Year 5: Adding and subtracting mixed numbers
Part of the Year 5 equivalent fractions and mixed numbers chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Adding and subtracting mixed numbers
To add mixed numbers, add the whole numbers first, then add the fractions. Put the answers together. 2
Crossing a whole. If the fractions add to 1 or more, you must carry a whole. 2
Subtracting. If the fraction of the first number is big enough, subtract the wholes and the fractions separately: 4
Key ideas
- Add: add the wholes, add the fractions (same denominator first), then put them together.
- If the fractions add to 1 or more, change the fraction part to a whole and a fraction and add the whole.
- Subtract: if the first fraction is big enough, subtract wholes and fractions separately.
- If the fraction you take away is bigger, change both numbers to improper fractions, subtract, then change back to a mixed number.
- Always simplify the fraction at the end.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Check the denominators. To add fractions, the parts must be the same size.Both denominators are 5, so we can add straight away.
- Add the whole numbers. Add the wholes first, then deal with the fractions.2 + 1 = 3
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
1 5 2 5 1 + 2 5 3 5 - Write the answer. 2
1 5 2 5 3 5
Check. Take away: 3
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Check the denominators. To add fractions, the parts must be the same size.Both denominators are 4, so we can add straight away.
- Add the whole numbers. Add the wholes first, then deal with the fractions.2 + 1 = 3
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
3 4 3 4 3 + 3 4 6 4 - The fraction part is 1 or more, so change it to a whole number and a fraction.
6 4 6 4 2 4
3 + 12 4 2 4 - Simplify the fraction part. 2 and 4 can both be divided by 2.
2 4 2 ÷ 2 4 ÷ 2 1 2
So the answer is 41 2 - Write the answer. 2
3 4 3 4 1 2
Check. Take away: 4
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 4, so 4 will do.4 ÷ 2 = 2, so 2 goes into 4
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.3
1 2 1 2 1 × 2 2 × 2 2 4 - Add the whole numbers. Add the wholes first, then deal with the fractions.3 + 2 = 5
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
2 4 1 4 2 + 1 4 3 4 - Write the answer. 3
1 2 1 4 3 4
Check. Take away: 5
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 6, so 6 will do.6 ÷ 3 = 2, so 3 goes into 6
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.2
1 3 1 3 1 × 2 3 × 2 2 6 - Add the whole numbers. Add the wholes first, then deal with the fractions.1 + 2 = 3
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
5 6 2 6 5 + 2 6 7 6 - The fraction part is 1 or more, so change it to a whole number and a fraction.
7 6 7 6 1 6
3 + 11 6 1 6 - Write the answer. 1
5 6 1 3 1 6
Check. Take away: 4
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Check the denominators. To subtract fractions, the parts must be the same size.Both denominators are 6, so we can subtract straight away.
- Subtract the whole numbers. The fraction part of the first number is big enough, so we can subtract the wholes and the fractions separately.4 − 1 = 3
- Subtract the fractions. Subtract the numerators. The denominator stays the same.
5 6 1 6 4 6 - Simplify the fraction part. 4 and 6 can both be divided by 2.
4 6 4 ÷ 2 6 ÷ 2 2 3
So the answer is 32 3 - Write the answer. 4
5 6 1 6 2 3
Check. Add back: 3
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 4 = 2, so 4 goes into 8
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.2
3 4 3 4 3 × 2 4 × 2 6 8 - Subtract the whole numbers. The fraction part of the first number is big enough, so we can subtract the wholes and the fractions separately.5 − 2 = 3
- Subtract the fractions. Subtract the numerators. The denominator stays the same.
7 8 6 8 1 8 - Write the answer. 5
7 8 3 4 1 8
Check. Add back: 3
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Check the denominators. To subtract fractions, the parts must be the same size.Both denominators are 5, so we can subtract straight away.
- The first fraction part (1) is smaller than the second (3), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 5 fifths, so the numbers become fractions over 5.3
1 5 3 × 5 + 1 5 16 5
13 5 1 × 5 + 3 5 8 5 - Subtract the numerators. Now both numbers are fractions with the same denominator.
16 5 8 5 16 − 8 5 8 5 - The answer is 1 or more, so change it to a mixed number or a whole number.
8 5 8 5 3 5 - Write the answer. 3
1 5 3 5 3 5
Check. Add back: 1
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- The first fraction part (0) is smaller than the second (3), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 8 eighths, so the numbers become fractions over 8.4
0 8 4 × 8 + 0 8 32 8
13 8 1 × 8 + 3 8 11 8 - Subtract the numerators. Now both numbers are fractions with the same denominator.
32 8 11 8 32 − 11 8 21 8 - The answer is 1 or more, so change it to a mixed number or a whole number.
21 8 21 8 5 8 - Write the answer. 4 − 1
3 8 5 8
Check. Add back: 2
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 4, so 4 will do.4 ÷ 2 = 2, so 2 goes into 4
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
1 2 1 × 2 2 × 2 2 4 - The first fraction part (1) is smaller than the second (2), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 4 quarters, so the numbers become fractions over 4.2
1 4 2 × 4 + 1 4 9 4 2 4 0 × 4 + 2 4 2 4 - Subtract the numerators. Now both numbers are fractions with the same denominator.
9 4 2 4 9 − 2 4 7 4 - The answer is 1 or more, so change it to a mixed number or a whole number.
7 4 7 4 3 4 - Write the answer. 2
1 4 1 2 3 4
Check. Add back: 1
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Watch out
Do not take the smaller fraction from the bigger one in each column. 3Exercise 6F Adding and subtracting mixed numbers
Non-calculatorKey words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Check the denominators. To add fractions, the parts must be the same size.Both denominators are 5, so we can add straight away.
- Add the whole numbers. Add the wholes first, then deal with the fractions.1 + 2 = 3
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
1 5 2 5 1 + 2 5 3 5 - Write the answer. 1
1 5 2 5 3 5
Check. Take away: 3
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Check the denominators. To add fractions, the parts must be the same size.Both denominators are 7, so we can add straight away.
- Add the whole numbers. Add the wholes first, then deal with the fractions.3 + 1 = 4
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
2 7 3 7 2 + 3 7 5 7 - Write the answer. 3
2 7 3 7 5 7
Check. Take away: 4
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Check the denominators. To add fractions, the parts must be the same size.Both denominators are 8, so we can add straight away.
- Add the whole numbers. Add the wholes first, then deal with the fractions.2 + 4 = 6
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
1 8 3 8 1 + 3 8 4 8 - Simplify the fraction part. 4 and 8 can both be divided by 4.
4 8 4 ÷ 4 8 ÷ 4 1 2
So the answer is 61 2 - Write the answer. 2
1 8 3 8 1 2
Check. Take away: 6
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Check the denominators. To add fractions, the parts must be the same size.Both denominators are 10, so we can add straight away.
- Add the whole numbers. Add the wholes first, then deal with the fractions.5 + 2 = 7
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
3 10 4 10 3 + 4 10 7 10 - Write the answer. 5
3 10 4 10 7 10
Check. Take away: 7
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Check the denominators. To add fractions, the parts must be the same size.Both denominators are 4, so we can add straight away.
- Add the whole numbers. Add the wholes first, then deal with the fractions.2 + 1 = 3
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
3 4 3 4 3 + 3 4 6 4 - The fraction part is 1 or more, so change it to a whole number and a fraction.
6 4 6 4 2 4
3 + 12 4 2 4 - Simplify the fraction part. 2 and 4 can both be divided by 2.
2 4 2 ÷ 2 4 ÷ 2 1 2
So the answer is 41 2 - Write the answer. 2
3 4 3 4 1 2
Check. Take away: 4
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Check the denominators. To add fractions, the parts must be the same size.Both denominators are 6, so we can add straight away.
- Add the whole numbers. Add the wholes first, then deal with the fractions.3 + 2 = 5
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
5 6 3 6 5 + 3 6 8 6 - The fraction part is 1 or more, so change it to a whole number and a fraction.
8 6 8 6 2 6
5 + 12 6 2 6 - Simplify the fraction part. 2 and 6 can both be divided by 2.
2 6 2 ÷ 2 6 ÷ 2 1 3
So the answer is 61 3 - Write the answer. 3
5 6 3 6 1 3
Check. Take away: 6
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Check the denominators. To add fractions, the parts must be the same size.Both denominators are 5, so we can add straight away.
- Add the whole numbers. Add the wholes first, then deal with the fractions.1 + 3 = 4
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
4 5 3 5 4 + 3 5 7 5 - The fraction part is 1 or more, so change it to a whole number and a fraction.
7 5 7 5 2 5
4 + 12 5 2 5 - Write the answer. 1
4 5 3 5 2 5
Check. Take away: 5
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Check the denominators. To add fractions, the parts must be the same size.Both denominators are 8, so we can add straight away.
- Add the whole numbers. Add the wholes first, then deal with the fractions.2 + 1 = 3
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
7 8 5 8 7 + 5 8 12 8 - The fraction part is 1 or more, so change it to a whole number and a fraction.
12 8 12 8 4 8
3 + 14 8 4 8 - Simplify the fraction part. 4 and 8 can both be divided by 4.
4 8 4 ÷ 4 8 ÷ 4 1 2
So the answer is 41 2 - Write the answer. 2
7 8 5 8 1 2
Check. Take away: 4
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 4, so 4 will do.4 ÷ 2 = 2, so 2 goes into 4
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.1
1 2 1 2 1 × 2 2 × 2 2 4 - Add the whole numbers. Add the wholes first, then deal with the fractions.1 + 2 = 3
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
2 4 1 4 2 + 1 4 3 4 - Write the answer. 1
1 2 1 4 3 4
Check. Take away: 3
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 10, so 10 will do.10 ÷ 5 = 2, so 5 goes into 10
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.1
1 5 1 5 1 × 2 5 × 2 2 10 - Add the whole numbers. Add the wholes first, then deal with the fractions.3 + 1 = 4
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
3 10 2 10 3 + 2 10 5 10 - Simplify the fraction part. 5 and 10 can both be divided by 5.
5 10 5 ÷ 5 10 ÷ 5 1 2
So the answer is 41 2 - Write the answer. 3
3 10 1 5 1 2
Check. Take away: 4
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 6, so 6 will do.6 ÷ 3 = 2, so 3 goes into 6
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.2
2 3 2 3 2 × 2 3 × 2 4 6 - Add the whole numbers. Add the wholes first, then deal with the fractions.2 + 1 = 3
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
4 6 5 6 4 + 5 6 9 6 - The fraction part is 1 or more, so change it to a whole number and a fraction.
9 6 9 6 3 6
3 + 13 6 3 6 - Simplify the fraction part. 3 and 6 can both be divided by 3.
3 6 3 ÷ 3 6 ÷ 3 1 2
So the answer is 41 2 - Write the answer. 2
2 3 5 6 1 2
Check. Take away: 4
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 4 = 2, so 4 goes into 8
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.4
3 4 3 4 3 × 2 4 × 2 6 8 - Add the whole numbers. Add the wholes first, then deal with the fractions.4 + 1 = 5
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
6 8 5 8 6 + 5 8 11 8 - The fraction part is 1 or more, so change it to a whole number and a fraction.
11 8 11 8 3 8
5 + 13 8 3 8 - Write the answer. 4
3 4 5 8 3 8
Check. Take away: 6
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Check the denominators. To subtract fractions, the parts must be the same size.Both denominators are 6, so we can subtract straight away.
- Subtract the whole numbers. The fraction part of the first number is big enough, so we can subtract the wholes and the fractions separately.4 − 1 = 3
- Subtract the fractions. Subtract the numerators. The denominator stays the same.
5 6 1 6 4 6 - Simplify the fraction part. 4 and 6 can both be divided by 2.
4 6 4 ÷ 2 6 ÷ 2 2 3
So the answer is 32 3 - Write the answer. 4
5 6 1 6 2 3
Check. Add back: 3
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Check the denominators. To subtract fractions, the parts must be the same size.Both denominators are 8, so we can subtract straight away.
- Subtract the whole numbers. The fraction part of the first number is big enough, so we can subtract the wholes and the fractions separately.6 − 2 = 4
- Subtract the fractions. Subtract the numerators. The denominator stays the same.
7 8 3 8 4 8 - Simplify the fraction part. 4 and 8 can both be divided by 4.
4 8 4 ÷ 4 8 ÷ 4 1 2
So the answer is 41 2 - Write the answer. 6
7 8 3 8 1 2
Check. Add back: 4
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Check the denominators. To subtract fractions, the parts must be the same size.Both denominators are 10, so we can subtract straight away.
- Subtract the whole numbers. The fraction part of the first number is big enough, so we can subtract the wholes and the fractions separately.3 − 1 = 2
- Subtract the fractions. Subtract the numerators. The denominator stays the same.
9 10 4 10 5 10 - Simplify the fraction part. 5 and 10 can both be divided by 5.
5 10 5 ÷ 5 10 ÷ 5 1 2
So the answer is 21 2 - Write the answer. 3
9 10 4 10 1 2
Check. Add back: 2
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Check the denominators. To subtract fractions, the parts must be the same size.Both denominators are 5, so we can subtract straight away.
- Subtract the whole numbers. The fraction part of the first number is big enough, so we can subtract the wholes and the fractions separately.5 − 2 = 3
- Subtract the fractions. Subtract the numerators. The denominator stays the same.
4 5 1 5 3 5 - Write the answer. 5
4 5 1 5 3 5
Check. Add back: 3
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 4 = 2, so 4 goes into 8
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.2
3 4 3 4 3 × 2 4 × 2 6 8 - Subtract the whole numbers. The fraction part of the first number is big enough, so we can subtract the wholes and the fractions separately.5 − 2 = 3
- Subtract the fractions. Subtract the numerators. The denominator stays the same.
7 8 6 8 1 8 - Write the answer. 5
7 8 3 4 1 8
Check. Add back: 3
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 6, so 6 will do.6 ÷ 3 = 2, so 3 goes into 6
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.1
1 3 1 3 1 × 2 3 × 2 2 6 - Subtract the whole numbers. The fraction part of the first number is big enough, so we can subtract the wholes and the fractions separately.3 − 1 = 2
- Subtract the fractions. Subtract the numerators. The denominator stays the same.
5 6 2 6 3 6 - Simplify the fraction part. 3 and 6 can both be divided by 3.
3 6 3 ÷ 3 6 ÷ 3 1 2
So the answer is 21 2 - Write the answer. 3
5 6 1 3 1 2
Check. Add back: 2
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 10, so 10 will do.10 ÷ 5 = 2, so 5 goes into 10
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.2
2 5 2 5 2 × 2 5 × 2 4 10 - Subtract the whole numbers. The fraction part of the first number is big enough, so we can subtract the wholes and the fractions separately.6 − 2 = 4
- Subtract the fractions. Subtract the numerators. The denominator stays the same.
9 10 4 10 5 10 - Simplify the fraction part. 5 and 10 can both be divided by 5.
5 10 5 ÷ 5 10 ÷ 5 1 2
So the answer is 41 2 - Write the answer. 6
9 10 2 5 1 2
Check. Add back: 4
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 4, so 4 will do.4 ÷ 2 = 2, so 2 goes into 4
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.1
1 2 1 2 1 × 2 2 × 2 2 4 - Subtract the whole numbers. The fraction part of the first number is big enough, so we can subtract the wholes and the fractions separately.4 − 1 = 3
- Subtract the fractions. Subtract the numerators. The denominator stays the same.
3 4 2 4 1 4 - Write the answer. 4
3 4 1 2 1 4
Check. Add back: 3
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Check the denominators. To subtract fractions, the parts must be the same size.Both denominators are 5, so we can subtract straight away.
- The first fraction part (1) is smaller than the second (3), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 5 fifths, so the numbers become fractions over 5.3
1 5 3 × 5 + 1 5 16 5
13 5 1 × 5 + 3 5 8 5 - Subtract the numerators. Now both numbers are fractions with the same denominator.
16 5 8 5 16 − 8 5 8 5 - The answer is 1 or more, so change it to a mixed number or a whole number.
8 5 8 5 3 5 - Write the answer. 3
1 5 3 5 3 5
Check. Add back: 1
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Check the denominators. To subtract fractions, the parts must be the same size.Both denominators are 4, so we can subtract straight away.
- The first fraction part (1) is smaller than the second (3), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 4 quarters, so the numbers become fractions over 4.4
1 4 4 × 4 + 1 4 17 4
23 4 2 × 4 + 3 4 11 4 - Subtract the numerators. Now both numbers are fractions with the same denominator.
17 4 11 4 17 − 11 4 6 4 - The answer is 1 or more, so change it to a mixed number or a whole number.
6 4 6 4 2 4 - Simplify the fraction part. 2 and 4 can both be divided by 2.
2 4 2 ÷ 2 4 ÷ 2 1 2
So the answer is 11 2 - Write the answer. 4
1 4 3 4 1 2
Check. Add back: 1
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Check the denominators. To subtract fractions, the parts must be the same size.Both denominators are 8, so we can subtract straight away.
- The first fraction part (1) is smaller than the second (5), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 8 eighths, so the numbers become fractions over 8.2
1 8 2 × 8 + 1 8 17 8
15 8 1 × 8 + 5 8 13 8 - Subtract the numerators. Now both numbers are fractions with the same denominator.
17 8 13 8 17 − 13 8 4 8 - Simplify the fraction part. 4 and 8 can both be divided by 4.
4 8 4 ÷ 4 8 ÷ 4 1 2 - Write the answer. 2
1 8 5 8 1 2
Check. Add back:
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Check the denominators. To subtract fractions, the parts must be the same size.Both denominators are 10, so we can subtract straight away.
- The first fraction part (1) is smaller than the second (7), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 10 tenths, so the numbers become fractions over 10.6
1 10 6 × 10 + 1 10 61 10
37 10 3 × 10 + 7 10 37 10 - Subtract the numerators. Now both numbers are fractions with the same denominator.
61 10 37 10 61 − 37 10 24 10 - The answer is 1 or more, so change it to a mixed number or a whole number.
24 10 24 10 4 10 - Simplify the fraction part. 4 and 10 can both be divided by 2.
4 10 4 ÷ 2 10 ÷ 2 2 5
So the answer is 22 5 - Write the answer. 6
1 10 7 10 2 5
Check. Add back: 2
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- The first fraction part (0) is smaller than the second (3), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 8 eighths, so the numbers become fractions over 8.4
0 8 4 × 8 + 0 8 32 8
13 8 1 × 8 + 3 8 11 8 - Subtract the numerators. Now both numbers are fractions with the same denominator.
32 8 11 8 32 − 11 8 21 8 - The answer is 1 or more, so change it to a mixed number or a whole number.
21 8 21 8 5 8 - Write the answer. 4 − 1
3 8 5 8
Check. Add back: 2
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- The first fraction part (0) is smaller than the second (1), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 4 quarters, so the numbers become fractions over 4.5
0 4 5 × 4 + 0 4 20 4
21 4 2 × 4 + 1 4 9 4 - Subtract the numerators. Now both numbers are fractions with the same denominator.
20 4 9 4 20 − 9 4 11 4 - The answer is 1 or more, so change it to a mixed number or a whole number.
11 4 11 4 3 4 - Write the answer. 5 − 2
1 4 3 4
Check. Add back: 2
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- The first fraction part (0) is smaller than the second (2), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 5 fifths, so the numbers become fractions over 5.3
0 5 3 × 5 + 0 5 15 5
12 5 1 × 5 + 2 5 7 5 - Subtract the numerators. Now both numbers are fractions with the same denominator.
15 5 7 5 15 − 7 5 8 5 - The answer is 1 or more, so change it to a mixed number or a whole number.
8 5 8 5 3 5 - Write the answer. 3 − 1
2 5 3 5
Check. Add back: 1
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- The first fraction part (0) is smaller than the second (7), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 10 tenths, so the numbers become fractions over 10.6
0 10 6 × 10 + 0 10 60 10
27 10 2 × 10 + 7 10 27 10 - Subtract the numerators. Now both numbers are fractions with the same denominator.
60 10 27 10 60 − 27 10 33 10 - The answer is 1 or more, so change it to a mixed number or a whole number.
33 10 33 10 3 10 - Write the answer. 6 − 2
7 10 3 10
Check. Add back: 3
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 4, so 4 will do.4 ÷ 2 = 2, so 2 goes into 4
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.2
1 2 1 2 1 × 2 2 × 2 2 4 - Add the whole numbers. Add the wholes first, then deal with the fractions.2 + 1 = 3
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
2 4 3 4 2 + 3 4 5 4 - The fraction part is 1 or more, so change it to a whole number and a fraction.
5 4 5 4 1 4
3 + 11 4 1 4 - Write the answer. 2
1 2 3 4 1 4
Check. Take away: 4
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Make sure the denominators are the same. Add the whole numbers, then add the numerators. Change the answer to a mixed number and simplify if you can.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 4, so 4 will do.4 ÷ 2 = 2, so 2 goes into 4
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.1
1 2 1 2 1 × 2 2 × 2 2 4 - Add the whole numbers. Add the wholes first, then deal with the fractions.1 + 2 = 3
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
2 4 3 4 2 + 3 4 5 4 - The fraction part is 1 or more, so change it to a whole number and a fraction.
5 4 5 4 1 4
3 + 11 4 1 4 - Write the answer. 1
1 2 3 4 1 4
Check. Take away: 4
Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 4, so 4 will do.4 ÷ 2 = 2, so 2 goes into 4
- Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.1
1 2 1 2 1 × 2 2 × 2 2 4 - Subtract the whole numbers. The fraction part of the first number is big enough, so we can subtract the wholes and the fractions separately.2 − 1 = 1
- Subtract the fractions. Subtract the numerators. The denominator stays the same.
3 4 2 4 1 4 - Write the answer. 2
3 4 1 2 1 4
Check. Add back: 1
Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Add the two pieces that are cut off, then take the total away from the whole plank.
- Draw a bar model. The plank is 5 m. The two cut pieces and the piece left make the whole.
- Find the total length of the two pieces. Add the two lengths.1
3 4 1 2 7 4 10 4 17 4 1 4 - Take the total from 5 m. What is left is the missing piece. Write 5 as an improper fraction.5 − 4
1 4 20 4 17 4 3 4 - Write the answer.
3 4
Check. 4
Watch out. This is a two-step problem. The answer is not the total of the pieces.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Use the inverse (opposite) operation to find the missing number.
- Choose the operation. We know 2
3 4 1 4 3 4 1 4 41 4 3 4 1 2 - Check the denominators. To subtract fractions, the parts must be the same size.Both denominators are 4, so we can subtract straight away.
- The first fraction part (1) is smaller than the second (3), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 4 quarters, so the numbers become fractions over 4.4
1 4 4 × 4 + 1 4 17 4
23 4 2 × 4 + 3 4 11 4 - Subtract the numerators. Now both numbers are fractions with the same denominator.
17 4 11 4 17 − 11 4 6 4 - The answer is 1 or more, so change it to a mixed number or a whole number.
6 4 6 4 2 4 - Simplify the fraction part. 2 and 4 can both be divided by 2.
2 4 2 ÷ 2 4 ÷ 2 1 2
So the answer is 11 2 - Write the answer. 4
1 4 3 4 1 2
Check. Put it back in: 2
Watch out. The missing number is not always the first or second number. Use the opposite operation.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Use the inverse (opposite) operation to find the missing number.
- Choose the operation. We know ? − 1
1 5 3 5 1 5 3 5 23 5 1 5 4 5 - Check the denominators. To add fractions, the parts must be the same size.Both denominators are 5, so we can add straight away.
- Add the whole numbers. Add the wholes first, then deal with the fractions.2 + 1 = 3
- Add the fractions. Add the numerators. The denominator stays the same because the parts are the same size.
3 5 1 5 3 + 1 5 4 5 - Write the answer. 2
3 5 1 5 4 5
Check. Put it back in: 3
Watch out. The missing number is not always the first or second number. Use the opposite operation.
Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Work the question out yourself first. Then compare your working with the working in the question and find where it goes wrong.
- Work it out correctly. We need the right answer to compare with.3
1 5 16 5 3 5 8 5 16 5 8 5 8 5 3 5 - Find the mistake. Ravi did 3 − 1 = 2 for the wholes, and then took the smaller fraction from the bigger one: 3 fifths − 1 fifth = 2 fifths. But the first number only has 1 fifth, and we need to take away 3 fifths. He has to change to improper fractions.Ravi wrote 3
1 5 3 5 2 5 - Write the correct answer. The correct answer is 1
3 5
Check. 1
Watch out. If the fraction you take away is bigger, change to improper fractions.
Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like
Method. Work the question out yourself first. Then compare your working with the working in the question and find where it goes wrong.
- Work it out correctly. We need the right answer to compare with.2
3 4 3 4 3 4 3 4 6 4 1 2 1 2 1 2 - Find the mistake. Mia added correctly, but she stopped too soon. The fraction part
6 4 Mia wrote 23 4 3 4 6 4 - Write the correct answer. The correct answer is 4
1 2
Check. 3
Watch out. The fraction part of a mixed number must always be less than 1.
Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.
Method. Add all four sides. Add the length and the width, then double the total.
- Find the total of the two side lengths. A rectangle has two long sides and two short sides. Half the perimeter is one long side plus one short side.2
1 2 3 4 2 4 3 4 5 4 1 4 - Double it. The perimeter goes all the way round, so there are two of these totals.4
1 4 1 4 2 4 1 2 1 2 - Write the answer with the unit. The sides are in centimetres.The perimeter is 8
1 2
Check. 2 × 2
Watch out. Perimeter is the distance all the way round: four sides, not two.