Level 3 · Ages 11–13
Read it again any time, including while you work through the exercises.
Sale: 30% off! Battery: 45%! Fruit juice: 100% pure juice! Percentages are everywhere. A percentage is simply a proportion out of 100: saying 30% means 30 out of 100, in other words the fraction 30/100.
To apply a percentage, you multiply by this fraction. Computing 30% of 60 means computing 60 × 30/100 = 18. In practice, you can go through 10%: 10% of 60 is 60 ÷ 10 = 6, so 30% is 3 times more, 18. This 10% trick makes lots of mental calculations easy.
Some landmarks to know by heart: 50% is one half. 25% is one quarter. 10% is one tenth. 100% is the whole thing. With these landmarks you can estimate almost any percentage in your head.
In the other direction, you can find a percentage: if you score 45 shots out of 60, what is your success rate? You compute 45/60 = 3/4, and 3/4 = 75/100, so 75%. Finding a percentage means bringing a fraction to a denominator of 100.
In this lesson you will practise both directions: applying a percentage to a quantity, and uncovering the percentage hidden in a situation.
Compute 30% of 60 €.
10% de 60 = 6
I start with 10%: that is one tenth, so 60 ÷ 10 = 6.
6 × 3 = 18
30% is 3 times 10%, so 3 × 6 = 18.
60 × 30/100 = 18
I check with the fraction: 60 × 30/100 = 1800/100 = 18. Both methods agree.
Result: 30% of 60 € = 18 €
You scored 12 baskets out of 48 shots. What is your success percentage?
12/48 = 1/4
I write the proportion as a fraction: 12 out of 48. I simplify: 12/48 = 1/4.
1/4 = 25/100
I bring it to a denominator of 100: one quarter is 25 out of 100.
Result: Your success percentage is 25%.