 # Fractions, decimals and percentages

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Fractions, decimals and percentages
To be able to convert fraction to: Decimals and percentages Must – be able to convert a percentage to and from a decimal. Should – be able to convert a fraction into a percentage. Could – be able to convert a percentage into a fraction and cancel it down.

Percentages A percentage is just a special type of fraction. 1%
1 part per hundred means 100 1 0.01 or = Explain the meaning of 1% with reference to fractions and decimals. We can work out 1% of something by dividing it by 100.

Percentages A percentage is just a special type of fraction. 25%
25 parts per hundred means 100 25 4 1 0.25 or = = Explain the meaning of 25% with reference to fractions and decimals. We can work out 25% of something by dividing it by 4.

Percentages A percentage is just a special type of fraction. 100%
100 parts per hundred means 100 1 or = Explain that 100% means 1 whole one or ‘all of it’. Discuss the meaning of 100% in different contexts. For example, ‘I’m 100% sure’ or ‘100% extra free’. Ask pupils what 200% means or 300%.

Writing percentages as fractions
‘Per cent’ means ‘out of 100’. To write a percentage as a fraction we write it over a hundred. For example, 23 46 100 46 100 = 23 50 46% = Cancelling: 50 9 180 100 180 100 = 9 5 = 1 4 5 180% = Cancelling: Explain that we can easily write a whole number percentage as a fraction over 100. However, if there is a common factor between the numerator and the denominator, we must cancel the fraction down to its lowest terms. If the percentage is not a whole number, as in the last example, we must find an equivalent fraction with a whole number numerator and denominator. We can then cancel if necessary. 5 3 7.5 100 = 15 200 15 200 = 3 40 7.5% = Cancelling: 40

Percentages into fractions
What is 26% as a fraction?

Percentages into fractions
What is 26% as a fraction? 26 = 13

Percentages into fractions
What is 162% as a fraction? 162 = 81 = 1 31

Writing percentages as decimals
We can write percentages as decimals by dividing by 100. For example, 46 100 46% = = 46 ÷ 100 = 0.46 7 100 7% = = 7 ÷ 100 = 0.07 Explain that to convert a percentage to a decimal we simply divide the percentage by 100. 130 100 130% = = 130 ÷ 100 = 1.3 0.2 100 0.2% = = 0.2 ÷ 100 = 0.002

Percentages into decimals
What is 37% as a decimal? Divide by 100 Move Decimal to the left 2 times Top Tip 37. .37 =

Percentages into decimals
What is 95% as a decimal?

Percentages into decimals
What is 113% as a decimal?

Writing fractions as percentages
To write a fraction as a percentage, we can find an equivalent fraction with a denominator of 100. For example, × 5 = 100 85 = 17 20 85 and 85% 100 × 5 If the denominator of the fraction is a factor of 100 we can make an equivalent fraction over a hundred. Remind pupils that as long as we multiply the numerator and the denominator of a fraction by the same number it will have the same value. Talk through both examples. For the second example, we write the fraction as an improper fraction first. An alternative would be to recognise that 1 = 100% and then convert 7/25 to 28/100. Adding 100% and 28% gives 128%. × 4 = 7 25 28 = 100 28 and 28% 100 × 4

Writing decimals as percentages
To write a decimal as a percentage you can multiply it by 100%. For example, 0.08 = 0.08 × 100% 1.375 = 1.375 × 100% What is 0.47 as a percentage? 0.47 means 47 hundredths, so 0.47 is equivalent to 47%. We can perform this conversion by multiplying by 100%. Remember 100% means the same as ‘1 whole’ or ‘all of it’. So multiplying by 100% is the same as multiplying by 1. The amount remains unchanged. Reveal the examples on the board. = 8% = 137.5%

Writing fractions as percentages
To write a fraction as a percentage, we can find an equivalent fraction with a denominator of 100. For example, × 5 = 100 55 = 11 20 55 and 55% 100 × 5 If the denominator of the fraction is a factor of 100 we can make an equivalent fraction over a hundred. Remind pupils that as long as we multiply the numerator and the denominator of a fraction by the same number it will have the same value. Talk through both examples. For the second example, we write the fraction as an improper fraction first. An alternative would be to recognise that 1 = 100% and then convert 7/25 to 28/100. Adding 100% and 28% gives 128%. × 10 = 6 10 60 = 100 60 and 60% 100 × 10

Converting equivalents
Let’s fill in the gaps in this table …