How do I find 15% of an amount?

Find 10% by dividing by 10, then find 5% by halving that. Add them. For 15% of 360: 10% = 36, 5% = 18, so 15% = 54.

How do I change a fraction to a percentage?

Change the fraction to an equivalent fraction with 100 on the bottom. The top number is the percentage. For 7/20 multiply by 5 to get 35/100 = 35%.

Which is bigger, 0.4 or 0.35?

0.4 is bigger. Write 0.4 as 0.40 and compare 40 hundredths with 35 hundredths.

How do I multiply a decimal by a whole number?

Either partition the whole number (4.6 x 12 = 4.6 x 10 + 4.6 x 2) or ignore the point, multiply, and put the point back so the answer has the same number of decimal places.

Year 6 decimals and percentages lesson to download as PDF

This Year 6 decimals and percentages lesson is written for pupils aged 10-11 and follows the National Curriculum. In short, it shows you how to multiply and divide decimals, find percentages of amounts and convert between fractions, decimals and percentages. Before you start, it helps to revise the four operations, order of operations and long division and fractions: add, subtract, multiply and divide, because this lesson builds on them.

Table of Contents

Year 6 decimals and percentages lesson: what you will learn

Decimals and percentages are used in money, measures and sales. In Year 6 you multiply and divide decimals and find percentages of amounts.

Starter activity

Aisha is shopping. A pair of trainers costs £45 and has a sign "20% off". She also has 3 items that cost £2.45 each. How much will she pay altogether? To answer this you need to calculate with decimals and percentages. In this chapter you will learn how to read and round decimals, multiply and divide them, and write fractions, decimals and percentages in different ways.

Place value with decimals

Definition: decimal place value

The digits after the decimal point are tenths, hundredths and thousandths. In 5.372, the 3 is worth 0.3, the 7 is worth 0.07 and the 2 is worth 0.002.

Definition: decimal

A decimal is a number with a decimal point that separates the whole part from the parts smaller than one.

Example 1

What is the value of the 4 in 8.742?

The 4 is in the hundredths column, so it is worth 0.04.

Rounding decimals

Rule: rounding

Look at the next digit. If it is 5 or more, round up. If it is 4 or less, round down.

Example 2

Round 7.846 to 1 decimal place and to the nearest whole number.

1 decimal place: the hundredths digit is 4, so 7.8. Nearest whole number: the tenths digit is 8, so 8.

Multiplying and dividing by 10, 100 and 1 000

Key fact: moving digits

When multiplying by 10, 100 or 1 000, digits move 1, 2 or 3 places to the left. When dividing, digits move to the right. So 3.45 × 100 = 345 and 62 ÷ 1 000 = 0.062.

Multiplying and dividing decimals by whole numbers

Method: multiplying a decimal by a whole number

Ignore the decimal point and multiply the digits.
Count the decimal places in the original number.
Put the decimal point back so the answer has the same number of decimal places.

Example 3

Work out 2.4 × 6.

24 × 6 = 144. 2.4 has 1 decimal place, so the answer is 14.4.

Example 4

Work out 7.5 ÷ 5.

75 ÷ 5 = 15. Two digits after the point become one decimal place: 1.5.

Watch out

Do not forget the decimal point. Estimate first: 2.4 × 6 is a bit more than 12, so 14.4 makes sense, but 1.44 does not.

Fractions, decimals and percentages

Key fact: equivalents

\(\frac{1}{2}\) = 0.5 = 50%. \(\frac{1}{4}\) = 0.25 = 25%. \(\frac{3}{4}\) = 0.75 = 75%. \(\frac{1}{10}\) = 0.1 = 10%. \(\frac{1}{5}\) = 0.2 = 20%.

Example 5

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

\(\frac{7}{20}=\frac{35}{100}\), which is 0.35 or 35%.

Percentages of amounts

Method: finding a percentage of an amount

Find 10% by dividing by 10, and 1% by dividing by 100.
Build up the percentage you need.
Add or subtract as needed.

Example 6

Find 15% of £80.

10% = £8 and 5% = £4. So 15% = £12.

Example 7

A coat costing £60 has 35% off. Find the sale price.

10% = £6, so 30% = £18 and 5% = £3. 35% = £21. The sale price is £60 − £21 = £39.

More about decimals and percentages

Method: converting a fraction to a decimal

Divide the numerator by the denominator.
Or make an equivalent fraction with a denominator of 10, 100 or 1 000.
Write the numerator as a decimal with the right number of places.
Multiply by 100 to find the percentage.

Example 8

Write \(\frac{5}{8}\) as a decimal and as a percentage.

Divide 5 by 8: 5 ÷ 8 = 0.625. To find the percentage, multiply by 100, so 0.625 × 100 = 62.5%.

Example 9

Work out 4.6 × 12.

First estimate: 5 × 10 = 50. Now calculate 46 × 12 = 46 × 10 + 46 × 2 = 460 + 92 = 552. The number 4.6 has one decimal place, so the answer has one decimal place: 55.2. This is close to the estimate.

Example 10

A pupil scores 21 out of 25 in a test. What is the score as a percentage?

Make an equivalent fraction out of 100. 25 × 4 = 100, so multiply the top by 4 as well: 21 × 4 = 84. The score is \(\frac{84}{100}\), which is 84%.

Example 11

A bike costs £84. In a sale it is reduced by 25%. What is the sale price?

25% is the same as \(\frac{1}{4}\), and £84 ÷ 4 = £21. The reduction is £21. The sale price is £84 − £21 = £63. You could also find 75% directly: 75% of £84 = 3 × £21 = £63.

Watch out: common mistakes

A longer decimal is not always bigger: 0.45 is smaller than 0.5 because 4 tenths is less than 5 tenths. Be careful with zeros as place holders, so that "five thousandths" is 0.005 and not 0.05. Also, 7% is 0.07 and not 0.7.

Percentages you can find in your head

50% is half, 25% is a quarter, 10% is one tenth and 1% is one hundredth. To find 5%, halve 10%. To find 15%, add 10% and 5%. To find 75%, find 25% and multiply by 3. These facts make most percentage questions quick.

Did you know?

The word "percent" comes from the Latin "per centum", which means "by the hundred". The percent sign % developed from a way of writing "per cento" in Italian merchants\' notebooks about 600 years ago. Today it is used in shops, banks and weather forecasts all over the world.

Otto’s tip

Percentages are just fractions out of 100. Find 10% first, and build every other percentage from it!

How to use this Year 6 decimals and percentages lesson

First, read the key points so that you know where the Year 6 decimals and 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 decimals and 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 decimals and 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 6 decimals and 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.