Thorp Academy

Outcomes focused, child centred

Numeracy

FOCUS OF THE TERM: PERCENTAGES


One number as a Percentage of another

1)Write as a fraction

2)Multiply by 100

e.g. Jamie scores 32 out of 80 in his test. What is his percentage score?

32/80x 100 = 40%

e.g. 23 pupils out of a class of 32 enjoyed reading Fever Pitch. What percentage of the class enjoyed the book?

23/32x 100 = 72%

Comparisons using Percentages

1)Convert both numbers to percentages

e.g. Sally scored 17 shots out of 25. Jamie scored 29 shots out of 40. Who is the better shooter?

Sally

17/25x 100 = 68%

Jamie

29/40x 100 = 72.5% Jamie is the better shooter

Finding a Percentage Change

1)Find the actual change

2)change/original×100

e.g. At the start of the year Emma can complete 52 sit ups. At the end of the year she can complete 80 sit ups. Calculate the percentage change?

80 – 52 = 28

28/52×100 = 53.8% increase

Finding a Percentage

1)Change the percentage to a decimal

2)Multiply the amount by the decimal

e.g. Find 17% of £320

17% becomes 0.17

320 x 0.17 = £54.40

e.g. Find 39% of $480

39% becomes 0.39

480 x 0.39 = $187.20

Completing a Percentage Change

1)Add or subtract the percentage to 100

2)Change the percentage to a decimal

3)Multiply the amount by the decimal

e.g. A country receives £320 million in revenue from tourism. This increases by 19%. What is the new revenue?

100%+19% = 119%

119% becomes 1.19

320 x 1.19 = £380.8 million

e.g. A city has a population of 500000. The population decreases by 7%. What is the new population

100%-7% = 93%

93% becomes 0.93

500000 x 0.93 = 465000

Reverse Percentages

1)Calculate the percentage

2)Change the percentage to a decimal

3)Divide the amount by the decimal

e.g. In 1900 in Blaydon 3,500 people worked in a factory or manufacturing. This was a 85% increase from 1850. How many people worked in a factory of manufacturing in 1850?

100% + 85% = 185%

185% becomes 1.85

3500 ÷ 1.85 = 1892 people

e.g. After a chemical reaction the amount of metal remaining was 320g. This was a 30% reduction from the start of the experiment. How much metal was there before the experiment?

100% - 30% = 70%

70% becomes 0.7

320 ÷ 0.7 = 457g