$\frac{4}{5}$ $\times$ 2$\frac{3}{6}$ = 9$\frac{1}{2}$

Example 2: Solve 1$\frac{3}{4}$ $\times$ 2$\frac{2}{3}$. Simplify the answer.

Solution:

Step 1: Convert given fractions to improper fractions

1$\frac{3}{4}$ = $\frac{7}{4}$

2$\frac{2}{3}$ = $\frac{8}{3}$

Step 2: Multiply the numerators and then denominators

$\frac{7}{4}$ $\times$ $\frac{8}{3}$ = $\frac{7 \times 8}{4 \times 3}$

= $\frac{56}{12}$

= $\frac{14}{3}$ (By simplifying)

= 4$\frac{2}{3}$ (By converting in mixed number)

=> 1$\frac{3}{4}$ $\times$ 2$\frac{2}{3}$ = 4$\frac{2}{3}$


Solved Examples

Question 1: Multiply the following fraction and the mixed number $\frac{3}{4}$ x 2$\frac{3}{5}$
Solution:
The problem here is to multiply, $\frac{3}{4}$ x 2$\frac{3}{5}$

Here, We are going to multiply the fraction and a mixed number

Given fraction is `3/4` and the mixed number is 2$\frac{3}{5}$

First convert the mixed number in to an improper fraction that is 2$\frac{3}{5}$ = $\frac{13}{5}$

Now the fractions become $\frac{3}{4}$ x $\frac{13}{5}$

We can directly multiply the numerators, then denominators

= $\frac{3\times13}{4\times5}$

= $\frac{39}{20}$, which is the improper fraction

= $\frac{39}{20}$


Correct answer is 1$\frac{19}{20}$
Question 2: Multiply the following fraction and the mixed number $\frac{5}{6}$ x 4$\frac{5}{4}$
Solution:
The problem here is to multiply, $\frac{5}{6}$ x 4$\frac{5}{4}$

Here, We are going to multiply the fraction and a mixed number

Given fraction is `5/6` and the mixed number is 4$\frac{5}{4}$

First convert the mixed number in to an improper fraction that is 4$\frac{5}{4}$ = $\frac{21}{4}$

Now the fractions become  $\frac{5}{6}$ x $\frac{21}{4}$

We can directly multiply the numerators, then denominators

= $\frac{5\times21}{6\times4}$

= $\frac{105}{24}$ which is the improper fraction

= $\frac{105}{24}$


Correct answer is 4$\frac{9}{24}$
Question 3: Multiply the following fraction and the mixed number $\frac{6}{7}$ x 5$\frac{8}{5}$
Solution:
The problem here is to multiply, $\frac{6}{7}$ x 5$\frac{8}{5}$

Here, we are going to multiply the fraction and a mixed number

Given fraction is `6/7` and the mixed number is 5$\frac{8}{5}$

First convert the mixed number in to an improper fraction that is 5$\frac{8}{5}$ = $\frac{33}{5}$

Now the fractions become $\frac{6}{7}$ x $\frac{33}{5}$

We can directly multiply the numerators, then denominators

= $\frac{6\times33}{7\times5}$

= $\frac{198}{35}$ , which is the improper fraction

= $\frac{23}{35}$


Correct answer is $\frac{23}{35}$

Practice Problems

Question 1: Multiply the following fraction and the mixed number $\frac{6}{4}$ x 2$\frac{3}{5}$
Question 2: Multiply the following fraction and the mixed number $\frac{6}{4}$ x 2$\frac{3}{5}$
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