# How to Multiply Mixed FractionsSupport Page

Welcome to our How to Multiply Mixed Fractions support page.

This page will support you in learning how to multiply two mixed fractions together, and show you some worked examples.

## How to Multiply Mixed Fractions

### How to Multiply Mixed Fractions Support

Frazer says "To multiply two mixed fractions, follow these simple steps." Step 1)

• Convert any mixed numbers into improper fractions;
• Put any integers over a denominator of 1.

Step 2)

Multiply the numerators and denominators of the two fractions together. This will give you the answer.

Step 3

And that's how to multiply mixed fractions!

#### Example 1) Calculate   $2 {3 \over 5} \times 1 {2 \over 3}$

Step 1) Convert the mixed numbers into improper fractions

$2 {3 \over 5} = {13 \over 5}$ and $1 {2 \over 3} = {5 \over 3}$

This gives us: $2 {3 \over 5} \times 1 {2 \over 3} = {13 \over 5} \times {5 \over 3}$

Step 2) Multiply the numerators together, and the denominators together

${13 \over 5} \times {5 \over 3} = {13 \times 5 \over 5 \times 3} = {65 \over 15}$

Step 3) Simplify and convert the answer

Simplify the answer by dividing numerator and denominator by 5: ${65 \over 15} \; = \; {65 ÷ 5 \over 15 ÷ 5} = {13 \over 3}$

Now convert this to simplest form:

${13 \over 3} = 4 {1 \over 3}$

Final answer: $2 {3 \over 5} \times 1 {2 \over 3} = {13 \over 3} \; or \; 4 {1 \over 3}$

#### Example 2) Calculate   $1 {3 \over 4} \times 2{1 \over 6}$

Step 1) Convert the mixed numbers into improper fractions

$1 {3 \over 4} = {7 \over 4}$ and $2 {1 \over 6} = {13 \over 6}$

So $1 {3 \over 4} \times 2{1 \over 6} = {7 \over 4} \times {13 \over 6}$

Step 2) Multiply the numerators together, and the denominators together

${7 \over 4} \times {13 \over 6} = {7 \times 13 \over 4 \times 6} = {91 \over 24}$

Step 3) Simplify and convert the answer

The answer is already in simplest form as their are no common factors apart from 1.

Converting the answer to a mixed number gives us: ${91 \over 24} = 3 {19 \over 24}$

Final answer: $1 {3 \over 4} \times 2{1 \over 6} = {91 \over 24} \; or \; 3 {19 \over 24}$

#### Example 3) Calculate   $3 {1 \over 2} \times 2 {1 \over 5}$

Step 1) Convert the mixed numbers into improper fractions

$3 { 1 \over 2} = {7 \over 2}$ and $2 {1 \over 5} = {11 \over 5}$

So $3 {1 \over 2} \times 2 {1 \over 5} = {7 \over 2} \times {11 \over 5}$

Step 2) Multiply the numerators together, and the denominators together

${7 \over 2} \times {11 \over 5} = {7 \times 11 \over 2 \times 5} = {77 \over 10}$

Step 3) Simplify and convert the answer

Converting to a mixed number gives us: ${77 \over 10} = 7 {7 \over 10}$

Final answer: $3 {1 \over 2} \times 2 {1 \over 5} = {77 \over 10} \; or \; 7 {7 \over 10}$

#### Example 4) Work out $1 {2 \over 3} \times 3 {1 \over 2}$

Step 1) Convert both fractions to improper fractions

$1 {2 \over 3} \; = \; {5 \over 3}$ and $3 {1 \over 2} \; = \; {7 \over 2}$

So this gives us: $1 {2 \over 3} \times 3 {1 \over 2} \; = \; {5 \over 3} \times {7 \over 2}$

Step 2) Multiply the numerators and the denominators together.

${5 \over 3} \times {7 \over 2} \; = \; {5 \times 7 \over 3 \times 2} \; = \; {35 \over 6}$

Step 3) Convert back to a mixed fraction.

Converting back to a mixed fraction gives us ${35 \over 6} \; = \; 5 {5 \over 6}$

Final answer $1 {2 \over 3} \times 3 {1 \over 2} \; = \; 5 {5 \over 6}$

#### Example 5) Work out $2 {1 \over 5} \times 1 {3 \over 4}$

Step 1) Convert both fractions to improper fractions

$2 {1 \over 5} \; = \; {11 \over 5}$ and $1 {3 \over 4} \; = \; {7 \over 4}$

So this gives us: $2 {1 \over 5} \times 1 {3 \over 4} \; = \; {11 \over 5} \times {7 \over 4}$

Step 2) Multiply the numerators and the denominators together.

${11 \over 5} \times {7 \over 4} \; = \; {11 \times 7 \over 5 \times 4} \; = \; {77 \over 20}$

Step 3) Convert back to a mixed fraction.

Converting back to a mixed fraction gives us ${77 \over 20} \; = \; 3 {17 \over 20}$

Final answer $2 {1 \over 5} \times 1 {3 \over 4} \; = \; 3 {17 \over 20}$

#### Example 6) Work out $4 {2 \over 7} \times 5$

Step 1) Convert both fractions to improper fractions

$4 {2 \over 7} \; = \; {30 \over 7}$ and $5 \; = \; {5 \over 1}$

So this gives us: $4 {2 \over 7} \times 5 \; = \; {30 \over 7} \times {5 \over 1}$

Step 2) Multiply the numerators and the denominators together.

${30 \over 7} \times {5 \over 1} \; = \; {30 \times 5 \over 7 \times 1} \; = \; {150 \over 7}$

Step 3) Convert back to a mixed fraction.

Converting back to a mixed fraction gives us ${150 \over 7} \; = \; 21 {3 \over 7}$

Final answer $4 {2 \over 7} \times 5 \; = \; 21 {3 \over 7}$

#### Example 7) Calculate   $7 \times 2 {2 \over 3}$

Step 1) Convert the mixed numbers into improper fractions

First we need to put the integer over a denominator of 1. $7 = {7 \over 1}$ and $2 {2 \over 3} = {8 \over 3}$

So $7 \times 2 {2 \over 3} = {7 \over 1} \times {8 \over 3}$

Step 2) Multiply the numerators together, and the denominators together

${7 \over 1} \times {8 \over 3} = {7 \times 8 \over 1 \times 3} = {56 \over 3}$

Step 3) Simplify and convert the answer

Converting to a mixed number gives us: ${56 \over 3} = 18 {2 \over 3}$

Final answer: $7 \times 2 {2 \over 3} = {56 \over 3} \; or \; 18 {2 \over 3}$

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