KS3 Maths · Year 8 · Chapter 7: Fractions · Lesson 1

Adding and subtracting fractions

Year 8About 65 minutesNo calculator51 marks

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Quick questions to start.

A1
Needed today
Find the lowest common multiple of $8$ and $12$ .
[1 mark]
Answer
A2
Needed today
Write $3 \frac{5}{8}$ as an improper fraction.
[1 mark]
Answer
A3
Last lesson
A triangle has sides $20$ cm, $21$ cm and $29$ cm. Is it right-angled? Show how you know.
[1 mark]
Answer
A4
From chapter 1
Increase £ $80$ by $15%$ .
[1 mark]
Answer

Example, then your turn

Year 8

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

Example 1

Work out $\frac{7}{9} + \frac{5}{12}$ . Give your answer as a mixed number.

Hint The lowest common multiple of

9

and

12

36

. Change both fractions to thirty-sixths.

B1
Work out (i) $\frac{7}{10} + \frac{5}{6}$ (ii) $\frac{11}{12} - \frac{3}{8}$ . Give each answer in its simplest form.
[2 marks]
Answer(i) $\dots\dots$ (ii) $\dots\dots$

Example 2

Work out $3 \frac{5}{8} + 2 \frac{3}{4}$ .

Hint Add the whole numbers first. Then add the fraction parts, using eighths.

B2
Work out $4 \frac{2}{3} + 3 \frac{5}{7}$ .
[2 marks]
Answer

Example 3

Work out $7 \frac{1}{4} - 3 \frac{5}{6}$ .

Hint

\frac{1}{4}

is smaller than

\frac{5}{6}

. Either change both to improper fractions, or exchange one whole for twelfths.

B3
Work out $9 \frac{1}{6} - 4 \frac{4}{9}$ .
[2 marks]
Answer

Example 4

Work out $5 \frac{1}{2} - 2 \frac{2}{3} + 1 \frac{3}{4}$ .

Hint Deal with the whole numbers:

5 - 2 + 1 = 4

. Then the fractions, in twelfths.

B4
Work out $6 \frac{1}{3} - 3 \frac{3}{4} + 2 \frac{1}{6}$ .
[3 marks]
Answer

Example 5

A ribbon is $6 \frac{3}{4}$ m long. Ella cuts off a piece $1 \frac{5}{6}$ m long and another piece $2 \frac{2}{3}$ m long. How much ribbon is left?

Hint Add the two pieces first, then take the total away from

6 \frac{3}{4}

B5
A tank holds $10$ litres of water. Jay pours out $2 \frac{3}{5}$ litres and then $1 \frac{3}{4}$ litres. How much water is left in the tank?
[3 marks]
Answer

Practice

Year 8

C1
The cross-multiply method says $\frac{a}{b} + \frac{c}{d} = \frac{a d + b c}{b d}$ Use it to work out $\frac{3}{8} + \frac{5}{12}$ . Give your answer in its simplest form.
[2 marks]
Answer
C2
Work out the missing number: $2 \frac{4}{5} + □ = 7 \frac{1}{3}$ .
[2 marks]
Answer

C3
Work out the mean of these three lengths: $1 \frac{5}{6}$ cm, $2 \frac{1}{4}$ cm and $3 \frac{2}{3}$ cm.
[3 marks]
Answer
C4
You are told that $5 \frac{3}{4} + 2 \frac{5}{7} = 8 \frac{13}{28}$ Use this to write down (i) $8 \frac{13}{28} - 2 \frac{5}{7}$ (ii) $\frac{3}{4} + \frac{5}{7}$ .
[2 marks]
Answer(i) $\dots\dots$ (ii) $\dots\dots$
C5
Which is larger, $\frac{3}{4} + \frac{2}{9}$ or $\frac{5}{6} + \frac{1}{8}$ ? Show your working.
[2 marks]
Answer $\dots\dots\dots$ is larger

Exam-style questions

GCSE Foundation

D1
Ben works out $6 \frac{1}{3} - 2 \frac{3}{4}$ . He writes: " $6 - 2 = 4$ and $\frac{3}{4} - \frac{1}{3} = \frac{5}{12}$ , so the answer is $4 \frac{5}{12}$ ."
Ben is wrong. Explain his mistake and work out the correct answer.
[3 marks]
AnswerCorrect answer $\dots\dots$

D2
The diagram shows a triangle.
Not drawn accurately
(a)
Work out the perimeter of the triangle.
[2 marks]
Answer
(b)
A second triangle has a perimeter of $12 \frac{1}{2}$ cm. How much longer is this perimeter than the first?
[2 marks]
Answer
Total for D2: 4 marks
D3
Jo has a garden. She uses $\frac{3}{8}$ of it for vegetables and $\frac{1}{3}$ of it for flowers. The rest of the garden is grass.
(a)
What fraction of the garden is grass?
[2 marks]
Answer
(b)
The grass covers $35$ m². Work out the area of the whole garden.
[2 marks]
Answer
(c)
How many more square metres are used for vegetables than for flowers?
[2 marks]
Answer
Total for D3: 6 marks
D4
A rectangle has a perimeter of $15 \frac{1}{2}$ cm. Its length is $4 \frac{5}{6}$ cm. Work out its width, $w$ . You must show your working.
[4 marks]
Not drawn accurately
Answer $w = \dots\dots$ cm
D5
Show that $\frac{1}{2} + \frac{1}{3} + \frac{1}{7} + \frac{1}{42} = 1$ .
[3 marks]

Extension

Stretch

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

E1
$a$ and $b$ are positive whole numbers and $\frac{a}{6} + \frac{b}{10} = \frac{47}{30}$ . Find every possible pair of values of $a$ and $b$ .
[4 marks]
Hint 1 · What to try
Write both fractions with the denominator $30$ .
Hint 2 · The first line
$\frac{5 a}{30} + \frac{3 b}{30} = \frac{47}{30}$ , so $5 a + 3 b = 47$ .
Hint 3 · The full method
Try $a = 1, 2, 3, \dots$ up to $9$ . Keep each $a$ that makes $47 - 5 a$ a multiple of $3$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can add and subtract fractions with different denominators.
I can add and subtract mixed numbers, exchanging a whole when I need to.
I can choose an efficient method for a calculation.
I can solve problems in words with fractions.

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