How to Multiply Mixed Fractions
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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

Simplify the answer and convert your answer back into a mixed number if needed.

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

The answer is already in simplest form.

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

The answer is already in simplest form.

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

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