Year 6 Arithmetic (SATs): Adding and subtracting fractions

Method. The bottoms are the same, so add the tops.

1. The bottom numbers are the same. So add the top numbers and keep the bottom number.
   2 + 4 = 6, so 6/9
2. Simplify the answer. Divide the top and bottom by 3.
   6/9 = 2/3
3. Write the answer.
   2/3

Check. The total is less than one whole, so it is less than 1. ✓

Method. The bottoms are the same, so add the tops.

1. Find a common denominator. 10 and 2 both divide into 10.
   10
2. Make equivalent fractions. Multiply each top and bottom to get the common denominator.
   3/10 = 3/10 and 1/2 = 5/10
3. Add the top numbers. The bottom number stays the same.
   3 + 5 = 8, so 8/10
4. Simplify the answer. Divide the top and bottom by 2.
   8/10 = 4/5
5. Write the answer.
   4/5

Check. The total is less than one whole, so it is less than 1. ✓

Method. The bottoms are the same, so add the tops.

1. The bottom numbers are the same. So add the top numbers and keep the bottom number.
   4 + 2 = 6, so 6/7
2. Write the answer. The fraction cannot be simplified.
   6/7
3. Write the answer.
   6/7

Check. The total is less than one whole, so it is less than 1. ✓

Method. Find a common denominator, make equivalent fractions, then add.

1. Find a common denominator. 2 and 3 both divide into 6.
   6
2. Make equivalent fractions. Multiply each top and bottom to get the common denominator.
   1/2 = 3/6 and 1/3 = 2/6
3. Add the top numbers. The bottom number stays the same.
   3 + 2 = 5, so 5/6
4. Write the answer. The fraction cannot be simplified.
   5/6
5. Write the answer.
   5/6

Check. 5/6 is the sum in its simplest form. ✓

Method. Find a common denominator, make equivalent fractions, then add.

1. Find a common denominator. 4 and 8 both divide into 8.
   8
2. Make equivalent fractions. Multiply each top and bottom to get the common denominator.
   3/4 = 6/8 and 1/8 = 1/8
3. Add the top numbers. The bottom number stays the same.
   6 + 1 = 7, so 7/8
4. Write the answer. The fraction cannot be simplified.
   7/8
5. Write the answer.
   7/8

Check. 7/8 is the sum in its simplest form. ✓

Method. Find a common denominator, make equivalent fractions, then add.

1. Find a common denominator. 5 and 10 both divide into 10.
   10
2. Make equivalent fractions. Multiply each top and bottom to get the common denominator.
   2/5 = 4/10 and 1/10 = 1/10
3. Add the top numbers. The bottom number stays the same.
   4 + 1 = 5, so 5/10
4. Simplify the answer. Divide the top and bottom by 5.
   5/10 = 1/2
5. Write the answer.
   1/2

Check. 1/2 is the sum in its simplest form. ✓

Method. Find a common denominator, make equivalent fractions, then subtract.

1. Find a common denominator. 6 and 3 both divide into 6.
   6
2. Make equivalent fractions. Multiply each top and bottom to get the common denominator.
   5/6 = 5/6 and 1/3 = 2/6
3. Subtract the top numbers. The bottom number stays the same.
   5 - 2 = 3, so 3/6
4. Simplify the answer. Divide the top and bottom by 3.
   3/6 = 1/2
5. Write the answer.
   1/2

Check. 1/2 + 1/3 = 5/6. ✓

Method. Find a common denominator, make equivalent fractions, then subtract.

1. Find a common denominator. 8 and 4 both divide into 8.
   8
2. Make equivalent fractions. Multiply each top and bottom to get the common denominator.
   7/8 = 7/8 and 1/4 = 2/8
3. Subtract the top numbers. The bottom number stays the same.
   7 - 2 = 5, so 5/8
4. Write the answer. The fraction cannot be simplified.
   5/8
5. Write the answer.
   5/8

Check. 5/8 + 1/4 = 7/8. ✓

Method. Find a common denominator, make equivalent fractions, then subtract.

1. Find a common denominator. 3 and 9 both divide into 9.
   9
2. Make equivalent fractions. Multiply each top and bottom to get the common denominator.
   2/3 = 6/9 and 2/9 = 2/9
3. Subtract the top numbers. The bottom number stays the same.
   6 - 2 = 4, so 4/9
4. Write the answer. The fraction cannot be simplified.
   4/9
5. Write the answer.
   4/9

Check. 4/9 + 2/9 = 2/3. ✓

Method. Change each mixed number to an improper fraction, then add.

1. Change to improper fractions. 2 1/3 = 7/3 and 1 1/2 = 3/2.
   7/3 and 3/2
2. Make the bottoms the same. A common denominator of 3 and 2 is 6: 7/3 = 14/6 and 3/2 = 9/6.
   14/6 and 9/6
3. Add the tops. 14 + 9 = 23, so 23/6.
   23/6
4. Change back to a mixed number. 23 ÷ 6 = 3 remainder 5.
   3 5/6
5. Write the answer.
   3 5/6

Check. 3 5/6 = 23/6. ✓

Method. Both mixed numbers have the same bottom, so subtract the whole numbers and the fractions.

1. Subtract the whole numbers. 3 - 1 = 2.
   2
2. Subtract the fractions. 3/4 - 1/4 = 2/4, which is 1/2.
   2/4 = 1/2
3. Put them together. 2 + 1/2 = 2 1/2.
   2 1/2
4. Write the answer.
   2 1/2

Check. 2 1/2 + 1 1/4 = 3 3/4. ✓

Method. Add the two fractions with a common denominator.

1. Find a common denominator. 5 and 4 both divide into 20.
   20
2. Make equivalent fractions. Multiply each top and bottom to get the common denominator.
   3/5 = 12/20 and 1/4 = 5/20
3. Add the top numbers. The bottom number stays the same.
   12 + 5 = 17, so 17/20
4. Write the answer. The fraction cannot be simplified.
   17/20
5. Write the answer.
   17/20

Check. 17/20 is about 0.85 km. ✓

Method. Find a common denominator before you add.

1. Make equivalent fractions. 1/2 = 3/6 and 1/3 = 2/6.
   3/6 and 2/6
2. Add the tops. 3 + 2 = 5, so 5/6.
   5/6
3. Write the answer.
   No, the correct answer is 5/6, because 1/2 is 3/6 and 1/3 is 2/6.

Check. 5/6 is 0.83, not 2/5 which is 0.4. ✓

Method. Find a common denominator of 10 and 5, which is 10.

1. Find a common denominator. 10 and 5 both divide into 10.
   10
2. Make equivalent fractions. Multiply each top and bottom to get the common denominator.
   9/10 = 9/10 and 3/5 = 6/10
3. Subtract the top numbers. The bottom number stays the same.
   9 - 6 = 3, so 3/10
4. Write the answer. The fraction cannot be simplified.
   3/10
5. Write the answer.
   3/10

Check. 3/5 = 6/10, so 9/10 - 6/10 = 3/10. ✓