Order these decimals from smallest to largest: 0.45, 0.405, 0.54, 0.045
(2)
5
Calculate 15% of 60.
(2)
6
A school has 200 pupils. 35% of the pupils walk to school, 1/4 of the pupils travel by car, and the rest travel by bus.
(a)How many pupils walk to school?(1)
(b)How many pupils travel by car?(1)
(c)How many pupils travel by bus?(1)
7
Convert 7/20 to a decimal, and then to a percentage.
(2)
8
Tick the calculation with the largest answer: 1/3 of 90, 0.4 of 60, 45% of 50
A) 1/3 of 90
B) 0.4 of 60
C) 45% of 50
9
Show that 3/8 is greater than 0.35.
(3)
10
A recipe uses 250g of flour to make 8 buns. Amelia wants to make 20 buns. How much flour does she need?
(2)
11
Jamal has GBP 45. He spends 2/5 of it on a book, then spends 20% of what remains on a magazine. How much money does he have left?
(3)
12
Write these fractions with a common denominator, then order them from smallest to largest: 2/3, 5/6, 7/12
(2)
13
A decimal number rounds to 7.2 when rounded to 1 decimal place. Give two different numbers it could have been.
(2)
14
In a survey of 60 people, 3/10 preferred tea, 45% preferred coffee, and the rest preferred juice. How many more people preferred coffee than tea?
(3)
15
The number 3.847 is shown.
(a)Round 3.847 to 1 decimal place.(1)
(b)Round 3.847 to the nearest whole number.(1)
16
A jacket normally costs GBP 68. In a sale it is reduced by 15%. Calculate the sale price of the jacket.
(3)
17
Two pupils are discussing fractions and decimals. Priya says: "If you multiply a decimal number by 10, all the digits move one place to the left." Selin says: "3/5 is bigger than 0.65 because 3/5 has a bigger numerator than 0.65 has in its decimal digits."
(a)Explain why Priya is correct. Use an example to support your answer.(2)
(b)Explain why Selin is wrong. Show the correct comparison.(2)
18
A number is decreased by 20% and the result is 96. Work out the original number.
(3)
19
Work out (1/4 + 1/6) x 0.5. Give your answer as a fraction in its simplest form.
(3)
20
A charity raised money over three days. On day 1 they raised 3/8 of the total amount. On day 2 they raised 25% of the total amount. On day 3 they raised the remaining GBP 90. Work out the total amount raised.
(4)
Mark scheme · KS2.M-R2 Reasoning: Fractions, Decimals and Percentages
Question 1
B1 3/6 circled; cao
Answer: 3/6
Question 2
M1 24 / 4 = 6 (finds one quarter) oe
A1 18 cao
Answer: 18
Question 3
B1 3/5 oe; cao
Answer: 3/5
Question 4
M1 compares hundredths/thousandths correctly (e.g. states 0.405 < 0.45) oe
A1 0.045, 0.405, 0.45, 0.54 cao (all four in correct order)
Answer: 0.045, 0.405, 0.45, 0.54
Question 5
M1 finds 10% of 60 = 6 and 5% of 60 = 3 oe
A1 9 cao
Answer: 9
Question 6
(a) B1 70 cao
(a) Answer: 70
(b) B1 50 cao
(b) Answer: 50
(c) B1 80 cao, ft from parts (a) and (b)
(c) Answer: 80
Question 7
B1 0.35 oe cao
B1 35% cao, ft decimal x 100
Answer: 0.35; 35%
Question 8
B1 1/3 of 90 ticked; cao
Answer: 1/3 of 90 (= 30)
Question 9
M1 sets up a common form for comparison, e.g. converts 3/8 towards a decimal or 0.35 towards a fraction /1000 oe
A1 3/8 = 0.375 cao
A1 cso; correct comparison stated, e.g. 0.375 > 0.35 so 3/8 is greater (answer given, method must be shown)
Answer: 3/8 = 0.375, and 0.375 > 0.35, so 3/8 is greater than 0.35.
Question 10
M1 finds the scale factor 20 / 8 = 2.5, or finds flour per bun 250 / 8 = 31.25g, oe
A1 625g cao
Answer: 625g
Question 11
M1 2/5 of 45 = GBP 18 spent on the book, so GBP 27 remains oe
dM1 20% of 27 = GBP 5.40 spent on the magazine, ft from a correct remaining amount
A1 GBP 21.60 cao
Answer: GBP 21.60
Question 12
M1 converts to twelfths: 8/12, 10/12, 7/12 oe
A1 7/12, 2/3, 5/6 cao (correct order using original fractions)
Answer: 7/12, 2/3, 5/6
Question 13
B1 any valid value with 7.15 ≤ x < 7.25, not equal to 7.2, e.g. 7.18
B1 a second different valid value in the same range, e.g. 7.23
Answer: Any two values in the range 7.15 ≤ x < 7.25, e.g. 7.18 and 7.23
Question 14
M1 3/10 of 60 = 18 (tea) oe
M1 45% of 60 = 27 (coffee) oe, ft
A1 9 cao
Answer: 9
Question 15
(a) B1 3.8 cao
(a) Answer: 3.8
(b) B1 4 cao
(b) Answer: 4
Question 16
M1 finds 10% of 68 = 6.80 and 5% of 68 = 3.40 oe
M1 15% of 68 = 10.20, ft
A1 GBP 57.80 cao
Answer: GBP 57.80
Question 17
(a) B1 correct general statement that each digit's place value multiplies by 10 (moves one column to the left)
(a) B1 correct supporting example, e.g. 4.2 x 10 = 42, showing the 4 and 2 each shift one place left
(a) Answer: Priya is correct: multiplying by 10 moves every digit one column to the left, e.g. 4.2 x 10 = 42.
(b) M1 converts 3/5 to a decimal: 3/5 = 0.6
(b) A1 cso; correct conclusion that 0.6 < 0.65, so 3/5 is smaller than 0.65, not bigger (Selin's reasoning about numerators is invalid)
(b) Answer: 3/5 = 0.6, and 0.6 < 0.65, so 3/5 is smaller than 0.65; Selin is wrong.
Question 18
M1 recognises 96 represents 80% of the original number oe
M1 finds 1% = 96 / 80 = 1.2, or equivalent method (e.g. 96 / 0.8), ft
A1 120 cao
Answer: 120
Question 19
M1 converts to a common denominator: 1/4 = 3/12, 1/6 = 2/12, sum = 5/12 oe
dM1 multiplies 5/12 by 0.5 (= 1/2), ft from a correct sum
A1 5/24 oe cao (in simplest form)
Answer: 5/24
Question 20
M1 converts 25% to 1/4 (or 2/8), to compare with eighths oe
M1 days 1 and 2 together = 3/8 + 2/8 = 5/8 of the total oe
dM1 day 3 fraction = 1 - 5/8 = 3/8, so 3/8 of the total = GBP 90, ft from a correct fraction