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13+ · Mathematics

CE.M2 Fractions, Decimals and Percentages

ISEB CE CE.M2 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write down the value of each of the following.

(a)Write 7/10 as a decimal.(1)

(b)Write 0.45 as a percentage.(1)

(c)Write 30% as a fraction in its simplest form.(1)

(Total for Question 1 is 3 marks)

Which of these values has the greatest size?

A) 0.6
B) 3/8
C) 55%
D) 0.58

(Total for Question 2 is 1 mark)

Put these values in order of size, starting with the smallest.
7/20 0.3 32% 0.28

(Total for Question 3 is 2 marks)

Find 3/8 of 96.

(Total for Question 4 is 2 marks)

Find 15% of 220 grams.

(Total for Question 5 is 2 marks)

A laptop costs 540 pounds before VAT is added. VAT is charged at 20%. Calculate the total price of the laptop including VAT.

(Total for Question 6 is 2 marks)

The price of a jacket is 48 pounds. The price is increased by 25%. Calculate the new price of the jacket.

(Total for Question 7 is 3 marks)

A bicycle normally costs 260 pounds. In a sale, the price is reduced by 15%. Calculate the sale price of the bicycle.

(Total for Question 8 is 3 marks)

Work out 2/3 + 3/4. Give your answer as a mixed number in its simplest form.

(Total for Question 9 is 3 marks)

Convert the recurring decimal 0.4545... (where the digits 45 recur) to a fraction in its simplest form.

(Total for Question 10 is 3 marks)

Grace is paying for a family holiday. She pays a deposit of 20% of the total price, and then pays the remaining 640 pounds.

(a)Work out the total price of the holiday.(3)

(b)Work out the amount of Grace's deposit.(1)

(Total for Question 11 is 4 marks)

Priya receives a monthly allowance of 60 pounds. She spends 2/5 of her allowance on clothes. She then spends 1/4 of what remains on books. Work out how much money Priya has left.

(Total for Question 12 is 4 marks)

Tom invests 2500 pounds in a savings account that pays 3% per annum compound interest. Calculate the value of his investment after 3 years, giving your answer to the nearest penny.

(Total for Question 13 is 4 marks)

A car is bought for 12000 pounds. In the first year its value decreases by 20%. In the second year its value decreases by a further 15% of its value at the start of that year.

(a)Calculate the value of the car at the end of the second year.(4)

(b)Calculate the overall percentage decrease in the value of the car over the two years.(3)

(Total for Question 14 is 7 marks)

In a sale, a coat is reduced by 15%. The sale price of the coat is 76.50 pounds.

(a)Calculate the original price of the coat before the sale.(3)

(b)Calculate the amount of money saved by buying the coat in the sale.(1)

(Total for Question 15 is 4 marks)

There are 840 pupils at a school. 3/8 of the pupils are boys. 45% of the girls play a musical instrument. Show that the number of girls who play a musical instrument is 236, correct to the nearest whole number.

(Total for Question 16 is 3 marks)

A market trader buys 150 scarves at 4.20 pounds each. She sells all 150 scarves for a total of 819 pounds. Calculate her percentage profit.

(Total for Question 17 is 4 marks)

In a fruit box, apples, oranges and pears are in the ratio 5:3:5. There are 40 apples in the box. 1/4 of the oranges and 1/5 of the pears in the box are found to be rotten and are removed. Calculate the total number of pieces of fruit remaining in the box.

(Total for Question 18 is 4 marks)

A number is increased by 40% and then the result is decreased by 40%.

(a)Show that the overall effect is a decrease from the original number.(1)

(b)Find the overall percentage change, giving your answer as a percentage decrease.(2)

(Total for Question 19 is 3 marks)

A charity receives a donation of 3600 pounds. 5/12 of the money is spent on food parcels. Of the money remaining, 35% is spent on heating, and the rest is saved. Calculate the amount of money that is saved.

(Total for Question 20 is 4 marks)

Mark scheme · CE.M2 Fractions, Decimals and Percentages

Question 1

(a) B1 0.7 oe cao
(a) Answer: 0.7
(b) B1 45% cao
(b) Answer: 45%
(c) B1 3/10 oe cao, simplest form required
(c) Answer: 3/10

Question 2

B1 A cao
Answer: A) 0.6

Question 3

M1 convert all four values to decimals: 0.35, 0.3, 0.32, 0.28
A1 correct order cao: 0.28, 0.3, 32%, 7/20
Answer: 0.28, 0.3, 32%, 7/20

Question 4

M1 96 / 8 = 12 oe
A1 36 cao
Answer: 36

Question 5

M1 10% of 220 = 22 (or 15/100 x 220 seen) oe
A1 33 cao
Answer: 33 g

Question 6

M1 20% of 540 = 108 seen, or 540 x 1.2 oe
A1 648 cao
Answer: 648 pounds

Question 7

M1 25% of 48 = 12 oe
dM1 48 + 12 (dependent on previous method)
A1 60 cao
Answer: 60 pounds

Question 8

M1 15% of 260 = 39 oe
dM1 260 - 39 (dependent on previous method)
A1 221 cao
Answer: 221 pounds

Question 9

M1 common denominator of 12 used: 8/12 + 9/12
A1 17/12 seen
A1 1 5/12 oe cao
Answer: 1 5/12

Question 10

M1 let x = 0.4545..., 100x = 45.4545... seen
M1 99x = 45 (subtracting correctly, dependent on previous method)
A1 5/11 oe cao (accept 45/99 unsimplified for M marks only)
Answer: 5/11

Question 11

(a) M1 recognise 640 represents 100% - 20% = 80%
(a) M1 640 / 0.8 oe (dependent on previous method)
(a) A1 800 cao
(a) Answer: 800 pounds
(b) B1 160 ft from their total in part a
(b) Answer: 160 pounds

Question 12

M1 2/5 x 60 = 24 (clothes)
M1 60 - 24 = 36 (remainder)
M1 1/4 x 36 = 9 (books)
A1 27 cao
Answer: 27 pounds

Question 13

M1 multiplier 1.03 identified, or year-by-year method started
M1 2500 x 1.03³ oe (dependent on previous method)
A1 2731.8175 seen (unrounded value)
A1 2731.82 cao, nearest penny
Answer: 2731.82 pounds

Question 14

(a) M1 12000 x 0.8 oe
(a) A1 9600 (value after year 1)
(a) M1 9600 x 0.85 oe (dependent on previous method)
(a) A1 8160 cao
(a) Answer: 8160 pounds
(b) M1ft (12000 - their 8160) / 12000 oe, ft from part a
(b) M1 x 100 (dependent on previous method)
(b) A1 32% cao
(b) Answer: 32% decrease

Question 15

(a) M1 recognise 76.50 represents 100% - 15% = 85%
(a) M1 76.5 / 0.85 oe (dependent on previous method)
(a) A1 90 cao
(a) Answer: 90 pounds
(b) B1 13.50 ft from their answer to part a
(b) Answer: 13.50 pounds

Question 16

M1 girls = 840 - (3/8 x 840), or 5/8 x 840, = 525
M1 45% of 525 = 236.25 (dependent on previous method)
A1 236 cso, full working shown, answer given in question
Answer: 236

Question 17

M1 cost = 150 x 4.20 = 630
M1 profit = 819 - 630 = 189 (dependent on previous method)
M1 189 / 630 oe (dependent on previous method)
A1 30% cao
Answer: 30%

Question 18

M1 one share = 40 / 5 = 8
M1 oranges = 24, pears = 40 (dependent on previous method)
M1 rotten fruit removed: oranges 1/4 x 24 = 6, pears 1/5 x 40 = 8 (dependent on previous method)
A1 90 cao
Answer: 90 pieces of fruit

Question 19

(a) B1 1.4 x 0.6 = 0.84 shown and 0.84 < 1 stated, so it is a decrease, cso
(a) Answer: 0.84 < 1, so the overall effect is a decrease
(b) M1 100 - 84 = 16 oe, using multiplier 0.84 from part a
(b) A1 16% decrease cao
(b) Answer: 16% decrease

Question 20

M1 5/12 x 3600 = 1500 (food parcels)
M1 3600 - 1500 = 2100 (remainder, dependent on previous method)
M1 35% of 2100 = 735 (heating, dependent on previous method)
A1 1365 cao
Answer: 1365 pounds

Fractions, Decimals and Percentages - Worksheets, Questions and Revision