Calculating fractions
How do we find \(\frac{3}{5}\) of \(20\)?
Here are two different methods you can use.
Method 1
Find \(\frac{1}{5}\) of \(20\), then multiply by \(3\).
Find \(\frac{1}{5}\) of \(20\) by dividing \(20\) by \(5\).
\(20 \div 5 = 4\).
We need \(\frac{3}{5}\) of \(20\), so we multiply this \(4\) by \(3\).
\(\frac{3}{5}\) of \(20\)
\(= 3 \times \frac{1}{5}\)
\(= 3 \times 4\)
\(= 12\)
Method 2
Multiply \(\frac{3}{5}\) by \(20\).
Writing \(20\) as a fraction (\(\frac{20}{1}\)) might help.
\(\frac{3}{5} \times 20\)
\(= \frac{3}{5} \times \frac{{20}}{1}\)
\(= \frac{{60}}{5}\)
\(=12\)
Question
Use either method to find \(\frac{3}{7}\) of \(35\).
The answer is \(15\).
Method 1:
\(\frac{1}{7}\) of \(35 = 5\)
\(3 \times 5 = 15\)
Method 2:
\(\frac{3}{7} \times 35\)
\(=\frac{3}{7} \times \frac{35}{1}\)
\(= \frac{105}{7}\)
\(= 15\)
Calculating fractions with a calculator
With larger numbers you might want to use a calculator to work out how much a fraction of something is but you can use versions of the two methods shown above.
What is \(\frac{15}{24}\) of \(\pounds{116}\)?
Method 1
Divide the numerator (top number) of the fraction by the denominator (bottom number) and multiply by the other number:
\(15 \div 24 \times 116 = \pounds72.50\)
Method 2
Multiply the number you are finding a fraction of by the numerator (top number) of the fraction then divide by the denominator (bottom number):
\(116 \times 15 \div 24 = \pounds72.50\)
Question
Use either method to find \(\frac{13}{28}\) of \(252\).
The answer is \(15\).
Method 1:
\(13 \div 28 \times 252 = 117\)
Method 2:
\(252 \times 13 \div 28 = 117\)