Pack B — Fluency

Mathematics

Year 7 · 7.5 Fractions & Percentages

Pack B · Fluency

Name: _________________________________

Date: _________________ Class: ___________

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

BronzeQuestions 1–10

1.
Find a fraction equivalent to $\dfrac{{num}}{{den}}$ with a denominator greater than 50. Justify that it is equivalent.
2.
Simplify $\dfrac{{num}}{{den}}$ fully. State the HCF you used and why dividing by it gives the simplest form.
3.
Which fraction is larger: $\dfrac{{a}}{{d}}$ or $\dfrac{{b}}{{d}}$ ? Justify by explaining what the numerator tells you.
4.
Calculate $\dfrac{{a}}{{d}} + \dfrac{{b}}{{d}}$ and simplify your answer. Explain why the denominator does not change when adding.
5.
Calculate $\dfrac{{a}}{{d}} - \dfrac{{b}}{{d}}$ in its simplest form. Check your answer by adding back.
6.
Find $\dfrac{{num}}{{den}}$ of 32. Explain why you divide by the denominator to find a unit fraction of an amount.
7.
Find 50% of 60 in two different ways. Show both methods give the same answer.
8.
Write 2 $\,\dfrac{{num}}{{den}}$ as an improper fraction. Justify by explaining what each whole number contributes.
9.
Write $\dfrac{{num}}{{den}}$ as a mixed number. Check by converting back to an improper fraction.
10.
Write $\dfrac{{num}}{{den}}$ as a decimal. Explain the connection between the fraction and the decimal.

SilverQuestions 11–20

11.
Calculate $\dfrac{{a}}{{p}} + \dfrac{{b}}{{q}}$ . Give your answer in its simplest form.
12.
Calculate $\dfrac{{a}}{{p}} - \dfrac{{b}}{{q}}$ . Give your answer in its simplest form.
13.
Calculate $\dfrac{{a}}{{p}} \times \dfrac{{b}}{{q}}$ . Give your answer in its simplest form.
14.
Calculate $\dfrac{{a}}{{p}} \div \dfrac{{b}}{{q}}$ . Give your answer in its simplest form.
15.
Find $\dfrac{{num}}{{den}}$ of 60.
16.
Write 60% as (a) a decimal and (b) a fraction in its simplest form.
17.
Find 30% of 90.
18.
Calculate $1\,\dfrac{{a}}{{p}} + 2\,\dfrac{{b}}{{q}}$ .
19.
Write $\dfrac{{a}}{{p}}$ , $\dfrac{{b}}{{q}}$ , and $\dfrac{{c}}{{r}}$ in order from smallest to largest.
20.
Increase £60 by 15%.

GoldQuestions 21–30

21.
Find the HCF of 30 and 42, then use it to simplify $\dfrac{{a}}{{b}}$ fully.
22.
What is 15% of −£60?
23.
Calculate $1\,\dfrac{{a}}{{p}} \times 2\,\dfrac{{b}}{{q}}$ .
24.
Calculate $3\,\dfrac{{a}}{{p}} \div 1\,\dfrac{{b}}{{q}}$ .
25.
Decrease £200 by 45%.
26.
Write $\dfrac{{num}}{{den}}$ as a decimal. State whether it is terminating or recurring.
27.
Write $-\dfrac{{a}}{{p}}$ and $-\dfrac{{b}}{{q}}$ in order from smallest to largest.
28.
Find the value of $3a + 1$ when $a = \dfrac{{num}}{{den}}$ .
29.
Find $\dfrac{{num}}{{den}}$ of 3 m. Give your answer in centimetres.
30.
35% of a number is 63. What is the number?

PlatinumQuestions 31–40

31.
A jacket costs £120. It is reduced by 20% and then by a further 15%. What is the final price?
32.
After a 25% increase, a price is £90. What was the original price?
33.
Solve $\dfrac{{num}}{{den}} \times x = 18$ .
34.
Find the value of $a^2 + b$ when $a = \dfrac{{anum}}{{aden}}$ and $b = \dfrac{{bnum}}{{bden}}$ .
35.
Calculate $2\,\dfrac{{a}}{{p}} + 1\,\dfrac{{b}}{{q}} - \dfrac{{c}}{{r}}$ .
36.
Arrange in order from smallest to largest: $-\dfrac{3}{4},\; \dfrac{1}{3},\; -\dfrac{1}{2},\; \dfrac{2}{5}$ .
37.
Convert the recurring decimal $0.\overline{{dig}}$ to a fraction in its simplest form.
38.
A price changes from £60 to £45. Find the percentage change and state whether it is an increase or decrease.
39.
$\dfrac{{a}}{{b}}$ of a class of 48 students passed a test. Of those who passed, $\dfrac{{c}}{{d}}$ also completed the homework. How many students both passed and completed the homework?
40.
Shop A sells 250g of cereal for £0.90. Shop B sells the same cereal: 400g for £1.32. Which is the better value? Show your working.