Question 1:
Calculate the following
Question 1(a): [1 mark]
\dfrac{1}{3} + \dfrac{1}{3}
Answer type: Fraction
ANSWER: \dfrac{2}{3}
WORKING: \dfrac{1}{3} + \dfrac{1}{3} = \dfrac{2}{3}
Question 1(b): [1 mark]
\dfrac{1}{5} + \dfrac{3}{6}
Answer type: Fraction
ANSWER: \dfrac{7}{10}
WORKING: \dfrac{1}{5} + \dfrac{3}{6} = \dfrac{1}{5} + \dfrac{1}{2} = \dfrac{2}{10} + \dfrac{5}{10} = \dfrac{7}{10}
Question 1(c): [1 mark]
\dfrac{5}{7} - \dfrac{1}{3}
Answer type: Fraction
ANSWER: \dfrac{8}{21}
WORKING: \dfrac{5}{7} - \dfrac{1}{3} = \dfrac{15}{21} - \dfrac{7}{21} = \dfrac{8}{21}
Question 1(d): [2 marks]
\dfrac{8}{11} + \dfrac{3}{6} - \dfrac{1}{11}
Answer type: Fraction
ANSWER: \dfrac{8}{21}
WORKING: \dfrac{8}{11} + \dfrac{3}{6} - \dfrac{1}{11} = \dfrac{16}{22} + \dfrac{11}{22} - \dfrac{2}{22} = \dfrac{27}{22} - \dfrac{2}{22} = \dfrac{25}{22}
Question 2: [3 marks]
John is paid on the first day of every month.
He spends \dfrac{1}{3} of his pay on food and \dfrac{1}{4} of his pay on rent.
What fraction of his pay will John have left? Write your answer in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{5}{12}
WORKING: \dfrac{1}{4} + \dfrac{1}{3} = \dfrac{3}{12} + \dfrac{4}{12} = \dfrac{7}{12}
1 - \dfrac{7}{12} = \dfrac{5}{12}
Question 3: [3 marks]
Sarah has started reading a new book.
On Saturday she reads \dfrac{2}{15} of the book.
On Sunday she reads a further \dfrac{1}{3} of the total number of pages in the book.
On Monday she reads another \dfrac{1}{5} of the total number of pages in the book.
On Tuesday she finishes the book.
What fraction of the book did she read on Tuesday? Write your answer in its simplest form.
Answer type: Fraction
ANSWER: \dfrac{1}{3}
WORKING: \dfrac{2}{15} + \dfrac{1}{3} + \dfrac{1}{5} = \dfrac{2}{15} + \dfrac{5}{15} + \dfrac{3}{15} = \dfrac{10}{15}
1 - \dfrac{10}{15} = \dfrac{5}{15} = \dfrac{1}{3}
Question 4:
A conservation group try to estimate the population of different types of tress that are found in a nearby forest:
\dfrac{1}{18} of the trees are oak, \dfrac{2}{9} of the trees are beech and \dfrac{1}{4} of the trees are pine.
Question 4(a): [3 marks]
What fraction of the trees in the forest are not oak, beech or pine?
Answer type: Fraction
ANSWER: \dfrac{17}{36}
WORKING: \dfrac{1}{18} + \dfrac{2}{9} + \dfrac{1}{4} = \dfrac{2}{36} + \dfrac{8}{36} + \dfrac{9}{36} = \dfrac{19}{36}
1 - \dfrac{19}{36} = \dfrac{17}{36}
Question 4(b): [3 marks]
The group estimates there are 720 trees in the forest. How many of these trees are not oak or pine?
Answer type: Simple text answer
ANSWER: 500
WORKING: \dfrac{2}{36} are oak, hence \dfrac{40}{720} of the trees in the forest are oak.
\dfrac{9}{36} are pine hence \dfrac{180}{720} of the trees are pine.
Hence there are a total of 220 oak and pine trees. So there are 720 -220 = 500 trees in the forest that are not oak or pine.
Question 5: [3 marks]
A rectangular field is measured to be \dfrac{9}{4} km by \dfrac{11}{8} km.
What is the perimeter of the field? Choose the correct answer.
Answer type: Multiple choice type 1
A: 7\dfrac{1}{8} km
B: 3\dfrac{5}{8} km
C: 7\dfrac{1}{4} km
D: 3\dfrac{3}{32} km
ANSWER: C: 7\dfrac{1}{4} km
WORKING: Total perimeter = \dfrac{9}{4} + \dfrac{9}{4} + \dfrac{11}{8} + \dfrac{11}{8} = \dfrac{18}{8} + \dfrac{18}{8} + \dfrac{11}{8} + \dfrac{11}{8} = \dfrac{58}{8} = 7\dfrac{1}{4} km
Question 6: [3 marks]
The passenger list on a cruise ship shows that:
\dfrac{1}{10} of the passengers come from Italy.
\dfrac{1}{4} of the passengers come from Sweden.
520 passengers come from the UK.
How many passengers are there all together?
Answer type: Simple text answer
ANSWER: 800
WORKING: \dfrac{4}{40} from Italy and \dfrac{10}{40} from Sweden.
1 - \bigg( \dfrac{4}{40} + \dfrac{10}{40} \bigg) = \dfrac{26}{40} from the UK.
\dfrac{26}{40} is equivalent to \dfrac{520}{800}, so 520 out of 800 passengers are from the UK.
Hence there are 800 passengers in total.