Edexcel Maths GCSE - Fractions (FH) PhysicsAndMathsTutor.
com
Q1. (a) Change to a decimal.
.........................
(2)
(b) Work out
.........................
(2)
(c) Work out
.........................
(3)
(Total 7 marks)
Q2. Alan bought 20 melons for £15.
of the melons were bad so he threw them away.
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He sold the remaining melons for £1.50 each.
Work out Alan’s profit.
£ .................................
(Total 4 marks)
Q3. Work out .
....................................
(Total 2 marks)
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Q4. Work out .
..........................
(Total 2 marks)
Q5. Last year, Jora spent
30% of his salary on rent
of his salary on entertainment
of his salary on living expenses.
He saved the rest of his salary.
Jora spent £3600 on living expenses.
Work out how much money he saved.
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£ ........................
(Total 5 marks)
Q6. Mrs White wants to buy a new washing machine.
Three shops sell the washing machine she wants.
Clean Machines Electrics Wash ‘n’ Go
Washing machine Washing machine Washing machine
Buy now pay later! off the usual price £280
£50 deposit plus of plus
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10 equal payments of £27 £420 VAT at
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Mrs White wants to buy the cheapest one.
She decides to buy her washing machine from one of these 3 shops.
From which of these shops should she buy her washing machine?
You must show how you decided on your answer.
.....................................
(Total 6 marks)
Q7. Anwar, Bethany and Colin each earn the same weekly wage.
Each week, Anwar saves 12% of his wage and spends the rest.
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Each week, Bethany spends of her wage and saves the rest.
The ratio of the money Colin saves each week to what he spends is 1 : 9
Which of Anwar, Bethany and Colin, saves the most money each week?
You must show each stage of your working.
.....................................
(Total 4 marks)
Q8. (a) Write down the reciprocal of 4
....................................
(1)
(b) Work out the value of
Give your answer as a fraction in its simplest form.
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.....................................
(3)
(c) Sundas says that is equal to 4.3
Sundas is wrong.
Explain why.
.........................................................................................................................
.........................................................................................................................
(1)
(Total 5 marks)
Q9. (a) Work out
....................................
(2)
(b) Work out
....................................
(1)
(Total 3 marks)
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Q10. Work out
....................
(Total 2 marks)
Q11. There are 600 counters in a bag.
90 of the counters are yellow.
(a) Work out 90 as a fraction of 600.
Give your answer in its simplest form.
.....................................
(2)
180 of the 600 counters in the bag are red.
(b) Work out 180 as a percentage of 600.
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........................................ %
(2)
The rest of the counters in the bag are blue or green.
There are twice as many blue counters as green counters.
(c) Work out the number of green counters in the bag.
.....................................
(2)
(Total 6 marks)
Q12. Peter won £75 as a prize.
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He gave of the prize money as a present to Roger and Bethan.
Roger and Bethan shared the present in the ratio 2 : 3
Work out how much they each got.
Roger .....................................
Bethan .....................................
(Total 4 marks)
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Q13. Jennie’s council has a target of for households to recycle their waste.
In January, Jennie recycled of her household waste.
In February, she recycled 15 kg of her 120 kg of household waste.
Her result for March was 13% recycled out of 112 kg of household waste.
Has Jennie met the council’s target?
Which was her best month for recycling?
Show clearly how you got your answers.
(Total 4 marks)
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M1.
Working Answer Mark Additional Guidance
(a) 5.000 ÷ 8 0.625 2 M1 for 5 ÷ 8 or 1 ÷ 8 × 5
A1 cao
(b) 2 M1 for correct common denominator of two
fractions with at least one numerator correct
oe
A1 for oe (for example )
Alternative Alternative
0.4 + 0.143 M1 for 0.4 and 0.14(2857…) (correct to 2dp.)
A1 for 0.54 or better
(c) 4 3
M1 for or oe
M1 for
A1 for 4 oe (accept )
Alternative Alternative
2.5 × 1.6 M1 For 2.5 and 1.6
M1 For 4 with any number of 0s with or without a
decimal point
A1 4
Total for Question: 7 marks
M2.
Working Answer Mark Additional Guidance
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20 ÷ 5 (= 4) 9 4 M1 for 20 ÷ 5
20 – “4” (= 16) M1 for 20 – “4” where 0 < “4” < 20
“16” × 1.50 (= 24) M1 for “16” × 1.50 where 0 < “16” < 20
A1 cao
Total for Question: 4 marks
M3.
Answer Mark Additional Guidance
2 M1 for clear attempt to multiply numerators and
multiply denominators e.g
A1 for oe
Total for Question: 2 marks
M4.
Working Answer Mark Additional Guidance
M1 for OR correct attempt to make fractions have a
common denominator with at least one fraction correct
OR for 0.125 and 0.75 seen
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A1 for oe or 0.875
Total for Question: 2 marks
M5.
Working Answer Mark Additional Guidance
3600 × 4 = 14400 £720 5 M1 3600 × 4 (= 14400)
= 40% B1 for = 40% or = 25%
M1 for 30% + 40% + 50% (= 95%)
M1 for complete method to find 5% of 14400
= 25%
A1 cao
OR
30 + 40 + 25 = 95%
M1 for 3600 × 4 (= 14400)
Saved 5% B1 for 30% = 3/10
10% of 14400 = 1440
M1 for oe
5% of 1440 = 1440 ÷ 2
M1 for complete method to find of 14400
A1 cao
OR
M1 3600 × 4 (= 14400)
M1 for 0.3 × 14400 oe (= 4320)
M1 for oe (= 5760)
M1 14400 – 3600 – 4320 – 5760
A1 cao
SC if no other marks award
M1 for 0.3 x 3600 (= 1080)
M1 for × 3600 (= 1440)
Total for Question: 5 marks
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M6.
Working Answer Mark Additional Guidance
QWC 280 × 0.175 + 280 (= £315, 6 M1 for 50 + 10 × 27
(ii, iii) 329) Electrics
FE 420 ÷ 4 (= 315)
50 + 10 × 27 (= 320)
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Total for Question: 6 marks
M7.
Working Answer Mark Additional Guidance
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Bethany 4
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Total for Question: 4 marks
M8.
Working Answer Mark Additional Guidance
(a) 1
B1 for or 0.25 or 4–1
(b) 3 M1 for attempt to convert to fractions with
(2 – 1) + common
denominator, e.g. two fractions denominator 20
=1+
or
A1 correct conversion: and oe,
or or or oe
2.8-1.75
A1 for or 1
OR
M1 for 0.8 – 0.75 (or 2.8 – 1.75)
A2 for 1.05
(A1 for 0.05)
(c) Reason 1 B1 for correct reason, e.g. ‘1/3 = 0.3 recurring
(accept 0.33)’ or ‘0.3 = 3/10’
Total for Question: 5 marks
M9.
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Working Answer Mark Additional Guidance
(a) 2
M1 for or for attempting to use a suitable
common denominator other than 12, at least one
of the two fractions correct.
A1 for oe
OR
Attempt to use decimals, must use at least 2 d.p.
M1 for 0.33(33...) + 0.08(33...)
A1 for 0.416 recurring
(b) 1
B1 for oe
Total for Question: 3 marks
M10.
Working Answer Mark Additional Guidance
2 M1 for correct common denominator of two
fractions with at least one numerator correct
oe
A1 for oe (for example )
Alternative Alternative
0.4 + 0.143 M1 for 0.4 and 0.14(2857…) (correct to 2dp.)
A1 for 0.54 or better
Total for Question: 2 marks
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M11.
Working Answer Mark Additional Guidance
(a) 2
M1
A1 cao
[SC: B1 for 0.15 or 15% if M0 scored]
(b) 30 2
× 100 M1
A1 cao
OR OR
M1 or attempt to cancel to 100
A1 cao
(c) 600 – (90 +180) = 110 2 M1 [“600 – (90 + 180)“] ÷ 3
330 blue or green A1 cao
330 ÷ 3 [SC: B1 for an answer of 140 or 170 if M0 scored]
Total for Question: 6 marks
M12.
Working Answer Mark Additional Guidance
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Roger 24 4
3 × 12 = 36 Bethan 36
2 × 12 = 24
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Total for Question: 4 marks
M13.
Working Answer Mark Additional Guidance
QWC Best month 4 M1 Converts for at least 2 months to a common
iii and format (fractions, decimals or %age)
FE supporting
explanation A1 all correct
See table at end
C1 for Council target: No (yes) dep on M1 and
consistent with the candidates calculations
QWC: Decisions should be started, following
through from working out
C1 March with all calculations correct for the 3
months
QWC: Decisions should be started, following
through from working out
Total for Question: 4 marks
Fraction Decimal % kg
Jan
0.1 10% Not known
Feb
0.125 12.5% 15 kg
Mar
0.13 13% 14.56 kg
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E1. (a) The many students who got this wrong fell mainly into 3 camps.. Those who did
not know that to convert 85to a decimal requires the division of 5 by 8 or its
equivalent, those that could not carry out the division and those who tried to work
out 58÷. A small number of candidates tried to do a chunking method along the lines
of 0.5 + 0.5 ÷ 4 with the second part being worked out by repeated halving.
(b) Responses to this straightforward question were often disappointing, with the usual
errors of 2/5 + 1/7 = 3/12 or 3/35 + 1/35 + =4/35 appearing.
(c) Many candidates were unaware of the standard method of multiplying mixed
numbers by changing them to improper fractions. Of those that did write 5825× a
surprising number went on to find either 5/2 × 8/5 (a confusion with division) or
25/10 × 16/10 = 400/10 (a confusion with addition)
E2. Once again a surprising number of candidates could not apply the appropriate
arithmetical skills correctly. The major problem came with 16 × £1.50 with many
candidates failing to see that the most direct way of working this out was to do 16 + half of
16. Some candidates were confused by the context and worked out one fifth of 15 and
then used that answer in various inventive ways. Others found one fifth of 20 as 4 and
then used that to get £6 as the profit, in this case ignoring most of the information given in
the question. Many failed to complete the final step of the question which was performing
a subtraction to calculate the profit.
E3. A standard, context free fraction multiplication with no cancelling required. As with
question 1 there was a great deal of evidence pointing to poor arithmetical as well as
conceptual/ process skills. The major error was where the multiplication process is
confused with addition, so the candidates write ,making the denominators the
same and then go on to work this out as or 3. (Of course, was an acceptable
answer). Further common wrong answers were from adding the numerators of the
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equivalent fractions and from possibly 3 × 1 = 4, or from simply multiplying the
denominators of the original fractions and adding the numerators. Some clearly confused
the methods required for multiplication and division and turned the second fraction upside
down before multiplying to reach A few candidates replaced the fractions by
decimals. They were allowed full marks on a correct decimal answer.
E4. This question was not done well. More than two thirds of the candidates scored 0
marks in this question. By far the most common incorrect approach was to simply add the
numerators and add the denominators to get 4/12. A significant number of those
candidates using the tabular approach got confused somewhere in their method.
##
Foundation
Another question which candidates preferred not to attempt. The significance of the £3600 was
missed by nearly all the candidates who used this as figure for his salary, rather than 4 × £3600.
Some credit was given for candidates who demonstrated 2/5 and 30% of the £3600, but in too
many cases these calculations were done badly. There were several different routes to the
solution, including conversion to fractions, to decimals, or to percentages. This was again a
question in which candidates had to order their work logically on the page in order for examiners
to understand their order of calculations, and the chosen method of solution. Overall few marks
were gained on this question. Centres need to emphasise at all opportunities the need for
candidates to set out work logically and clearly.
Higher
Candidates need to be encouraged to set their work out in a logical order when tackling a
multi-stage problem. Haphazard working led to loss of zeros, incorrect subtraction and
candidates seeming to lose track of their method. Often when finding 2/5 of 14400, candidates
found 1/5 but then did not carry on to double their answer. Many candidates knew how to find
the correct proportions but were let down by poor multiplication skills. A significant number did
not appreciate the detail of the question and found proportions of £3600 rather than £14400.
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E8. In part (a), an increasing number of candidates are able to write down the reciprocal
of a number. Common incorrect answers here were 2, 16 and 4/1. In part (b), most
candidates were able to score at least 1 mark for writing the fractions with a common
denominator (generally 20), but poor arithmetic often hindered candidates from gaining full
marks, 14/5 – 7/4 = 46/20 – 35/20was a typical error. Those candidates who dealt with the
integers and fractions separately, i.e. (2 – 1) + (4/5/ – 3/4), where a little more successful
than those who converted the mixed numbers to improper fractions. In part (c), about half
the candidates were able to write down a suitable reason for why Sundas was wrong.
Most reasons were based either on 1/3 = 0.33…or on 3/10 not being the same as 1/3.
E9. The addition of fractions is a difficult topic for candidates at the Foundation tier and
part (a) was answered poorly. Many candidates did not appreciate the need for a common
denominator and the most common answer was 2/15 from adding the numerators and
adding the denominators. Even when candidates attempted to find a suitable common
denominator, errors occurred in converting one or both of the fractions and some
candidates, having correctly expressed both fractions with a common denominator,
proceeded to add the denominators as well as the numerators. Candidates were more
successful in part (b) with just under a half multiplying the two fractions correctly.
E10. This question was usually answered correctly, however a good proportion of the
candidature failed to score full marks. Even at this level many candidates gave an
incorrect answer of 3/12 = 1/4, simply adding the numerators and denominators of the
given fractions. Some, after finding a common denominator of 35, failed to correctly
convert the numerators; 2/35 + 1/35 or 10/35 + 7/35 or 14/35 +7/35 were often seen.
On occasions, was seen, where the candidate had attempted a form of
simplification after quoting the correct answer. Having seen the correct answer, full marks
were awarded in these cases.
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E11. In many cases in part (a), candidates gave a fraction of and then either failed
to simplify it correctly or failed to complete the simplifying process.
Part (b) was quite poorly answered, many candidates misunderstanding the demand of
the question and trying to find 180% of 600. Many tried partitioning methods and often
statements like “10% = 60” were seen but solutions were unable to progress and no
marks could be awarded.
In part (c), the most popular misconception was to divide 330 by 2 (instead of 3) and then
to divide their answer by 2 again; 82.5 or similar being a common incorrect answer seen.
Some candidates failed to take account of both the yellow and red counters already
having been used, omitting usually just one of them, leading to an answer of 140 or 170.
One mark was awarded in these cases.
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