Year 6 Arithmetic (SATs) Fractions: check-up and practice test questions

Method. Divide the top and bottom by the highest common factor.

1. Find a number that divides into both the top and the bottom. The highest common factor of 42 and 56 is 14.
   HCF of 42 and 56 is 14
2. Divide the top and the bottom by it. Dividing both by the same number keeps the fraction the same size.
   42 ÷ 14 = 3, 56 ÷ 14 = 4
3. Write the answer.
   3/4

Check. 3/4 × 14 = 42/56 when both are simplified. ✓

Method. Multiply the top and bottom by 3.

1. Multiply the top and the bottom by the same number. Both are multiplied by 3, so the value of the fraction does not change.
   5 × 3 = 15 and 8 × 3 = 24
2. Write the answer.
   5/8

Check. 15/24 = 5/8. ✓

Method. Use the common denominator 24.

1. Find a common denominator. 6 and 8 both divide into 24.
   24
2. Write both fractions with that denominator. Multiply each top and bottom by the same number.
   5/6 = 20/24 and 7/8 = 21/24
3. Compare the top numbers. 20 and 21 tell us which fraction is bigger.
   20 < 21, so 5/6 < 7/8
4. Write the answer.
   <

Check. 5/6 = 20/24 and 7/8 = 21/24. ✓

Method. Divide 19 by 6.

1. Divide the top number by the bottom number. 19 ÷ 6 = 3 with 1 left over.
   19 ÷ 6 = 3 r 1
2. Write the answer as a mixed number. The whole number is 3, and the 1 left over goes over 6.
   3 1/6
3. Write the answer.
   3 1/6

Check. 3 × 6 + 1 = 19. ✓

Method. Multiply the whole number by the bottom and add the top.

1. Multiply the whole number by the bottom number. Each whole has 9 parts, so 3 wholes have 3 × 9 parts.
   3 × 9 = 27
2. Add the top number. Add the 5 parts that are left over.
   27 + 5 = 32
3. Keep the same bottom number. The size of each part does not change.
   32/9
4. Write the answer.
   32/9

Check. 32/9 = 3 5/9. ✓

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.
   3 + 2 = 5, so 5/7
2. Write the answer. The fraction cannot be simplified.
   5/7
3. Write the answer.
   5/7

Check. 5/7 - 2/7 = 3/7. ✓

Method. Make the bottoms the same, then subtract.

1. Find a common denominator. 9 and 3 both divide into 9.
   9
2. Make equivalent fractions. Multiply each top and bottom to get the common denominator.
   7/9 = 7/9 and 1/3 = 3/9
3. Subtract the top numbers. The bottom number stays the same.
   7 - 3 = 4, so 4/9
4. Write the answer. The fraction cannot be simplified.
   4/9
5. Write the answer.
   4/9

Check. 4/9 + 3/9 = 7/9. ✓

Method. Multiply the top by 15, 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 × 5 = 30 and 2 × 15 = 30, so the answer is 6. ✓

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. 15/60 = 1/4. ✓

Method. Make the bottom 10 by multiplying by 2.

1. Make the bottom number a power of 10. 5 goes into 10 exactly, so multiply the top and bottom by 2.
   3/5 = 6/10
2. Read the fraction as a decimal. 6 hundredths or thousandths is written with 1 decimal place.
   6/10 = 0.6
3. Write the answer.
   0.6

Check. 0.6 × 5 = 3. ✓

Method. Divide the top and bottom by the highest common factor.

1. Find a number that divides into both the top and the bottom. The highest common factor of 48 and 64 is 16.
   HCF of 48 and 64 is 16
2. Divide the top and the bottom by it. Dividing both by the same number keeps the fraction the same size.
   48 ÷ 16 = 3, 64 ÷ 16 = 4
3. Write the answer.
   3/4

Check. 3/4 is the simplest form. ✓

Method. Multiply the top and bottom by 4.

1. Multiply the top and the bottom by the same number. Both are multiplied by 4, so the value of the fraction does not change.
   2 × 4 = 8 and 3 × 4 = 12
2. Write the answer.
   2/3

Check. 8/12 = 2/3. ✓

Method. Use the common denominator 35.

1. Find a common denominator. 5 and 7 both divide into 35.
   35
2. Write both fractions with that denominator. Multiply each top and bottom by the same number.
   3/5 = 21/35 and 4/7 = 20/35
3. Compare the top numbers. 21 and 20 tell us which fraction is bigger.
   21 > 20, so 3/5 > 4/7
4. Write the answer.
   >

Check. 21/35 and 20/35. ✓

Method. Add the tops.

1. The bottom numbers are the same. So add the top numbers and keep the bottom number.
   5 + 2 = 7, so 7/9
2. Write the answer. The fraction cannot be simplified.
   7/9
3. Write the answer.
   7/9

Check. 7/9 - 2/9 = 5/9. ✓

Method. Find the common denominator 12, make equivalent fractions, then add.

1. Find a common denominator. 4 and 6 both divide into 12.
   12
2. Make equivalent fractions. Multiply each top and bottom to get the common denominator.
   3/4 = 9/12 and 1/6 = 2/12
3. Add the top numbers. The bottom number stays the same.
   9 + 2 = 11, so 11/12
4. Write the answer. The fraction cannot be simplified.
   11/12
5. Write the answer.
   11/12

Check. 9/12 + 2/12 = 11/12. ✓

Method. Change to improper fractions with the same bottom, then subtract.

1. Improper fractions. 4 1/2 = 18/4 and 2 3/4 = 11/4.
   18/4 and 11/4
2. Subtract. 18 - 11 = 7, so 7/4.
   7/4
3. Change back. 7 ÷ 4 = 1 remainder 3.
   1 3/4
4. Write the answer.
   1 3/4

Check. 1 3/4 + 2 3/4 = 4 1/2. ✓

Method. Multiply the top by 16, then simplify.

1. Multiply the top number by the whole number. 5 × 16 = 80, so the top becomes 80.
   5 × 16 = 80
2. Simplify the fraction. Divide the top and the bottom by 8.
   80/8 = 10
3. Write the answer.
   10

Check. 10 × 8 = 80 and 80/8 = 10. ✓

Method. Multiply the tops and bottoms, then simplify.

1. Multiply the top numbers. 3 × 4 = 12.
   3 × 4 = 12
2. Multiply the bottom numbers. 5 × 9 = 45.
   5 × 9 = 45
3. Simplify. Divide the top and bottom by 3.
   12/45 = 4/15
4. Write the answer.
   4/15

Check. 12/45 = 4/15. ✓

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

1. Keep the top number the same. The top stays at 4.
   4
2. Multiply the bottom number by the whole number. Sharing into 2 equal parts makes each part 2 times smaller.
   9 × 2 = 18
3. Simplify. Divide the top and bottom by 2.
   4/18 = 2/9
4. Write the answer.
   2/9

Check. 2/9 × 2 = 4/9. ✓

Method. Make the bottom 100 by multiplying by 5.

1. Make the bottom number a power of 10. 20 goes into 100 exactly, so multiply the top and bottom by 5.
   7/20 = 35/100
2. Read the fraction as a decimal. 35 hundredths or thousandths is written with 2 decimal places.
   35/100 = 0.35
3. Write the answer.
   0.35

Check. 0.35 × 20 = 7. ✓

Method. Multiply the top by 3, then simplify.

1. Multiply the top. 2 × 3 = 6, so 6/3.
   6/3
2. Simplify. Divide 6 by 3 to get a whole number.
   2
3. Write the answer.
   2 cups, because 2/3 × 3 = 6/3 = 2.

Check. 2/3 of a cup for each batch: 3 batches make 2 cups. ✓