Year 6 Arithmetic (SATs): Mixed numbers and improper fractions

Method. Multiply the whole number by the bottom, then add the top.

1. Multiply the whole number by the bottom number. Each whole has 3 parts, so 1 wholes have 1 × 3 parts.
   1 × 3 = 3
2. Add the top number. Add the 2 parts that are left over.
   3 + 2 = 5
3. Keep the same bottom number. The size of each part does not change.
   5/3
4. Write the answer.
   5/3

Check. 5/3 = 1 2/3, because 1 × 3 + 2 = 5. ✓

Method. Multiply the whole number by the bottom, then add the top.

1. Multiply the whole number by the bottom number. Each whole has 2 parts, so 3 wholes have 3 × 2 parts.
   3 × 2 = 6
2. Add the top number. Add the 1 parts that are left over.
   6 + 1 = 7
3. Keep the same bottom number. The size of each part does not change.
   7/2
4. Write the answer.
   7/2

Check. 7/2 = 3 1/2, because 3 × 2 + 1 = 7. ✓

Method. Multiply the whole number by the bottom, then add the top.

1. Multiply the whole number by the bottom number. Each whole has 8 parts, so 2 wholes have 2 × 8 parts.
   2 × 8 = 16
2. Add the top number. Add the 3 parts that are left over.
   16 + 3 = 19
3. Keep the same bottom number. The size of each part does not change.
   19/8
4. Write the answer.
   19/8

Check. 19/8 = 2 3/8, because 2 × 8 + 3 = 19. ✓

Method. Multiply the whole number by the bottom, then add the top.

1. Multiply the whole number by the bottom number. Each whole has 4 parts, so 5 wholes have 5 × 4 parts.
   5 × 4 = 20
2. Add the top number. Add the 1 parts that are left over.
   20 + 1 = 21
3. Keep the same bottom number. The size of each part does not change.
   21/4
4. Write the answer.
   21/4

Check. 21/4 = 5 1/4, because 5 × 4 + 1 = 21. ✓

Method. Multiply the whole number by the bottom, then add the top.

1. Multiply the whole number by the bottom number. Each whole has 5 parts, so 4 wholes have 4 × 5 parts.
   4 × 5 = 20
2. Add the top number. Add the 3 parts that are left over.
   20 + 3 = 23
3. Keep the same bottom number. The size of each part does not change.
   23/5
4. Write the answer.
   23/5

Check. 23/5 = 4 3/5, because 4 × 5 + 3 = 23. ✓

Method. Multiply the whole number by the bottom, then add the top.

1. Multiply the whole number by the bottom number. Each whole has 6 parts, so 2 wholes have 2 × 6 parts.
   2 × 6 = 12
2. Add the top number. Add the 1 parts that are left over.
   12 + 1 = 13
3. Keep the same bottom number. The size of each part does not change.
   13/6
4. Write the answer.
   13/6

Check. 13/6 = 2 1/6, because 2 × 6 + 1 = 13. ✓

Method. Divide the top by the bottom.

1. Divide the top number by the bottom number. 11 ÷ 4 = 2 with 3 left over.
   11 ÷ 4 = 2 r 3
2. Write the answer as a mixed number. The whole number is 2, and the 3 left over goes over 4.
   2 3/4
3. Write the answer.
   2 3/4

Check. 2 3/4, because the whole number times 4 plus the remainder is 11. ✓

Method. Divide the top by the bottom.

1. Divide the top number by the bottom number. 17 ÷ 6 = 2 with 5 left over.
   17 ÷ 6 = 2 r 5
2. Write the answer as a mixed number. The whole number is 2, and the 5 left over goes over 6.
   2 5/6
3. Write the answer.
   2 5/6

Check. 2 5/6, because the whole number times 6 plus the remainder is 17. ✓

Method. Divide the top by the bottom.

1. Divide the top number by the bottom number. 23 ÷ 5 = 4 with 3 left over.
   23 ÷ 5 = 4 r 3
2. Write the answer as a mixed number. The whole number is 4, and the 3 left over goes over 5.
   4 3/5
3. Write the answer.
   4 3/5

Check. 4 3/5, because the whole number times 5 plus the remainder is 23. ✓

Method. Divide the top by the bottom.

1. Divide the top number by the bottom number. 14 ÷ 3 = 4 with 2 left over.
   14 ÷ 3 = 4 r 2
2. Write the answer as a mixed number. The whole number is 4, and the 2 left over goes over 3.
   4 2/3
3. Write the answer.
   4 2/3

Check. 4 2/3, because the whole number times 3 plus the remainder is 14. ✓

Method. Divide the top by the bottom.

1. Divide the top number by the bottom number. 19 ÷ 8 = 2 with 3 left over.
   19 ÷ 8 = 2 r 3
2. Write the answer as a mixed number. The whole number is 2, and the 3 left over goes over 8.
   2 3/8
3. Write the answer.
   2 3/8

Check. 2 3/8, because the whole number times 8 plus the remainder is 19. ✓

Method. Change 4 3/8 to an improper fraction.

1. Multiply the whole number by the bottom number. Each whole has 8 parts, so 4 wholes have 4 × 8 parts.
   4 × 8 = 32
2. Add the top number. Add the 3 parts that are left over.
   32 + 3 = 35
3. Keep the same bottom number. The size of each part does not change.
   35/8
4. Write the answer.
   35/8

Check. 35/8 = 4 3/8, and 35 ÷ 8 = 4 remainder 3. ✓

Method. Divide 50 by 7 and write the remainder over 7.

1. Divide the top number by the bottom number. 50 ÷ 7 = 7 with 1 left over.
   50 ÷ 7 = 7 r 1
2. Write the answer as a mixed number. The whole number is 7, and the 1 left over goes over 7.
   7 1/7
3. Write the answer.
   7 1/7

Check. 7 × 7 + 1 = 50, so 50/7 = 7 1/7. ✓

Method. Divide 9 by 4 and read the answer as wholes and parts.

1. Divide. 9 ÷ 4 = 2 remainder 1.
   9 ÷ 4 = 2 r 1
2. Read the answer. Two wholes and one quarter left over.
   2 1/4
3. Write the answer.
   9/4 means 9 quarters; 4 quarters make one whole, so 9 quarters is 2 wholes and 1 quarter.

Check. 2 × 4 + 1 = 9. ✓

Method. Divide 13 by 4.

1. Divide the top number by the bottom number. 13 ÷ 4 = 3 with 1 left over.
   13 ÷ 4 = 3 r 1
2. Write the answer as a mixed number. The whole number is 3, and the 1 left over goes over 4.
   3 1/4
3. Write the answer.
   3 1/4

Check. 3 × 4 + 1 = 13. ✓

Method. Multiply the whole number by 5, add 2, and keep the bottom.

1. Multiply the whole number by the bottom number. Each whole has 5 parts, so 3 wholes have 3 × 5 parts.
   3 × 5 = 15
2. Add the top number. Add the 2 parts that are left over.
   15 + 2 = 17
3. Keep the same bottom number. The size of each part does not change.
   17/5
4. Write the answer.
   17/5

Check. 3 × 5 + 2 = 17. ✓