Pack B — Fluency

Mathematics

Year 8 · 8.1 Fractions review

Pack B · Fluency

Name: _________________________________

Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10

1.
Convert the improper fraction $\dfrac{{n}}{{d}}$ to a mixed numeral.
2.
Convert the mixed numeral $3\tfrac{{n}}{{d}}$ to an improper fraction.
3.
Simplify the fraction $\dfrac{{n}}{{d}}$ to its simplest form.
4.
Write $\dfrac{{n}}{{d}}$ as an equivalent fraction with denominator 30.
5.
Calculate $\dfrac{{a}}{{d}} + \dfrac{{b}}{{d}}$ and simplify if possible.
6.
Calculate $\dfrac{{a}}{{d1}} + \dfrac{{b}}{{d2}}$ . Give your answer in simplest form.
7.
Calculate $\dfrac{{a}}{{d1}} \times \dfrac{{b}}{{d2}}$ . Give your answer in simplest form.
8.
Calculate $\dfrac{{a}}{{d1}} \div \dfrac{{b}}{{d2}}$ . Give your answer in simplest form.
9.
Write 65% as (a) a decimal and (b) a fraction in its simplest form.
10.
Write $\dfrac{{n}}{{d}}$ as a decimal and as a percentage.

SilverQuestions 11–20

11.
Calculate $\dfrac{{a}}{{d1}} - \dfrac{{b}}{{d2}}$ . Give your answer in simplest form.
12.
Calculate $3\tfrac{{n1}}{{d1}} + 2\tfrac{{n2}}{{d2}}$ .
13.
Find $\dfrac{{num}}{{den}}$ of 450 g.
14.
Calculate $\dfrac{{a}}{{d1}} \times 27$ where $n$ is a whole number. Give the answer in simplest form.
15.
Calculate $\dfrac{{a}}{{d1}} \div 6$ .
16.
Order from smallest to largest: $\dfrac{2}{3}$ , $\dfrac{5}{8}$ , $\dfrac{7}{12}$ .
17.
Convert the recurring decimal $0.\overline{{d}}$ to a fraction in its simplest form.
18.
Calculate $\dfrac{{a}}{{d1}} + \dfrac{{b}}{{d2}} - \dfrac{{c}}{{d3}}$ .
19.
Write 0.625 as a fraction in its simplest form.
20.
Calculate $3\tfrac{{n1}}{{d1}} \times \dfrac{{n2}}{{d2}}$ .

GoldQuestions 21–30

21.
A pizza is cut into 8 equal slices. Tomás eats $\tfrac{3}{8}$ , and his sister eats $\tfrac{1}{4}$ of the whole pizza. What fraction of the pizza is left?
22.
A bottle holds 800 ml. Joëlle drinks $\tfrac{2}{5}$ of it on the way to school and $\tfrac{1}{4}$ of the remainder at break. How many ml are left?
23.
Find $25\%$ of $\dfrac{{num}}{{den}}$ of 400 chf.
24.
Calculate $\dfrac{{a}}{{d1}} \div \dfrac{{b}}{{d2}} + \dfrac{{c}}{{d3}}$ .
25.
In a school survey, $\tfrac{2}{5}$ of the students chose Maths and 30% chose English. The rest chose Science. What fraction chose Science? Give your answer as a fraction in simplest form.
26.
Calculate $6\tfrac{{n1}}{{d1}} - 3\tfrac{{n2}}{{d2}}$ .
27.
Order from smallest to largest: 0.6, $\tfrac{5}{8}$ , 62%.
28.
A recipe for 8 pancakes uses $\tfrac{3}{4}$ cup of flour. How much flour is needed for 12 pancakes? Give the answer as a mixed numeral if possible.
29.
Calculate $\left(\dfrac{{a}}{{d1}} + \dfrac{{b}}{{d2}}\right) \times \dfrac{{n}}{{m}}$ .
30.
Write 87.5% as a fraction in its simplest form.

PlatinumQuestions 31–40

31.
Calculate $\dfrac{\tfrac{2}{3} + \tfrac{1}{4}}{\tfrac{5}{6} - \tfrac{1}{3}}$ .
32.
A jug is $\tfrac{2}{3}$ full of juice. After pouring out 600 ml, it is $\tfrac{1}{4}$ full. How many ml does the jug hold when full?
33.
Convert the recurring decimal $0.\overline{{ab}}$ to a fraction in its simplest form.
34.
A test has 60 questions. Léa answered $\tfrac{3}{5}$ of them correctly. Of the remainder, $\tfrac{1}{4}$ were left blank and the rest were wrong. How many were wrong?
35.
Show that $0.\overline{9} = 1$ by an algebraic argument.
36.
A pile of marbles is shared among three children. Anna takes $\tfrac{1}{4}$ , Ben takes $\tfrac{2}{5}$ of what is left, and Carla takes the remaining 18. How many marbles were in the pile?
37.
Two fractions $\tfrac{a}{b}$ and $\tfrac{c}{d}$ are equivalent if $ad = bc$ . Determine whether $\tfrac{12}{18}$ and $\tfrac{20}{30}$ are equivalent, and explain.
38.
Find a fraction $\tfrac{p}{q}$ between $\tfrac{3}{8}$ and $\tfrac{1}{2}$ with a denominator less than 10.
39.
A fraction $\tfrac{n}{n+5}$ simplifies to $\tfrac{3}{4}$ . Find $n$ .
40.
Show that the sum $1 + \tfrac{1}{2} + \tfrac{1}{4} + \tfrac{1}{8}$ can be written as a single improper fraction, and explain whether the pattern $1 + \tfrac{1}{2} + \tfrac{1}{4} + \ldots + \tfrac{1}{2^n}$ ever reaches 2.