Percentages of one value combine

The idea

Percentages of the same value combine like the fractions they are: p% of y plus q% of y is (p + q)% of y, and a percentage twice as large gives a part twice as large.

20% of y plus 5% of y

Take any value and call it y. 20% of it is 20 parts out of 100. 5% of it is 5 parts out of 100.

What is 20% of y + 5% of y?

• 25% of y
• 100% of y
• 15% of y

Add the parts on a bar

Every bar is the whole value, 200. Set the percentages and compare the bars. The last bar of each case is the answer to check.

Percentages of one value add up

Percentages of the same value combine like the fractions they are: p% of y plus q% of y is (p + q)% of y, and a percentage twice as large gives a part twice as large.

Adding the parts: 20/100 × y + 5/100 × y = 25/100 × y 20 parts out of 100 plus 5 parts out of 100 is 25 parts out of 100.

Doubling: 20% is twice 10%, because 20 parts out of 100 is twice 10 parts out of 100. So 20% of a value is always twice 10% of the same value. For 200, 10% is 20 and 20% is 40.

Notes

Percentages of the same value combine like the fractions they are: p% of y plus q% of y is (p + q)% of y, and a percentage twice as large gives a part twice as large.

Check yourself

10% of a number is 35. What is 20% of the same number?

Answer: 70

20% is twice 10%, so the part is twice as large: 35 × 2 = 70.

Of 200 kg of fruit, 30% are apples and 45% are mangoes. How many kg of apples and mangoes are there together?

Answer: 150 kg

30% + 45% = 75%, and 75% of 200 = 150. Or: 60 kg of apples + 90 kg of mangoes = 150 kg.

40% of a length is 36 m. What is 20% of the same length?

Answer: 18 m

20% is half of 40%, so its part is half of 36 m: 36 ÷ 2 = 18 m.

Which of these is not equal to 40% of y?

• 10% of y + 20% of y — correct. Right! 10% + 20% = 30%, not 40%.
• 25% of y + 15% of y. 25% + 15% = 40%, so this is 40% of y.
• 2 × (20% of y). Twice 20% is 40%, so this is 40% of y.
• 4 × (10% of y). Four times 10% is 40%, so this is 40% of y.