Fractions, Year 8: more practice

3

HintWork from left to right and track the sign at each step.

The why−6 × 4 = −24, and −24 ÷ −8 = 3 because two negatives give a positive.

1/6

HintMultiply the tops, multiply the bottoms, then simplify.

The why3 × 2 = 6 and 4 × 9 = 36, so 6/36 = 1/6.

3 2/5

HintHow many whole fives are in 17?

The why17 ÷ 5 = 3 remainder 2, so 3 whole units and 2/5 more.

£9

HintBreak 15% into 10% and 5%.

The why10% of £60 is £6, 5% is £3, and £6 + £3 = £9.

£68

HintFind the reduction first, then subtract it.

The why15% of £80 = £12, so £80 − £12 = £68. The multiplier is 0.85.

3.46

HintThe third decimal place decides.

The whyThe third decimal digit is 6, so the second digit rounds up from 5 to 6: 3.46.

0.10

HintThe third decimal place is 9, so the round-up carries.

The whyRounding up 0.09 gives 0.10: the 9 becomes 10, carrying into the tenths. The final zero is kept to show two decimal places.

3,900

HintThe first non-zero digit is the first significant figure.

The whyThe two significant figures are 3 and 8, and the next digit, 6, rounds the 8 up to 9. Zeros then hold the place value: 3,900.

Put the −3 inside brackets before squaring

HintWhich number does the power act on if nothing encloses the minus sign?

The whyTyping −3² can square only the 3 and then apply the minus. Brackets make the minus sign part of the squared number.

20

HintPowers come before multiplication, which comes before subtraction.

The why2³ = 8, 3 × 8 = 24, and 24 − 4 = 20.