How do I change 0.35 to a percentage?

Multiply by 100, which moves the digits two places to the left. 0.35 = 35%.

How do I change 7/20 to a percentage?

Multiply the top and bottom by 5 to make 35/100. That is 35%.

Year 5 percentages lesson to download as PDF

Q: What does per cent mean?

Per cent means out of 100. For example 30% means 30 out of 100.

This Year 5 percentages lesson is written for pupils aged 9-10 and follows the National Curriculum. In short, it shows you how to write percentages as fractions and decimals and use equivalents of common fractions. Before you start, it helps to revise adding, subtracting and multiplying fractions and decimals and thousandths, because this lesson builds on them.

Table of Contents

Year 5 percentages lesson: what you will learn

Hello, I am Otto! Percentages are everywhere. Shops put them on sale signs, phones show them on the battery icon and sports teams use them to describe results. The word per cent means out of one hundred, and it lets us compare amounts that are measured out of different totals. In this chapter you link percentages, fractions and decimals and find simple percentages of amounts.

Starter activity

Look at a phone, tablet or laptop battery. It shows a percentage such as 60%. This means 60 out of every 100 parts of the battery are full. If the battery is cut into 100 tiny pieces, 60 of them are filled. How many pieces are empty? Think about this as you read: the full part and the empty part always add to 100%.

What does per cent mean?

Definition: per cent

Per cent means "out of one hundred". We write it with the symbol %. So 37% means 37 out of 100, which is \(\frac{37}{100}\) or 0.37. The whole thing is always 100%.

The 10 by 10 grid is one whole made of 100 squares. 37 squares are shaded, so 37% of the grid is shaded and 63% is not shaded.

Example 1

A hundred-square has 23 squares shaded red. Write the shaded part as a percentage, a fraction and a decimal.

23 out of 100 squares are shaded. As a percentage that is 23%, as a fraction it is \(\frac{23}{100}\) and as a decimal it is 0.23.

Percentages, fractions and decimals

Rule: converting

To change a percentage to a fraction, write it over 100 and simplify. To change a percentage to a decimal, divide by 100 (move the digits two places to the right). To change a decimal to a percentage, multiply by 100 (move the digits two places to the left).

Percentage	Fraction	Decimal
50%	\(\frac{1}{2}\)	0.5
25%	\(\frac{1}{4}\)	0.25
75%	\(\frac{3}{4}\)	0.75
10%	\(\frac{1}{10}\)	0.1
20%	\(\frac{1}{5}\)	0.2
40%	\(\frac{2}{5}\)	0.4
80%	\(\frac{4}{5}\)	0.8
1%	\(\frac{1}{100}\)	0.01

Example 2

Write 45% as a fraction in simplest form and as a decimal.

45% = \(\frac{45}{100}\). Divide top and bottom by 5 to get \(\frac{9}{20}\). As a decimal, 45 ÷ 100 = 0.45.

Method: fraction to percentage

Find a number that you can multiply the denominator by to make 100.
Multiply the numerator by the same number.
The new numerator is the percentage.

Example 3

Write \(\frac{7}{20}\) as a percentage.

20 × 5 = 100, so multiply the top by 5 too: 7 × 5 = 35. So \(\frac{7}{20}\) = \(\frac{35}{100}\) = 35%.

Watch out

A percentage is not always a whole number, but at Year 5 you work with whole percentages. Do not forget that 5% is 0.05, not 0.5. The decimal 0.5 is 50%. Check by asking: is 5% a small part or half?

Finding a percentage of an amount

Key fact: simple percentages

50% is one half, so divide by 2. 25% is one quarter, so divide by 4. 10% is one tenth, so divide by 10. 20% is one fifth, so divide by 5. 1% is one hundredth, so divide by 100.

Method: percentage of an amount using 10%

Find 10% by dividing the amount by 10.
Multiply 10% by the number of tens in the percentage. For example 30% is 3 × 10%.
For 5% halve the 10% value, for 1% divide the 10% value by 10.

Example 4

Find 30% of £60.

10% of £60 = £60 ÷ 10 = £6. 30% is three times that: 3 × £6 = £18.

Example 5

A coat costs £80. In a sale it is reduced by 25%. How much is the sale price?

25% is one quarter: £80 ÷ 4 = £20. That is the amount taken off. Sale price = £80 − £20 = £60.

Comparing and ordering

Method: ordering fractions, decimals and percentages

Change every number to a percentage (or every number to a decimal).
Compare the percentages as you would compare whole numbers.
Write the original numbers in order.

Example 6

Put in order, smallest first: \(\frac{3}{5}\), 0.58, 62%.

\(\frac{3}{5}\) = \(\frac{60}{100}\) = 60%. 0.58 = 58%. 62% stays the same. The order is 58%, 60%, 62%, so 0.58, \(\frac{3}{5}\), 62%.

Did you know?

The word "percent" comes from the Latin per centum, meaning "by the hundred". The Romans already used fractions with denominator 100 when they collected taxes. Today you see percentages in weather reports, on food labels and in sports statistics: a basketball player with 75% free throws scores 3 out of every 4 tries.

Otto's tip

Always check that your answer makes sense. 50% is half, so 50% of 80 must be 40. If your answer for 10% of an amount is bigger than the amount, something has gone wrong!

How to use this Year 5 percentages lesson

First, read the key points so that you know where the Year 5 percentages lesson is going. Then work through each definition and worked example, and cover the solution before you read it. After that, practise with the percentages worksheet and check every question with the worksheet answers. When you feel ready, test yourself with the multiple choice questions or the quick quiz. Finally, sit the percentages test and mark it with the test answers.

Also, the starters are a good warm-up, so you can keep the key facts fresh. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday. In short, this Year 5 percentages lesson gives you everything you need for the chapter.

To sum up, regular practice works better than one long session. For instance, ten minutes a day is often enough. Besides, mistakes are useful, because they show what to revise next. Then, once a method feels easy, try a harder question. As a result, you build confidence step by step.