Fractions, Year 7: more practice

−8, −5, −1, 0, 2

HintPicture them on a number line: further left means smaller.

The whyAmong negative numbers, the one with the larger digit is further below zero, so −8 is smaller than −5.

24

HintFind one eighth first, then take three of them.

The why64 ÷ 8 = 8, and 8 × 3 = 24.

6,480

HintLook at the digit in the units column.

The whyThe 3 in the units column is less than 5, so the tens digit stays as it is: 6,480.

8,500

HintThe digit in the tens column decides — and a 5 rounds up.

The whyThe tens digit is 5, so the hundreds digit goes up from 4 to 5: 8,500.

6.26

HintWrite 10 as 10.00 so the decimal points line up.

The why10.00 − 3.74 = 6.26. Check: 6.26 + 3.74 = 10.

0.24

HintMultiply 6 × 4 as whole numbers, then count the decimal places.

The why6 × 4 = 24 and there are two decimal places in total, so 0.24. The answer is less than either number multiplied.

8

HintMultiply both numbers by 10 to make the divisor whole.

The why7.2 ÷ 0.9 = 72 ÷ 9 = 8. Check: 0.9 × 8 = 7.2.

12/20

HintFind what 5 is multiplied by to give 20.

The why5 × 4 = 20, so the numerator must also be multiplied by 4: 3 × 4 = 12.

3/4

HintRewrite both over a common denominator.

The whyOver 28: 3/4 = 21/28 and 5/7 = 20/28, so 3/4 is larger.

3, 4, 5 and 6

HintCheck whether each end is included.

The whyThe open sign < means 2 is not included, and ≤ means 6 is included.