The idea, step by step
Three names for the same proportion
Percent means out of one hundred. Forty percent means 40 hundredths, so it is 0.40 as a decimal and 40/100=2/5 as a fraction. The whole must represent the same amount in each form.
Familiar equivalents are useful: 1/2=0.5=50%, 1/4=0.25=25%, 3/4=0.75=75% and 1/10=0.1=10%. Use equal parts to explain the connection, not only a remembered list.
Find a part of a quantity
To find 10% of an amount, divide it by 10. Use that result to build 20%, 30% or 40%. To find 25%, share into four equal groups; 50% means one half.
When a percentage describes students, tickets or litres, the final answer needs those units. Check whether the part should be smaller than the whole: a positive percentage below 100% gives a smaller amount.
A common trap
25% means 25 of the objects, whatever the whole contains.
Instead: 25% means one quarter of the whole. It is 25 objects only when the whole contains 100 objects.
See the thinking
Worked example 1
Find 40% of 80 counters.
- 10% of 80 is 8 counters.
- 40% is four lots of 10%, so 4×8=32.
- Check with a fraction: 2/5 of 80 is also 32.
Worked example 2
Three quarters of 60 students join a game. Write the proportion as a decimal and percentage, then find the number of students.
- 3/4=75/100, so it is 0.75 and 75%.
- One quarter of 60 is 15. Three quarters is 3×15=45.
Check your understanding
Write 0.6 as a percentage and a simple fraction.
Show answer
60% and 3/5.
0.6 is 6/10, which is 60/100 and simplifies to 3/5.
Your turn
6 questions · 11 marks · Work at your own pace.
Read the questions online
- Write as a decimal and a percentage.2 marks
- Find 20% of 45 metres.2 marks
- Find 60% of 30 counters.2 marks
- Find of 56 litres, then name this fraction as a percentage.2 marks
- Sixteen of 40 library books are about animals. What percentage is that?2 marks
- Find 25% of 28 students.1 mark
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Write as a decimal and a percentage.2 marks
7/10=70/100.
0.7 and 70%. - Find 20% of 45 metres.2 marks
10% is 4.5 m; twice that is 9 m.
9 m. - Find 60% of 30 counters.2 marks
10% is 3 counters; 6×3=18.
18 counters. - Find of 56 litres, then name this fraction as a percentage.2 marks
56÷8=7; 1/8 is half of 1/4, so half of 25% is 12.5%.
7 L; 12.5%. - Sixteen of 40 library books are about animals. What percentage is that?2 marks
16/40=4/10=40/100.
40%. - Find 25% of 28 students.1 mark
25%=1/4 and 28÷4=7.
7 students.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Fraction/decimal/percentage quantities; discounts; budgets/cost predictions; comparing choices, risks and consequences.
Official curriculum source ↗