GCSE Maths · Higher · Chapter 2: Fractions, ratio and proportion · Lesson 1

Calculating with fractions

Grades 4–7About 50 minutesNo calculator41 marks

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NameClassDate

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Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Write $\frac{3}{20}$ as a decimal.
[1 mark]
Answer
A2
Last lesson
Find the highest common factor of $28$ and $42$ .
[1 mark]
Answer
A3
Key Stage 3
Find the area of a triangle with base $10$ cm and height $8$ cm.
[1 mark]
Answer
A4
Key Stage 3
Find the mean of $7, 11, 7, 11, 9$ .
[1 mark]
Answer

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Work out $2 \frac{2}{3} + 1 \frac{3}{4}$ . Give your answer as a mixed number.

Hint Write both as improper fractions, then use a common denominator of 12.

B1
Work out $3 \frac{1}{6} - 1 \frac{4}{5}$ . Give your answer as a mixed number.
[2 marks]
Answer

Example 2

Work out $1 \frac{3}{4} \div 2 \frac{1}{3}$ .

Hint Write both as improper fractions. Dividing by a fraction is the same as multiplying by its reciprocal.

B2
Work out $2 \frac{2}{3} \div 1 \frac{1}{9}$ . Give your answer as a mixed number.
[3 marks]
Answer

Grades 5–6

C1
Write 750 g as a fraction of 2 kg. Give your answer in its simplest form.
[2 marks]
Answer
C2
Work out $\frac{7}{10} \times \frac{5}{14}$ . Give your answer in its simplest form.
[2 marks]
Answer

C3
Work out $5 \div \frac{2}{3}$ . Give your answer as a mixed number.
[2 marks]
Answer
C4
Which is larger, $\frac{5}{7}$ or $\frac{7}{10}$ ? Show how you decide.
[2 marks]
Answer
C5
Tom spends $\frac{2}{5}$ of his money on a game, then $\frac{1}{3}$ of what is left on food. What fraction of his money does he have left?
[2 marks]
Answer
C6
$\frac{3}{8}$ of a number is $27$ . What is the number?
[2 marks]
Answer
C7
A rectangle is $2 \frac{1}{4}$ m long and $1 \frac{2}{3}$ m wide. Work out its area. Give your answer as a mixed number.
[2 marks]
Not drawn accurately
Answer
C8
Work out $(\frac{1}{2} + \frac{2}{5}) \div \frac{3}{10}$ .
[2 marks]
Answer

Grades 6–7

D1
Ria says, " $2 \frac{1}{2} \times 3 \frac{1}{3} = 6 \frac{1}{6}$ , because $2 \times 3 = 6$ and $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$ ."
Explain why Ria is wrong, and work out the correct answer.
[2 marks]

D2
A baker has a bag holding $7 \frac{1}{2}$ kg of flour. Each loaf uses $\frac{5}{8}$ kg of flour.
(a)
How many loaves can be made from the whole bag?
[2 marks]
Answer
(b)
She makes 9 loaves. What fraction of the bag of flour is left? Give your answer in its simplest form.
[3 marks]
Answer
(c)
She uses the flour that is left to make rolls. Each roll uses $\frac{3}{16}$ kg. How many rolls does she make?
[2 marks]
Answer
Total for D2: 7 marks
D3
There are $480$ students in a school. $\frac{5}{12}$ of the students are boys. $\frac{3}{10}$ of the boys walk to school and $\frac{2}{7}$ of the girls walk to school. What fraction of all the students walk to school? Give your answer in its simplest form.
[4 marks]
Answer

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can add, subtract, multiply and divide fractions and mixed numbers.
I can write one quantity as a fraction of another.
I can solve problems with fractions of amounts.

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