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Home > Maths I > Numbers and Money > Basic fractions

Maths I

Basic fractions

Multiplying and dividing fractions

Multiplying fractions

Boy working on his maths homework.

To multiply fractions, you need to multiply the top numbers (numenators) together, and multiply the bottom numbers (denominators) together.

Remember that you cannot cancel numbers that are both on the top of a fraction.

Have a look at the example below.

{4 \over 5} \times {5 \over 6}

Multiply then cancel:

{4 \over 5} \times {5 \over 6} = {20 \over 30} = {2 \over 3}

OR cancel between the top and the bottom then multiply:

The fraction 4 over 5 is multiplied by the fraction 5 over 6. The answer is the farction 2 over 3. Beside 4 over 5 it says 2 over 1 in red, and beside 5 over 6 it says 1 over 3 in red.
Question

Calculate: {5 \over 6} \times {5 \over 8}

Answer

{5 \over 6} \times {5 \over 8} = {25 \over 48}

(The 5s do not cancel each other out because they are both on the top of the fraction).

Dividing a fraction by a whole number

 

{3 \over 4} divided by 3 should be 1 \over 3 of the original fraction, which would make the answer 1 \over 4.

So {3 \over 4} \div 3

 

= {3 \over 4} \div {3 \over 1}     (writing 3 as 3 \over 1)

 

= 1 \over 4.

Dividing by a fraction

The rule to remember when dividing fractions is that you turn the fraction you are dividing by upside down, and multiply.

So going back to the previous example we can work this out by turning the 3 \over 1 upside down.

{3 \over 4} \div {3 \over 1} = {3 \over 4} \times1 \over 3 = 1 \over 4

Dividing by 3 is the same as multiplying by 1 \over 3.

It works with all fractions. For example dividing by {3 \over 4} is the same as multiplying by 4 \over 3.

Question

Calculate: {3 \over 8} \div {3 \over 4}

Answer

{3 \over 8} \div {3 \over 4}

 

= {3 \over 8} \times {4 \over 3}

 

= 1 \over 2

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