How do you Multiply Fractions
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For those of you who like to see some algebra, here is the simple formula for multiplying two fractions:

Frazer says "To multiply a fraction by another fraction, follow these simple steps."

Before you start:

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

Step 1

Re-write the fraction equation into a single fraction.

Step 2 (optional)

Cancel any common factors of both the numerator and the denominator.

This make the next couple of steps easier!

Step 3 (this may not be needed after Step 2)

Work out the products in the numerator and denominator. This will give you the answer.

Step 4 (optional)

Simplify the answer if needed.

You should have now found your fraction of a number!

Example 1) Calculate   \[{3 \over 5} \times {4 \over 9} \]

Step 1)

\[{3 \over 4} \times {4 \over 9} = {3 \times 4 \over 4 \times 9}\]

Step 2) Cancel out common factors

\[{3 \times \cancel 4 \over \cancel 4 \times 9} = {3 \over 9} \]

Steps 3 & 4)

Simplify the answer by dividing numerator and denominator by 3: \[{3 \over 9} \; = \; {1 \over 3}\]

Final answer: \[{3 \over 4} \times {4 \over 9} \; = \; {1 \over 3}\]

Example 2) Calculate   \[{2 \over 5} \times {5 \over 8} \]

Step 1)

\[{2 \over 5} \times {5 \over 8} = {2 \times 5 \over 5 \times 8} \]

Step 2) Cancel out common factors

\[{2 \times \cancel 5 \over \cancel 5 \times 8} = {2 \over 8} \]

Steps 3 & 4)

Simplify the answer by dividing numerator and denominator by 2: \[{2 \over 8} \; = \; {1 \over 4}\]

Final answer: \[{2 \over 5} \times {5 \over 8} \; = \; {1 \over 4}\]

Example 3) Calculate   \[{7 \over 4} \times {9 \over 5} \]

Step 1)

\[{7 \over 4} \times {9 \over 5} = {7 \times 9 \over 4 \times 5} \]

Step 2)

There are no common factors so we can leave out this part.

Step 3)

\[{7 \times 9 \over 4 \times 5} = {63 \over 20}\]

Step 4)

This answer is already in simplest form, but we can convert it to a mixed number: \[{63 \over 20} \; = \; 3 {3 \over 20} \]

Final answer: \[{7 \over 4} \times {9 \over 5} \; = \; {63 \over 20} \; or \; 3 {3 \over 20}\]

Example 4) Calculate   \[{11 \over 7} \times 8 \]

First we need to put the integer over a denominator of 1. \[8 = {8 \over 1} \]

Step 1)

\[{11 \over 7} \times {8 \over 1} = {11 \times 8 \over 7 \times 1} \]

Step 2)

There are no common factors to cancel.

Step 3)

\[{11 \times 8 \over 7 \times 1} = {88 \over 7}\]

Step 4)

This fraction is already in its simplest form, but we can convert it into a mixed number: \[{88 \over 7} \; = \; 12 {4 \over 7} \]

Final answer: \[{11 \over 7} \times 8 \; = \; {88 \over 7} \; or \; 12 {4 \over 7} \]

Example 5) Calculate   \[{3 \over 5} \times {4 \over 7} \times {5 \over 9}\]

Step 1)

\[{3 \over 5} \times {4 \over 7} \times {5 \over 9} = {3 \times 4 \times 5 \over 5 \times 7 \times 9}\]

Step 2)

Cancel common factors.

\[{3 \times 4 \times \cancel 5 \over \cancel 5 \times 7 \times 9} = {3 \times 4 \over 7 \times 9} \]

Step 3)

\[{3 \times 4 \over 7 \times 9} = {12 \over 63}\]

Step 4)

Simplify the answer by dividing numerator and denominator by 3: \[{12 \over 63} = {4 \over 21}\]

Final answer: \[{3 \over 5} \times {4 \over 7} \times {5 \over 9} = {4 \over 21}\]