Year 6: Fractions, decimals and percentages
Part of the Year 6 sats maths revision chapter. Chapter overview · whole chapter on one page
Fractions, decimals and percentages
Fractions, decimals and percentages are three ways of writing the same amount. A fraction has a top and a bottom number. To add or subtract fractions, first make the bottom numbers the same. Then add or subtract the top numbers only.
A decimal uses a point. Each place after the point is a tenth, then a hundredth, then a thousandth. Multiplying by 10, 100 or 1000 moves each digit to the left. Dividing moves them to the right.
Per cent means out of 100. To find 35 per cent of an amount, find 1 per cent (divide by 100), then multiply by 35.
Key ideas
- Simplify by dividing the top and bottom by their highest common factor.
- Add or subtract fractions by making the bottom numbers the same first.
- Multiply a decimal by 100 by moving each digit two places to the left.
- Per cent means out of 100: 25 per cent is 25/100, which is 1/4.
Key words. A simplified fraction is in its lowest terms. A mixed number has a whole part and a fraction part. An improper fraction has a top number that is bigger than its bottom number.
Method. Divide the top and the bottom by the highest common factor.
- Find the highest common factor of the top and bottom. The biggest number that divides into both is the one to divide by.factors of 18 and 24: highest common factor = 6
- Divide the top and the bottom by 6. Dividing both by the same number keeps the fraction the same size.18 ÷ 6 = 3, and 24 ÷ 6 = 4
- Write the answer. This fraction cannot be simplified any more.3/4
Check. 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so the fraction keeps the same size. ✓
Watch out. Divide by the highest common factor, or by any common factor and then again, until nothing else divides.
Key words. A simplified fraction is in its lowest terms. A mixed number has a whole part and a fraction part. An improper fraction has a top number that is bigger than its bottom number.
Method. Make the bottom numbers the same, then add or subtract the top numbers.
- Find a common bottom number. The lowest common multiple of 4 and 6 is 12, so both fractions can use 12 as the bottom number.4 and 6: lowest common multiple = 12
- Change both fractions to have the same bottom number. Multiply the top and bottom of each fraction by the same number.3/4 = 9/12, and 1/6 = 2/12
- Add the top numbers. The bottom number stays the same.9 + 2 = 11, so 11/12
- Simplify the answer. Divide the top and bottom by the same number to get the lowest terms.11/12 is already in its simplest form, so 11/12
Check. Both forms are the same amount: 11/12 is equal to 11/12. ✓
Watch out. Only add the top numbers. The bottom number stays the same when the fractions are added.
Key words. Per cent means out of 100. So 35 per cent means 35 out of 100, which is 0.35 as a decimal and 35/100 as a fraction.
Method. Find 1 per cent of the amount, then multiply it by the number of per cent.
- Write the per cent and the amount. Per cent means out of 100.35 per cent of £80.00
- Find 1 per cent. Per cent means out of 100, so divide the amount by 100.£80.00 ÷ 100 = £0.80
- Multiply by 35. 35 per cent is 35 lots of 1 per cent.£0.80 × 35 = £28.00
Check. Check: £28.00 ÷ £80.00 = 0.35, which is 35 out of 100. ✓
Watch out. Divide by 100 first, then multiply. Do not multiply by 100.
Watch out
Common mistake: adding the bottom numbers when you add fractions. 1/4 + 1/4 is 2/4, not 2/8. The bottom number only changes when you make the fractions the same size.
Exercise 13C Timed set: fractions, decimals and percentages (about 12 minutes)
Non-calculatorKey words. A simplified fraction is in its lowest terms. A mixed number has a whole part and a fraction part. An improper fraction has a top number that is bigger than its bottom number.
Method. Divide the top and the bottom by the highest common factor.
- Find the highest common factor of the top and bottom. The biggest number that divides into both is the one to divide by.factors of 18 and 24: highest common factor = 6
- Divide the top and the bottom by 6. Dividing both by the same number keeps the fraction the same size.18 ÷ 6 = 3, and 24 ÷ 6 = 4
- Write the answer. This fraction cannot be simplified any more.3/4
Check. 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so the fraction keeps the same size. ✓
Watch out. Divide by the highest common factor, or by any common factor and then again, until nothing else divides.
Key words. A simplified fraction is in its lowest terms. A mixed number has a whole part and a fraction part. An improper fraction has a top number that is bigger than its bottom number.
Method. Make the bottom numbers the same, then add or subtract the top numbers.
- Find a common bottom number. The lowest common multiple of 4 and 6 is 12, so both fractions can use 12 as the bottom number.4 and 6: lowest common multiple = 12
- Change both fractions to have the same bottom number. Multiply the top and bottom of each fraction by the same number.3/4 = 9/12, and 1/6 = 2/12
- Add the top numbers. The bottom number stays the same.9 + 2 = 11, so 11/12
- Simplify the answer. Divide the top and bottom by the same number to get the lowest terms.11/12 is already in its simplest form, so 11/12
Check. Both forms are the same amount: 11/12 is equal to 11/12. ✓
Watch out. Only add the top numbers. The bottom number stays the same when the fractions are added.
Key words. A simplified fraction is in its lowest terms. A mixed number has a whole part and a fraction part. An improper fraction has a top number that is bigger than its bottom number.
Method. Make the bottom numbers the same, then add or subtract the top numbers.
- Find a common bottom number. The lowest common multiple of 6 and 4 is 12, so both fractions can use 12 as the bottom number.6 and 4: lowest common multiple = 12
- Change both fractions to have the same bottom number. Multiply the top and bottom of each fraction by the same number.5/6 = 10/12, and 1/4 = 3/12
- Subtract the top numbers. The bottom number stays the same.10 − 3 = 7, so 7/12
- Simplify the answer. Divide the top and bottom by the same number to get the lowest terms.7/12 is already in its simplest form, so 7/12
Check. Both forms are the same amount: 7/12 is equal to 7/12. ✓
Watch out. Only add the top numbers. The bottom number stays the same when the fractions are added.
Key words. A simplified fraction is in its lowest terms. A mixed number has a whole part and a fraction part. An improper fraction has a top number that is bigger than its bottom number.
Method. Multiply the whole number by the bottom number, add the top number, then keep the same bottom number.
- Multiply the whole number by the bottom number. Each whole has the same number of parts as the bottom number.3 × 5 = 15
- Add the top number. Add the parts that are left over.15 + 2 = 17
- Write it over the bottom number. The bottom number stays the same.17/5
Check. 17 ÷ 5 = 3 with 2 left over, so the answer is right. ✓
Watch out. Do not add the whole number to the top number. Multiply it by the bottom number first.
Key words. A simplified fraction is in its lowest terms. A mixed number has a whole part and a fraction part. An improper fraction has a top number that is bigger than its bottom number.
Method. Divide the top number by the bottom number. The answer is the whole part, and the remainder goes over the bottom number.
- Divide the top number by the bottom number. The whole number of times it goes in is the whole part.23 ÷ 4 = 5 remainder 3
- Write the remainder over the bottom number. The remainder is the top number of the fraction part.the fraction part is 3/4
- Write the answer. 5 3/4
Check. 5 whole and 3/4 is 23/4, which is the same as 23/4. ✓
Watch out. The remainder goes on top of the fraction. The bottom number stays the same.
Key words. A simplified fraction is in its lowest terms. A mixed number has a whole part and a fraction part. An improper fraction has a top number that is bigger than its bottom number.
Method. Divide by the bottom number to find one part, then multiply by the top number.
- Find one part. Divide 96 into 8 equal parts.96 ÷ 8 = 12
- Take 3 parts. The fraction is 3/8, so we need 3 of these parts.12 × 3 = 36
Check. 36 is 3 out of 8 equal parts of 96. ✓
Watch out. Divide by the bottom number first, then multiply by the top number.
Key words. A simplified fraction is in its lowest terms. A mixed number has a whole part and a fraction part. An improper fraction has a top number that is bigger than its bottom number.
Method. Write both fractions with the same bottom number, then compare the top numbers.
- Find a common bottom number. The lowest common multiple of 8 and 12 is 24.24
- Change both fractions. Use the same bottom number, so only the top numbers need comparing.5/8 = 15/24, and 7/12 = 14/24
- Compare the top numbers. The bigger top number is the bigger fraction.15 is bigger than 14
- Write the answer. 5/8
Check. Both fractions are now out of 24, so comparing 15 with 14 is a fair test. ✓
Watch out. A bigger bottom number does not mean a bigger fraction. Compare the fractions with the same bottom number.
Key words. A decimal uses a point to show tenths, hundredths and thousandths. When you multiply by 10, 100 or 1000, every digit moves left. When you divide, every digit moves right.
Method. Line up the decimal points, add the numbers as whole numbers, then put the decimal point back.
- Line up the decimal points. Write each number with 2 decimal places, so the digits in each column match.0.4 + 0.27
- Work with the whole numbers. Ignore the points for now and work with whole numbers.40 + 27
- Add the ones column. Add the two digits, and the carried number if there is one.0 + 7 = 7, so write 7
- Add the tens column. Add the two digits, and the carried number if there is one.4 + 2 = 6, so write 6
- Put the decimal point back. Put the point in the same place as the decimal points you lined up.0.67
Check. 0.67 − 0.27 = 0.4, so the sum is right. ✓
Watch out. Line up the decimal points first. Do not line up the last digits.
Key words. A decimal uses a point to show tenths, hundredths and thousandths. When you multiply by 10, 100 or 1000, every digit moves left. When you divide, every digit moves right.
Method. Line up the decimal points, subtract the numbers as whole numbers, then put the decimal point back.
- Line up the decimal points. Write each number with 2 decimal places, so the digits in each column match.3.6 − 1.85
- Work with the whole numbers. Ignore the points for now and work with whole numbers.360 − 185
- Subtract the ones column. Take the bottom digit from the top digit. If the top digit is too small, exchange 1 from the next column.0 is too small for 5, so exchange 1 ten: 10 − 5 = 5
- Subtract the tens column. Take the bottom digit from the top digit. If the top digit is too small, exchange 1 from the next column.6 - 1 (lent) is too small for 8, so exchange 1 ten: 15 − 8 = 7
- Subtract the hundreds column. Take the bottom digit from the top digit. If the top digit is too small, exchange 1 from the next column.3 - 1 (lent) − 1 = 1
- Put the decimal point back. Put the point in the same place as the decimal points you lined up.1.75
Check. 1.75 + 1.85 = 3.6, so the difference is right. ✓
Watch out. Line up the decimal points first. Do not line up the last digits.
Key words. A decimal uses a point to show tenths, hundredths and thousandths. When you multiply by 10, 100 or 1000, every digit moves left. When you divide, every digit moves right.
Method. Multiplying by 100 moves each digit 2 places left. Dividing moves them the other way.
- Count the places: 100 is 10 to the power 2. Each factor of 10 moves every digit 2 places left.4.07 × 100
- Move the decimal point. The point moves 2 places left, and empty places are filled with 0.4.07 × 100 = 407
Check. 407 ÷ 100 is 4.07, so the answer is right. ✓
Watch out. Move the digits, not the point. The decimal point stays where it is in the working, and the digits move instead.
Key words. A decimal uses a point to show tenths, hundredths and thousandths. When you multiply by 10, 100 or 1000, every digit moves left. When you divide, every digit moves right.
Method. Multiplying by 1000 moves each digit 3 places left. Dividing moves them the other way.
- Count the places: 1000 is 10 to the power 3. Each factor of 10 moves every digit 3 places left.0.056 × 1000
- Move the decimal point. The point moves 3 places left, and empty places are filled with 0.0.056 × 1000 = 56
Check. 56 ÷ 1000 is 0.056, so the answer is right. ✓
Watch out. Move the digits, not the point. The decimal point stays where it is in the working, and the digits move instead.
Key words. Per cent means out of 100. So 35 per cent means 35 out of 100, which is 0.35 as a decimal and 35/100 as a fraction.
Method. Find 1 per cent of the amount, then multiply it by the number of per cent.
- Write the per cent and the amount. Per cent means out of 100.25 per cent of £40.00
- Find 1 per cent. Per cent means out of 100, so divide the amount by 100.£40.00 ÷ 100 = £0.40
- Multiply by 25. 25 per cent is 25 lots of 1 per cent.£0.40 × 25 = £10.00
Check. Check: £10.00 ÷ £40.00 = 0.25, which is 25 out of 100. ✓
Watch out. Divide by 100 first, then multiply. Do not multiply by 100.
Key words. A simplified fraction is in its lowest terms. A mixed number has a whole part and a fraction part. An improper fraction has a top number that is bigger than its bottom number.
Method. Dividing by a whole number multiplies the bottom number, and keeps the top number.
- Multiply the bottom number by the whole number. Sharing a fraction into 2 equal parts makes each part 2 times smaller, so the bottom number gets 2 times bigger.4 × 2 = 8
- Keep the top number and simplify. The top number stays the same, then simplify if you can.3/8 = 3/8
Check. 3/8 × 2 = 3/4, so the division is right. ✓
Watch out. Multiply only the top number when you multiply by a whole number. Only the bottom number changes when you divide.
Key words. A decimal uses a point to show tenths, hundredths and thousandths. When you multiply by 10, 100 or 1000, every digit moves left. When you divide, every digit moves right.
Method. Look at the digit after the place you are rounding to, then decide whether to round up.
- Find the digit after the 2 decimal places. That digit decides whether to round up or down.4.678: the digit is 8
- Decide. 8 is 5 or more, so round up.round up
- Write the answer. Keep 2 decimal places.4.68
Check. 4.68 is the closest number to 4.678 with 2 decimal places. ✓
Watch out. Round the number, not the digits. Look only at the digit just after the place you are rounding to.
Key words. Per cent means out of 100. So 35 per cent means 35 out of 100, which is 0.35 as a decimal and 35/100 as a fraction.
Method. Multiply the decimal by 100 to change it to per cent.
- Multiply by 100. Per cent means out of 100, so the number of per cent is the decimal times 100.0.6 × 100
- Move the decimal point two places to the right. Multiplying by 100 moves every digit two places to the left, so the point moves right.60 per cent
Check. 60/100 = 0.6, so the answer is right. ✓
Watch out. 0.5 is 50 per cent, not 5 per cent. Multiply by 100, not by 10.
Key words. Per cent means out of 100. So 35 per cent means 35 out of 100, which is 0.35 as a decimal and 35/100 as a fraction.
Method. Divide the top number by the bottom number.
- Write the division. A fraction line means divide the top by the bottom.3 ÷ 8
- Do the division. Add a decimal point and zeros until the division ends.3 ÷ 8 = 0.375
Check. 0.375 × 8 = 3, so the decimal is right. ✓
Watch out. Keep adding zeros after the decimal point until the division ends.