Question 1:
Which is greater:
Question 1(a): [1 mark]
\dfrac{7}{25} or 0.3.
Answer type: Multiple choice type 1
A: \dfrac{7}{25}
B: 0.3
ANSWER: B: 0.3
WORKING: \dfrac{7}{25} = \dfrac{28}{100} = 0.28, so 0.3 is bigger.
Question 1(b): [1 mark]
\dfrac{2}{3} or 60 \%
Answer type: Multiple choice type 1
A: \dfrac{2}{3}
B: 60 \%
ANSWER: A: \dfrac{2}{3}
WORKING: \dfrac{2}{3} = 0. \dot 6 = 66. \dot 6 \% so \dfrac{2}{3} is bigger.
Question 2:
Express the following as fractions in their simplest form:
Question 2(a): [1 mark]
0.58
Answer type: Fraction
ANSWER: \dfrac{29}{50}
WORKING: 0.58 = \dfrac{58}{100} = \dfrac{29}{50}
Question 2(b): [1 mark]
0.256
Answer type: Fraction
ANSWER: \dfrac{32}{125}
WORKING: 0.256 = \dfrac{256}{1000} = \dfrac{32}{125}
Question 3:
Convert the following fractions to percentages:
Question 3(a): [1 mark]
\dfrac{6}{10}
Answer type: Simple text answer
ANSWER: 60 \%
WORKING: \dfrac{6}{10} = \dfrac{60}{100} = 60 \%
Question 3(b): [1 mark]
\dfrac{32}{50}
Answer type: Simple text answer
ANSWER: 64 \%
WORKING: \dfrac{32}{50} = \dfrac{64}{100} = 64 \%
Question 3(c): [1 mark]
\dfrac{3}{5}
Answer type: Simple text answer
ANSWER: 60 \%
WORKING: \dfrac{3}{5} = \dfrac{60}{100} = 60 \%
Question 3(d): [1 mark]
\dfrac{13}{20}
Answer type: Simple text answer
ANSWER: 65 \%
WORKING: \dfrac{13}{20} = \dfrac{65}{100} = 65 \%
Question 4:
Convert the following percentages to decimals:
Question 4(a): [1 mark]
77 \%
Answer type: Simple text answer
ANSWER: 0.77
Question 4(b): [1 mark]
25 \%
Answer type: Simple text answer
ANSWER: 0.25
Question 4(c): [1 mark]
60 \%
Answer type: Simple text answer
ANSWER: 0.6
Question 4(d): [1 mark]
10 \%
Answer type: Simple text answer
ANSWER: 0.1
Question 4(e): [1 mark]
75 \%
Answer type: Simple text answer
ANSWER: 0.75
Question 5:
Esther has baked 40 cookies.
20 \% of the cookies are chocolate.
\dfrac{1}{4} of the cookies are blueberry.
0.3 of the cookies are lemon.
The rest are plain.
Question 5(a): [2 marks]
How many cookies are plain?
Answer type: Simple text answer
ANSWER: 10
WORKING: 20 \% + \dfrac{1}{4} + 0.3 = 0.2 + 0.25 + 0.3 = 0.75
1 - 0.75 = 0.250.25 \times 40 = 10 cookies are plain.
Question 5(b): [1 mark]
Next week Esther bakes cookies again in the same ratio.
This time ester bakes 60 cookies. How many lemon cookies does she bake this week?
Answer type: Simple text answer
ANSWER: 18
WORKING: 0.3 \times 60 = 18
Question 6: [2 marks]
Tom’s Grandma has £60 to give to her four grandchildren.
Tom gets \dfrac{1}{3} of the amount, Alice gets 0.25 of the amount, John gets 20 \% of the amount and Susan gets the rest.
Who receives the most amount of money?
Answer type: Multiple choice type 1
A: Tom
B: Alice
C: John
D: Susan
ANSWER: A: Tom
WORKING: Tom: 60 \times \dfrac{1}{3} = £20
Alice: 60 \times 0.25 = £15
John: 20 \% of 60 = £12
Susan: 60 - 20 - 15 - 12 = £13
So Tom receives the most.
Question 7:
Four friends order pizza from a take away.
The amount of pizza each person eats is shown as a fraction below.
Matthew eats 0.8 of a pizza.
Lily eats \dfrac{3}{4} of a pizza.
George eats 77 \% of a pizza.
Sam eats 82 \% of a pizza.
Question 7(a): [2 marks]
Which person eats the most pizza?
Answer type: Multiple choice type 1
A: Matthew
B: Lily
C: George
D: Sam
ANSWER: D: Sam
WORKING: Equivalent percentages are 80 \%, \, 75 \%, \, 77 \%, \, 82 \%. Hence Sam eats the most at 82 \%.
Question 7(b): [2 marks]
4 pizzas are ordered in total. How much pizza is left? Write the answer as a fraction.
Answer type: Fraction
ANSWER: \dfrac{43}{200}
WORKING: \dfrac{314}{400} has been eaten, so the total fraction left is \dfrac{86}{400} = \dfrac{43}{200}