Year 6 Arithmetic (SATs): Multiplying and dividing fractions, and decimals

Method. Multiply the top by the whole number, then simplify.

1. Multiply the top number by the whole number. 3 × 4 = 12, so the top becomes 12.
   3 × 4 = 12
2. Simplify the fraction. Divide the top and the bottom by 4.
   12/8 = 1 1/2
3. Write the answer.
   1 1/2

Check. 1 1/2 = 3/8 × 4. ✓

Method. Multiply the top by the whole number, then simplify.

1. Multiply the top number by the whole number. 5 × 9 = 45, so the top becomes 45.
   5 × 9 = 45
2. Simplify the fraction. Divide the top and the bottom by 3.
   45/6 = 7 1/2
3. Write the answer.
   7 1/2

Check. 7 1/2 = 5/6 × 9. ✓

Method. Multiply the top by the whole number, then simplify.

1. Multiply the top number by the whole number. 2 × 15 = 30, so the top becomes 30.
   2 × 15 = 30
2. Simplify the fraction. Divide the top and the bottom by 5.
   30/5 = 6
3. Write the answer.
   6

Check. 6 = 2/5 × 15. ✓

Method. Multiply the top by the whole number, then simplify.

1. Multiply the top number by the whole number. 5 × 8 = 40, so the top becomes 40.
   5 × 8 = 40
2. Simplify the fraction. Divide the top and the bottom by 4.
   40/12 = 3 1/3
3. Write the answer.
   3 1/3

Check. 3 1/3 = 5/12 × 8. ✓

Method. Multiply the tops and the bottoms, then simplify.

1. Multiply the top numbers. 2 × 3 = 6.
   2 × 3 = 6
2. Multiply the bottom numbers. 3 × 5 = 15.
   3 × 5 = 15
3. Simplify. Divide the top and bottom by 3.
   6/15 = 2/5
4. Write the answer.
   2/5

Check. 2/5 is the answer in its simplest form. ✓

Method. Multiply the tops and the bottoms, then simplify.

1. Multiply the top numbers. 3 × 2 = 6.
   3 × 2 = 6
2. Multiply the bottom numbers. 4 × 9 = 36.
   4 × 9 = 36
3. Simplify. Divide the top and bottom by 6.
   6/36 = 1/6
4. Write the answer.
   1/6

Check. 1/6 is the answer in its simplest form. ✓

Method. Multiply the tops and the bottoms, then simplify.

1. Multiply the top numbers. 5 × 3 = 15.
   5 × 3 = 15
2. Multiply the bottom numbers. 6 × 10 = 60.
   6 × 10 = 60
3. Simplify. Divide the top and bottom by 15.
   15/60 = 1/4
4. Write the answer.
   1/4

Check. 1/4 is the answer in its simplest form. ✓

Method. Keep the top and multiply the bottom by the whole number.

1. Keep the top number the same. The top stays at 3.
   3
2. Multiply the bottom number by the whole number. Sharing into 6 equal parts makes each part 6 times smaller.
   4 × 6 = 24
3. Simplify. Divide the top and bottom by 3.
   3/24 = 1/8
4. Write the answer.
   1/8

Check. 1/8 × 6 = 3/4. ✓

Method. Keep the top and multiply the bottom by the whole number.

1. Keep the top number the same. The top stays at 2.
   2
2. Multiply the bottom number by the whole number. Sharing into 4 equal parts makes each part 4 times smaller.
   5 × 4 = 20
3. Simplify. Divide the top and bottom by 2.
   2/20 = 1/10
4. Write the answer.
   1/10

Check. 1/10 × 4 = 2/5. ✓

Method. Keep the top and multiply the bottom by the whole number.

1. Keep the top number the same. The top stays at 5.
   5
2. Multiply the bottom number by the whole number. Sharing into 10 equal parts makes each part 10 times smaller.
   6 × 10 = 60
3. Simplify. Divide the top and bottom by 5.
   5/60 = 1/12
4. Write the answer.
   1/12

Check. 1/12 × 10 = 5/6. ✓

Method. Make the bottom 10 by multiplying the top and bottom by 2.

1. Make the bottom number a power of 10. 5 goes into 10 exactly, so multiply the top and bottom by 2.
   4/5 = 8/10
2. Read the fraction as a decimal. 8 hundredths or thousandths is written with 1 decimal place.
   8/10 = 0.8
3. Write the answer.
   0.8

Check. 0.8 × 5 = 4. ✓

Method. Make the bottom 100 by multiplying by 25.

1. Make the bottom number a power of 10. 4 goes into 100 exactly, so multiply the top and bottom by 25.
   3/4 = 75/100
2. Read the fraction as a decimal. 75 hundredths or thousandths is written with 2 decimal places.
   75/100 = 0.75
3. Write the answer.
   0.75

Check. 0.75 × 4 = 3. ✓

Method. Make the bottom 1000 by multiplying by 125.

1. Make the bottom number a power of 10. 8 goes into 1000 exactly, so multiply the top and bottom by 125.
   1/8 = 125/1000
2. Read the fraction as a decimal. 125 hundredths or thousandths is written with 3 decimal places.
   125/1000 = 0.125
3. Write the answer.
   0.125

Check. 0.125 × 8 = 1. ✓

Method. Multiply 3/4 by 8.

1. Multiply the top number by the whole number. 3 × 8 = 24, so the top becomes 24.
   3 × 8 = 24
2. Simplify the fraction. Divide the top and the bottom by 4.
   24/4 = 6
3. Write the answer.
   6

Check. 8 jugs of 0.75 litres is 6 litres. ✓

Method. Divide 3/4 by 6.

1. Keep the top number the same. The top stays at 3.
   3
2. Multiply the bottom number by the whole number. Sharing into 6 equal parts makes each part 6 times smaller.
   4 × 6 = 24
3. Simplify. Divide the top and bottom by 3.
   3/24 = 1/8
4. Write the answer.
   1/8

Check. 6 × 1/8 = 6/8 = 3/4. ✓

Method. Multiply, then simplify by 5 or by 2.

1. Multiply the top numbers. 4 × 5 = 20.
   4 × 5 = 20
2. Multiply the bottom numbers. 5 × 6 = 30.
   5 × 6 = 30
3. Simplify. Divide the top and bottom by 10.
   20/30 = 2/3
4. Write the answer.
   2/3

Check. 20/30 = 2/3. ✓

Method. Divide the top and multiply the bottom by 2.

1. Divide the top and multiply the bottom. 1/2 ÷ 2 = 1/(2 × 2).
   1/4
2. Compare. 1/4 is smaller than 1/2.
   1/4 < 1/2
3. Write the answer.
   Because you are sharing half a whole into 2 equal parts, so each part is smaller than half: the answer is 1/4.

Check. 1/4 × 2 = 1/2. ✓