Percentage of a quantity

The idea

y% of a value z is y/100 × z, found by multiplying by the fraction or its decimal; the part is proportional to the whole, y : 100 :: part : whole.

How much sugar in 120 g?

Madhu ate 120 g of biscuits. The biscuits are 25% sugar. That means 25 g of sugar in every 100 g of biscuits.

How much sugar did Madhu eat in his 120 g?

• 25 g
• 30 g
• 3000 g

Percent bar above a quantity bar

The top bar is the percentage, from 0% to 100%. The bottom bar is the whole quantity. The same part is shaded on both bars. Set the percentage in all three cases.

The part is proportional to the whole

y% of a value z is y/100 × z, found by multiplying by the fraction or its decimal; the part is proportional to the whole, y : 100 :: part : whole.

Madhu's sugar is the blank in 25 : 100 :: s : 120 So s = 25/100 × 120 = 30 Madhu ate 30 g of sugar.

Three ways to find 80% of 75: 80/100 × 75 = 4/5 × 75 = 60 0.8 × 75 = 60 75 × 80/100 = 60 The answer is 60 each way.

Notes

y% of a value z is y/100 × z, found by multiplying by the fraction or its decimal; the part is proportional to the whole, y : 100 :: part : whole.

Check yourself

What is 30% of 150 g?

Answer: 45 g

30/100 × 150 = 45, so 30% of 150 g is 45 g.

A bucket holds 20 litres. It is 35% full. How many litres of water are in it?

Answer: 7 litres

35/100 × 20 = 7, so there are 7 litres of water.

A shop has 250 kg of rice. 12% of it is sold on Monday. How many kg are sold?

Answer: 30 kg

0.12 × 250 = 30, so 30 kg are sold.

Which of these is not the same as 25% of 40?

• 25 × 40 — correct. Right! 25 × 40 = 1000, but 25% of 40 is 10. A percentage is out of 100, so 25/100 × 40.
• 1/4 × 40. 25% = 25/100 = 1/4, so a quarter of 40 is the same as 25% of 40. Both are 10.
• 0.25 × 40. 25% = 0.25, so this is the same as 25% of 40. Both are 10.
• 25/100 × 40. This is 25% of 40 written as a fraction. It is 10.