Fractions of Amounts

Divide the amount into three equal parts.

The denominator tells you how many equal parts to make.

Find one fifth first, then take two parts.

Find one quarter, then multiply it by three.

Divide by the bottom number before multiplying by the top number.

Find one eighth of the money, then three eighths.

1. 24\div8=3, so one eighth is £3.
2. Three eighths is 3\times3=9. The book costs £9.

Put the number of blue counters over the total number of counters.

1. The fraction is \frac{15}{25}.
2. Divide top and bottom by 5: \frac{15}{25}=\frac{3}{5}.

Find the length cut off, then subtract it from the original length.

1. Cut off: 60\div4=15 metres.
2. Left: 60-15=45 metres.

First find one seventh, then take two of those parts.

1. The denominator 7 tells us to divide the whole into seven equal parts.
2. The numerator 2 tells us to take two parts: 35\div7\times2.
3. This would give 5\times2=10.

Six equal parts make the whole number.

1. One part is 7 and the whole has six parts.
2. 7\times6=42. Check: 42\div6=7.

The given 35 represents five parts. Find one part before finding all eight.

1. One eighth is 35\div5=7.
2. Eight eighths make the whole: 7\times8=56.
3. Check: 56\div8\times5=35.

Find the fractional donation first, then add the extra donation.

1. One tenth of £85 is 85\div10=£8.50.
2. Three tenths is 8.50\times3=£25.50.
3. Total donated: 25.50+4=£29.50.

Subtract the amount spent, or find the fraction she keeps.

1. One eighth is 64\div8=£8.
2. Spent: 8\times3=£24.
3. Left: 64-24=£40.

Convert the whole ribbon length to centimetres before writing part over whole.

1. 1.2 metres is 120 cm.
2. The fraction is \frac{45}{120}.
3. Divide top and bottom by 15: \frac{45}{120}=\frac{3}{8}.

The totals differ, so calculate each number of pencils before comparing.

1. From the box: 84\div3=28 pencils.
2. From the tin: 75\div5\times2=15\times2=30 pencils.
3. Difference: 30-28=2 more pencils from the tin.

Find what fraction remains. The £48 is that fraction of the starting money.

1. The fraction left is 1-\frac{3}{7}=\frac{4}{7}.
2. Four sevenths is £48, so one seventh is 48\div4=£12.
3. The original seven sevenths is 12\times7=£84.
4. Check: 84\div7\times3=£36 spent, and 84-36=£48 left.

Calculate a new remainder after each use; the second fraction acts on the first remainder.

1. First use: 240\div5\times2=96 litres.
2. First remainder: 240-96=144 litres.
3. Second use: 144\div3=48 litres.
4. Final remainder: 144-48=96 litres.

Recover the total number of children before subtracting both known groups.

1. Three eighths of the group is 12, so one eighth is 12\div3=4.
2. Total group: 4\times8=32 children.
3. There are 32-12=20 who do not cycle.
4. Bus travellers: 20-7=13 children.

Find each whole capacity from the fraction given, then compare those capacities.

1. For A, one quarter is 18\div3=6 litres, so capacity is 6\times4=24 litres.
2. For B, one fifth is 14\div2=7 litres, so capacity is 7\times5=35 litres.
3. Difference in capacity: 35-24=11 litres.

Work backwards: first find how much she had before the meal.

1. Before the meal she had 30+15=£45.
2. After the ticket she had 1-\frac{1}{4}=\frac{3}{4} of her savings, so \frac{3}{4} of her savings is £45.
3. One quarter is 45\div3=£15, so the original savings were 15\times4=£60.
4. Check: the ticket cost 60\div4=£15, leaving £45. The meal cost £15, leaving £30.