Convert each fraction to a decimal and to a percentage.
(a)Convert 1/4 to a decimal and a percentage.(1)
(b)Convert 3/5 to a decimal and a percentage.(1)
(c)Convert 7/10 to a decimal and a percentage.(1)
(d)Convert 1/8 to a decimal and a percentage.(1)
2
Write these values in order of size, starting with the smallest: 0.6, 3/4, 55%, 0.7
(2)
3
Simplify each fraction fully.
(a)Simplify 12/18(1)
(b)Simplify 15/20(1)
(c)Simplify 24/36(1)
4
Calculate the following percentages of amounts.
(a)A charity raises 340 pounds at a fun run. 15% of this is set aside for admin costs. Calculate the amount set aside for admin costs.(2)
(b)A hiking route is 65 km long. 8% of the route is uphill. Calculate the length of the uphill section, giving your answer in km.(2)
5
Work out each answer, giving your answer as a fraction in its simplest form.
(a)Work out 1/3 + 1/4(2)
(b)Work out 5/6 - 1/3(2)
6
Work out each answer, giving your answer as a fraction in its simplest form.
(a)Work out 2/3 x 3/5(2)
(b)Work out 3/4 divide by 1/2(2)
7
A recipe for 8 people uses 2 1/2 cups of flour. Priya wants to make enough of the recipe for 12 people, which is 1 1/2 times the original recipe. Calculate how many cups of flour Priya needs.
(3)
8
A coat has a normal price of 68 pounds. In a sale it is reduced by 15%. Calculate the sale price of the coat.
(3)
9
Sophie's annual salary increases from 24000 pounds to 25800 pounds. Calculate the percentage increase in her salary.
(3)
10
A television is reduced by 12% in a sale. The sale price is 220 pounds. Calculate the original price of the television.
(3)
11
A laptop has a price of 540 pounds before VAT is added. VAT is charged at 20%. Calculate the total price of the laptop including VAT.
(2)
12
Two furniture shops sell the same sofa. Shop A has a marked price of 84 pounds with 25% off in a sale. Shop B has a marked price of 88 pounds with 30% off in a sale.
(a)Work out the sale price at Shop A.(1)
(b)Work out the sale price at Shop B.(1)
(c)State which shop offers the cheaper price for the sofa and find the difference in price.(2)
13
A school has 1200 students. 5/8 of the students are girls. 3/10 of the girls study French. Calculate the number of girls who study French.
(3)
14
Show that 0.4 recurring (0.4444...) is equal to 4/9.
(3)
15
A car is valued at 12000 pounds. It depreciates by 15% in the first year, then by a further 10% of its new value in the second year. Calculate its value at the end of the second year.
(3)
16
A price of 150 pounds is increased by 20%, and then the new price is decreased by 20%.
(a)Calculate the final price after both changes.(3)
(b)Hence state, with a reason, whether the final price is equal to the original price of 150 pounds.(1)
17
Tom spends 2/5 of his monthly pay on rent. He then spends 1/4 of what remains on food. After paying for rent and food, Tom has 540 pounds left. Calculate Tom's monthly pay.
(4)
18
Aisha invests 2500 pounds in a savings account paying compound interest at a rate of 3.5% per annum. Calculate the value of her investment after 3 years. Give your answer to the nearest penny.
(4)
19
Fatima spends 3/8 of her savings on a laptop. She then spends 20% of what remains on accessories. After both purchases she has 210 pounds left. Calculate how much Fatima had in her savings originally.
(4)
20
A trader buys 60 identical phones for a total cost of 9000 pounds. She sells 3/4 of the phones at a profit of 25% on the cost price of each phone. She sells the remaining phones at a loss of 10% on the cost price of each phone. Calculate the trader's overall percentage profit or loss for the whole transaction. Give your answer correct to 1 decimal place.
(5)
Mark scheme · KS3.M-N2 Number: Fractions, Decimals, Percentages
Question 1
(a) B1 0.25 and 25% cao
(a) Answer: 0.25 = 25%
(b) B1 0.6 and 60% cao
(b) Answer: 0.6 = 60%
(c) B1 0.7 and 70% cao
(c) Answer: 0.7 = 70%
(d) B1 0.125 and 12.5% cao
(d) Answer: 0.125 = 12.5%
Question 2
M1 all four values correctly written as decimals: 0.6, 0.75, 0.55, 0.7 oe
A1 correct order cao
Answer: 55%, 0.6, 0.7, 3/4
Question 3
(a) B1 2/3 cao
(a) Answer: 2/3
(b) B1 3/4 cao
(b) Answer: 3/4
(c) B1 2/3 cao
(c) Answer: 2/3
Question 4
(a) M1 10% = 34 and 5% = 17, or 340 x 0.15 oe
(a) A1 51 (pounds) cao
(a) Answer: 51 pounds
(b) M1 65 x 0.08 oe
(b) A1 5.2 (km) cao
(b) Answer: 5.2 km
Question 5
(a) M1 common denominator of 12 used: 4/12 + 3/12 oe
(a) A1 7/12 cao
(a) Answer: 7/12
(b) M1 common denominator of 6 used: 5/6 - 2/6 oe
(b) A1 1/2 cao
(b) Answer: 1/2
Question 6
(a) M1 (2 x 3)/(3 x 5) = 6/15 oe
(a) A1 2/5 cao
(a) Answer: 2/5
(b) M1 3/4 x 2/1 oe (keep, change, flip shown)
(b) A1 1 1/2 oe 3/2 cao
(b) Answer: 1 1/2 (3/2)
Question 7
M1 2 1/2 and 1 1/2 written as improper fractions: 5/2 and 3/2 oe
M1 5/2 x 3/2 = 15/4 oe
A1 3 3/4 cups oe cao
Answer: 3 3/4 cups
Question 8
M1 15% of 68 = 10.20 oe, or multiplier 0.85 identified
M1 68 - 10.20 oe, or 68 x 0.85
A1 57.80 (pounds) cao
Answer: 57.80 pounds
Question 9
M1 increase = 25800 - 24000 = 1800 oe
M1 1800/24000 (x 100) oe
A1 7.5% cao
Answer: 7.5%
Question 10
M1 recognises sale price = 88% of original, e.g. 0.88 x P = 220 oe
M1 P = 220/0.88
A1 250 (pounds) cao
Answer: 250 pounds
Question 11
M1 540 x 1.2 oe, or 540 + (540 x 0.2)
A1 648 (pounds) cao
Answer: 648 pounds
Question 12
(a) B1 63 (pounds) cao
(a) Answer: 63 pounds
(b) B1 61.60 (pounds) cao
(b) Answer: 61.60 pounds
(c) B1 Shop B stated as cheaper ft from (a) and (b)
(c) B1 difference of 1.40 pounds cao
(c) Answer: Shop B is cheaper by 1.40 pounds
Question 13
M1 5/8 x 1200 = 750 oe (number of girls)
M1 3/10 x 750 oe
A1 225 cao
Answer: 225 girls
Question 14
M1 sets x = 0.4444... and forms 10x = 4.4444... oe
M1 subtracts to get 9x = 4 oe
A1 x = 4/9 cso (answer given, full method required)
Answer: 4/9
Question 15
M1 12000 x 0.85 = 10200 oe
M1 10200 x 0.9 oe
A1 9180 (pounds) cao
Answer: 9180 pounds
Question 16
(a) M1 150 x 1.2 = 180 oe
(a) M1 180 x 0.8 oe
(a) A1 144 (pounds) cao
(a) Answer: 144 pounds
(b) B1 no, with correct reason, e.g. final price 144 is 6 pounds less than 150 because the 20% decrease is taken from the larger, increased price (180) oe ft
(b) Answer: No; the final price is 144 pounds, 6 pounds less than the original 150 pounds
Question 17
M1 remaining after rent = 3/5 of pay oe
M1 food = 1/4 x 3/5 = 3/20 of pay oe
M1 remaining after food = 3/5 - 3/20 = 9/20 of pay, set equal to 540 oe