Question 1:
In the first round of a gymnastics competition, James is given a score of 2 \, \dfrac{2}{11}.
His score is later revised to account for the difficulty in that round.
His new score is 2 \, \dfrac{2}{11} \times 1 \, \dfrac{1}{12}
Question 1(a): [2 marks]
What is his new score as a mixed fraction? Choose the correct answer.
Answer type: Multiple choice type 1
A: 2 \, \dfrac{2}{11}
B: 2 \, \dfrac{1}{66}
C: 1 \, \dfrac{5}{6}
D: 2 \, \dfrac{4}{11}
ANSWER: D: 2 \, \dfrac{4}{11}
WORKING: 2 \, \dfrac{2}{11} \times 1 \, \dfrac{1}{12} = \dfrac{24}{11} \times \dfrac{13}{12} = \dfrac{312}{132} = \dfrac{26}{11} = 2 \, \dfrac{4}{11}
Question 1(b): [2 marks]
In the second round of the competition, James scores 7 \, \dfrac{1}{2}.
His score is again revised.
His score is now 7 \, \dfrac{1}{2} \div \dfrac{2}{3}
What is his new score as a mixed fraction? Choose the correct answer.
Answer type: Multiple choice type 1
A: 11 \, \dfrac{1}{4}
B: 10 \, \dfrac{1}{2}
C: 11 \, \dfrac{1}{2}
D: 10 \, \dfrac{1}{4}
ANSWER: A: 11 \, \dfrac{1}{4}
WORKING: 7 \, \dfrac{1}{2} \div \dfrac{2}{3} = \dfrac{15}{2} \div \dfrac{2}{3} = \dfrac{15}{2} \times \dfrac{3}{2} = \dfrac{45}{4} = 11 \, \dfrac{1}{4}
Question 2:
Esther has baked 48 muffins.
\dfrac{1}{6} of the muffins are chocolate.
\dfrac{1}{4} of the muffins are blueberry.
\dfrac{1}{3} of the muffins are lemon.
Question 2(a): [2 marks]
What fraction of the muffins are not chocolate, blueberry or lemon?
Give your answer as a fraction in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{1}{4}
WORKING: \dfrac{1}{6} + \dfrac{1}{4} + \dfrac{1}{3} = \dfrac{2}{12} + \dfrac{3}{12} + \dfrac{4}{12} = \dfrac{9}{12}
1 - \dfrac{9}{12} = \dfrac{3}{12} = \dfrac{1}{4}
Question 2(b): [1 mark]
How many of the muffins are not chocolate, blueberry or lemon?
Answer type: Simple text answer
ANSWER: 12
WORKING: 48 \times \dfrac{1}{4} = 12
Question 3:
Four friends are ordering pizza from a take away.
The amount of pizza each person eats is shown as a fraction below.
Matthew eats \dfrac{4}{5} of a pizza.
Lily eats \dfrac{3}{4} of a pizza.
George eats \dfrac{7}{8} of a pizza.
Sam eats \dfrac{5}{6} of a pizza.
Question 3(a): [2 marks]
Which person eats the most pizza?
Answer type: Multiple choice type 2
A: Matthew
B: Lily
C: George
D: Sam
ANSWER: George
WORKING: Equivalent fractions are: \dfrac{96}{120}, \, \dfrac{90}{120}, \, \dfrac{105}{120}, \, \dfrac{100}{120}.
The largest is \dfrac{105}{120}. So George ate the most pizza.
Question 3(b): [2 marks]
4 pizzas are ordered in total.
How much pizza is left ? Give your answer as a fraction in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{89}{120}
WORKING: Add together the amount each person has left.
\dfrac{24}{120} + \dfrac{30}{120} + \dfrac{15}{120} + \dfrac{20}{120} = \dfrac{89}{120}.
Question 4:
A farmer owns a field which has an area of 9 km^2.
Question 4(a): [2 marks]
He uses \dfrac{4}{5} of this field to grow potatoes.
How much of the field is used to grow potatoes? Give your answer as a fraction in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{36}{5} km^2
WORKING: 9 \times \dfrac{4}{5} = \dfrac{36}{5}.
Question 4(b): [2 marks]
The farmer owns another field which measures \dfrac{3}{8} km by 1 \, \dfrac{5}{12} km.
What is the area of the field? Give your answer as a fraction in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{17}{32} km^2
WORKING: \dfrac{3}{8} \times 1 \, \dfrac{5}{12} = \dfrac{3}{8} \times \dfrac{17}{12} = \dfrac{1}{8} \times \dfrac{17}{4} = \dfrac{17}{32}
Question 5:
If a = 1 \, \dfrac{1}{7} and b = 3 \, \dfrac{1}{3}:
Question 5(a): [2 marks]
What is the value of ab as a mixed fraction in simplest form? Choose the correct answer.
Answer type: Multiple choice type 1
A: 16 \, \dfrac{5}{21}
B: 3 \, \dfrac{17}{21}
C: 3 \, \dfrac{4}{21}
D: 3 \, \dfrac{20}{21}
ANSWER: B: 3 \, \dfrac{17}{21}
WORKING: 1 \, \dfrac{1}{7} \times 3 \, \dfrac{1}{3} = \dfrac{8}{7} \times \dfrac{10}{3} = \dfrac{80}{21} = 3 \, \dfrac{17}{21}
Question 5(b): [2 marks]
What is the value of a + b as a mixed fraction in simplest form? Choose the correct answer.
Answer type: Multiple choice type 1
A: 4 \, \dfrac{10}{21}
B: 3 \, \dfrac{17}{21}
C: 1 \, \dfrac{4}{5}
D: 4 \, \dfrac{20}{21}
ANSWER: A: 4 \, \dfrac{10}{21}
WORKING: 1 \, \dfrac{1}{7} + 3 \, \dfrac{1}{3} = \dfrac{8}{7} + \dfrac{10}{3} = \dfrac{24}{21} + \dfrac{70}{21} = \dfrac{94}{21} = 4 \, \dfrac{10}{21}
Question 6:
Natasha is cutting up rope.
She has 900 cm of rope.
Natasha uses \dfrac{1}{5} of the rope to tie up a parcel.
She uses \dfrac{1}{3} of the rope for a craft project.
Question 6(a): [2 marks]
What fraction of the original rope remains? Give your answer as a fraction in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{7}{15}
WORKING: \dfrac{1}{5} + \dfrac{1}{3} = \dfrac{3}{15} + \dfrac{5}{15} = \dfrac{8}{15}
1 - \dfrac{8}{15} = \dfrac{7}{15}
Question 6(b): [2 marks]
Natasha then cuts up the remaining rope into four equal pieces.
What size, in cm, is each of these equal pieces of rope?
Answer type: Simple text answer
ANSWER: 105 cm
WORKING: \dfrac{7}{15} \times 900 = 420
\dfrac{420}{4} = 105