Percentages and Ratios
Primary 6 · Mathematics
Percentages and Ratios
Lesson 3 of 6
15 min
Let's begin
Last year a kilogram of beans at Kimironko market cost 800 Frw. This year the seller says, "Prices went up by 15%." Umutoni's mother wants to know the new price before she goes shopping.
Prices, school numbers and harvests go up and down all the time. Percentages are the usual way to describe how much.
Way 1: find the increase, then add it.
15% of 800 = 10% + 5% = 80 + 40 = 120 Frw.
New price = 800 + 120 = 920 Frw.
Way 2: one multiplication. The old price is 100%. After a 15% increase, the new price is 100% + 15% = 115% of the old price.
115% of 800 = 1.15 × 800 = 920 Frw. The same answer.
Worked example
A shop reduces a school bag that costs 12 000 Frw by 20%.
Way 1: 20% of 12 000 = 2 400 Frw, and 12 000 − 2 400 = 9 600 Frw.
Way 2: 100% − 20% = 80%, and 0.8 × 12 000 = 9 600 Frw.
Use this rule:
percentage change = change ÷ original amount × 100
Worked example
(increase). A P6 class grew from 40 pupils to 50 pupils.
Change = 50 − 40 = 10 pupils.
Percentage increase = 10 ÷ 40 × 100 = 25%.
Worked example
(decrease). A litre of milk fell from 500 Frw to 450 Frw.
Change = 500 − 450 = 50 Frw.
Percentage decrease = 50 ÷ 500 × 100 = 10%.
Warning
Always divide by the original amount, the one you started with. If the class goes back down from 50 pupils to 40, the change is still 10, but now the original is 50: 10 ÷ 50 × 100 = 20%. A rise of 25% followed by a fall of 20% brings you back to where you started.
Tip
Increase? Add the percentage to 100%. Decrease? Take it away from 100%. Then multiply the original amount by that new percentage.
Answers
What you learned today
Sources and credits
Quick check
A bag of rice costs 20 000 Frw. The price goes up by 10%. What is the new price?
