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Percent as out of one hundred: fractions, decimals and percents
Discover Mathematics P6: Term 2, Unit 10, Lessons 7–9
GoalExplain percent as “out of 100” and move between fractions, decimals and percents.
New words
percent · a ratio that compares a number with 100; the sign is %per cent · “for each hundred”equivalent · different ways of writing the same amount
Explanation
Percent means “out of 100”. A hundred squares with 25 coloured is 25 out of 100, which is 25/100, 0.25 and 25%. These are four names for the same amount. To change a fraction into a percent, find an equivalent fraction whose denominator is 100. For 1/4, multiply top and bottom by 25 to get 25/100 = 25%. For 3/20, multiply by 5 to get 15/100 = 15%. For 7/25, multiply by 4 to get 28/100 = 28%. This works when the denominator divides 100: 2, 4, 5, 10, 20, 25 and 50. To change a percent into a decimal, divide by 100: 35% = 0.35.
| Fraction | Out of 100 | Decimal | Percent |
|---|---|---|---|
| 1/2 | 50/100 | 0.5 | 50% |
| 1/4 | 25/100 | 0.25 | 25% |
| 3/4 | 75/100 | 0.75 | 75% |
| 1/5 | 20/100 | 0.2 | 20% |
| 7/20 | 35/100 | 0.35 | 35% |
| 2/25 | 8/100 | 0.08 | 8% |
Worked examples
A tape of 100 equal parts has 35 coloured. The coloured part is 35 out of 100: 35/100 = 0.35 = 35%. The part that is not coloured is 100 − 35 = 65, so it is 65%. The two parts always make 100%.
Write 3/5 as a percent. The denominator 5 goes into 100 twenty times, so multiply top and bottom by 20: 3/5 = 60/100 = 60%.
Write 0.4 as a percent: 0.4 = 0.40 = 40/100 = 40%. Write 90% as a fraction: 90/100 = 9/10.
Class activity
Percents around us. Look for three percent signs at home or in the street (a sale sign, a battery, a food label). Write what each percent means as a fraction out of 100.
Practice
1
Write 1/5 as a percent.
1/5 = 20/100 = 20%.
2
Write 9/20 as a decimal and as a percent.
9/20 = 45/100 = 0.45 = 45%.
3
60 squares out of 100 are coloured. Write the fraction, the decimal and the percent.
60/100 = 0.6 = 60%.
4
Write 12% as a fraction with denominator 100 and as a decimal.
12/100 = 0.12.
5
In a class 40% of the children walk to school. What percent do not walk?
100% − 40% = 60%.