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Either paper 2 marks
Erin wins £200 in a raffle. She gives \(\frac{1}{ 10 }\) of the money to charity.
Calculate how much she gives to charity.
Show answer
\(\text{£}20\)Finding \(\frac{1}{ 10 }\) of an amount means dividing it by 10:
\(£200 \div 10 = £20\)
- M1divides \(£200\) by \(10\)
- A1\(£20\)
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Either paper 2 marks
Idris earns £45 each week. He saves \(\frac{ 2 }{ 9 }\) of it.
Calculate how much he saves each week.
Show answer
\(\text{£}10\)First find \(\frac{1}{ 9 }\) of the money:
\(£45 \div 9 = £5\)
Then multiply by 2:
\(2 \times £5 = £10\)
- M1one part \(£45 \div 9 = £5\)
- A1multiplies by \(2\) to get \(£10\)
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Either paper 3 marks
A water tank holds 253 litres of water. \(\frac{ 3 }{ 11 }\) of the water is used.
(a)Work out how many litres of water are used.
(b)Work out how many litres of water are left in the tank.
Show answer
(a) \(69\ \text{litres}\)
(b) \(184\ \text{litres}\)\(\frac{1}{ 11 }\) of 253 litres is \(253 \div 11 = 23\) litres.
\(\frac{ 3 }{ 11 }\) of 253 litres is \(3 \times 23 = 69\) litres.
\(253 - 69 = 184\) litres.
(The same answer comes from \(\frac{ 8 }{ 11 }\) of 253 litres.)
- (a) M1one part \(253 \div 11 = 23\) litres
- (a) A1multiplies by \(3\) to get \(69\) litres
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Either paper 4 marks(a)
Yusuf walks for \(\frac{ 1 }{ 12 }\) of an hour on a trail.
Work out how many minutes that is.
(b)Yusuf cycles for \(\frac{ 1 }{ 6 }\) of a day on a track.
Work out how many hours that is.
Show answer
(a) \(5\ \text{minutes}\)
(b) \(4\ \text{hours}\)There are 60 minutes in an hour.
\(60 \div 12 = 5\), then \(5 \times 1 = 5\) minutes.
There are 24 hours in a day.
\(24 \div 6 = 4\), then \(4 \times 1 = 4\) hours.
- (a) M1\(60 \div 12 = 5\) minutes for one part
- (a) A1\(5\) minutes
- (b) M1\(24 \div 6 = 4\) hours for one part
- (b) A1\(4\) hours
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Either paper 3 marks
A rope is 96 cm long.
Joel works out \(\frac{ 3 }{ 4 }\) of 96 like this.
\(96 \div 3 = 32\)
\(32 \times 4 = 128\)
(a)Explain what Joel has done wrong.
(b)Work out the correct answer.
Show answer
(a) Joel divided by the top of the fraction and multiplied by the bottom. It is the other way round: divide by 4 and multiply by 3.
(b) \(72\)To find a fraction of an amount, divide by the bottom number of the fraction and multiply by the top one.
Joel did it the other way round — divided by 3 and multiplied by 4.
\(96 \div 4 = 24\), then \(24 \times 3 = 72\)
- (b) M1divides \(96\) by the bottom \(4\) to get \(24\)
- (b) A1multiplies by the top \(3\) to get \(72\)
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Either paper 3 marksLeila has shaded some of the small squares on this centimetre grid.(a)
Work out the percentage of the grid that is shaded.
(b)Leila wants \(\frac{ 3 }{ 10 }\) of the grid to be shaded.
How many more small squares must she shade?
Show answer
(a) \(20\%\)
(b) \(4\)The grid has \(5 \times 8 = 40\) small squares and \(8\) are shaded.
\(\frac{ 8 }{ 40 } \times 100 = 20\%\)
\(\frac{ 3 }{ 10 }\) of \(40\) squares is \(40 \div 10 \times 3 = 12\) squares.
\(12 - 8 = 4\) more squares.
- (b) M1squares needed for the target fraction, \(12\)
- (b) A1takes away the \(8\) already shaded to get \(4\)
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Either paper 4 marksThe members of a club are seniors, adults or juniors. Every member is in one of these three groups. Here is a report about the members of the club.
Type of member Fraction of the members Senior \(\frac{ 3 }{ 8 }\) Adult \(\frac{ 1 }{ 5 }\) Junior \(\frac{ 1 }{ 3 }\) (a)Give a reason why there must be a mistake in the report.
(b)An adult membership fee is £65.
A junior membership fee is \(\frac{ 3 }{ 5 }\) of the adult fee.
Work out the total membership fee for 3 adults and 2 juniors.
Show answer
(a) The fractions add up to \(\frac{ 109 }{ 120 }\), which is less than 1, but every member is in one of the three groups so they should total 1.
(b) \(\text{£}273\)Write the fractions over a common denominator of 120:
\(\frac{ 3 }{ 8 } = \frac{ 45 }{ 120 }\), \(\frac{ 1 }{ 5 } = \frac{ 24 }{ 120 }\), \(\frac{ 1 }{ 3 } = \frac{ 40 }{ 120 }\)
Add them:
\(\frac{ 45 }{ 120 } + \frac{ 24 }{ 120 } + \frac{ 40 }{ 120 } = \frac{ 109 }{ 120 }\)
This is less than 1 whole, but every member is a senior, an adult or a junior, so the fractions should total exactly 1.
The junior fee is \(\frac{ 3 }{ 5 }\) of £65:
\(£65 \div 5 \times 3 = £39\)
3 adults pay \(3 \times £65 = £195\) and 2 juniors pay \(2 \times £39 = £78\).
\(£195 + £78 = £273\)
- (b) M1junior fee \(£39\) from \(£65 \div 5 \times 3\)
- (b) M1adults \(£195\) and juniors \(£78\)
- (b) A1total \(£273\)
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Either paper 3 marksThe table shows information about two workers on one day.
Priya says she spent more than one quarter of her total working time online. Is Priya correct? Tick a box. ☐ Yes ☐ No Show working to support your answer.Total working time (hours) Working time spent online (minutes) Priya 8 113 Callum 6 144 Show answer
No: one quarter of 480 minutes is 120 minutes, and Priya was online for 113 minutesThe total working time is in hours but the time online is in minutes, so change the hours to minutes first.
\(8 \times 60 = 480\) minutes
One quarter of the total working time:
\(480 \div 4 = 120\) minutes
Priya was online for \(113\) minutes, which is less than \(120\) minutes.
So the answer is No.
- M1total working time in minutes, \(8 \times 60 = 480\)
- M1one quarter of the total, \(480 \div 4 = 120\) minutes
- A1No, comparing 113 with 120
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Either paper 3 marks
Amara has saved £48 towards a new bike. This is \(\frac{ 3 }{ 5 }\) of the price of the bike.
Find the price of the bike.
Show answer
\(\text{£}80\)3 shares of the price come to £48, so one share is
\(£48 \div 3 = £16\)
The whole price is 5 shares:
\(5 \times £16 = £80\)
- M1divide by the numerator, \(48 \div 3 = 16\)
- M1multiply by the denominator, \(16 \times 5\)
- A1price \(£80\)
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Either paper 3 marks
A container holds 4.2 litres of juice. Priya pours out \(\frac{ 2 }{ 7 }\) of the juice.
How many millilitres of juice does she pour out?
Show answer
\(1200\ \text{ml}\)\(4.2\text{ litres} = 4200\text{ ml}\)
\(\frac{1}{ 7 }\) of 4200 ml is \(4200 \div 7 = 600\) ml.
\(2 \times 600 = 1200\) ml
- B1converts to \(4200\) ml
- M1one 7th \(600\) ml, or \(4200 \div 7\)
- A1\(1200\) ml