Multiplying and dividing fractions

Multiplying fractions

\frac{1}{2} of \frac{1}{2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}

\frac{2}{3} of \frac{4}{5} = \frac{2}{3} \times \frac{4}{5} = \frac{8}{15}

curriculum-key-fact
Multiply the numerators to find the new numerator, multiply the denominators to find the new denominator, then simplify where necessary.
Question

Calculate \frac{3}{4} \times \frac{2}{5}

\frac{3}{4} \times \frac{2}{5} = \frac{3 \times 2}{4 \times 5} = \frac{6}{20}

Now put the the answer into its simplest form:

\frac{6}{20}= \frac{3}{10}

Dividing fractions

When you divide {10} by {2}, you are working out how many {2}s there are in {10}.

10 \div 2 = 5, so there are five {2}s in {10}.

In a similar way, when dividing {2} by \frac{1}{2}, you are working out how many \frac{1}{2}s there are in {2}.

There are four \frac{1}{2}s in {2}, so:

2 \div \frac{1}{2} = 4

If you divide 1 \frac{1}{2} by \frac{1}{4} you are working out how many \frac{1}{4}s there are in 1 \frac{1}{2}.

There are six \frac{1}{4}s in 1 \frac{1}{2}, so:

1\frac{1}{2} \div \frac{1}{4} = 6

Do you see a pattern? Let's write out those calculations a different way.

  • 2 \div \frac{1}{2} = 4 and 2 \times 2 = 4, so 2 \div \frac{1}{2} is the same as 2 \times 2
  • 1\frac{1}{2} \div \frac{1}{4} = \frac{3}{2} \div \frac{1}{4} = 6, so \frac{3}{2} \div \frac{1}{4} is the same as \frac{3}{2} \times 4 = \frac{12}{2} = 6

So, ' \div\frac{1}{2}' is the same as ‘ \times 2’.

and ' \div\frac{1}{4}' is the same as ‘ \times 4’.

curriculum-key-fact
To divide fractions, turn the second fraction upside down, then multiply.
Question

Calculate \frac{3}{4} \div \frac{4}{5}

\frac{3}{4} \div \frac{4}{5}= \frac{3}{4} \times \frac{5}{4} = \frac{15}{16}

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