KS3 Maths · Year 7 · Chapter 12: Fractions and decimals · Lesson 1

Adding and subtracting fractions

Year 7About 75 minutesNo calculator47 marks

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Date

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Quick questions to start.

A1
From chapter 10
Write $2 a \times 3 a \times a$ using a power.
[1 mark]
Answer
A2
Needed today
Find the lowest common multiple of $6$ and $8$ .
[1 mark]
Answer
A3
Needed today
Write $2 \frac{3}{4}$ as an improper fraction.
[1 mark]
Answer
A4
Needed today
Write $\frac{15}{20}$ in its simplest form.
[1 mark]
Answer

Example, then your turn

Year 7

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

Example 1

Work out $\frac{5}{6} + \frac{3}{8}$ . Give your answer as a mixed number.

Hint The lowest common multiple of

6

and

8

24

. Change both fractions to twenty-fourths.

B1
Work out each one. Give your answers as simply as possible.
(a) $\frac{3}{4} + \frac{1}{10}$
(b) $\frac{7}{9} + \frac{5}{6}$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 2

Work out $2 \frac{3}{4} + 3 \frac{5}{6}$ .

Hint Add the whole numbers first. Then add the fractions, using twelfths.

B2
Work out each one.
(a) $3 \frac{5}{8} + 1 \frac{1}{6}$
(b) $2 \frac{7}{10} + 1 \frac{3}{4}$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 3

Work out (a) $5 \frac{1}{4} - 2 \frac{2}{3}$ (b) $6 - 2 \frac{3}{5}$ .

Hint In (a),

\frac{3}{12}

is smaller than

\frac{8}{12}

, so change one whole into

\frac{12}{12}

first. Or change both to improper fractions.

B3
Work out each one. Give your answers as simply as possible.
(a) $6 \frac{1}{3} - 2 \frac{5}{6}$
(b) $7 - 3 \frac{3}{8}$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 4

Work out the perimeter of this triangle.

Not drawn accurately

Hint Add the three sides. Whole numbers first, then the fractions in twelfths.

B4
Work out the perimeter of this rectangle.
[3 marks]
Not drawn accurately
Answer $\dots\dots$ cm

Practice

Year 7

C1
Work out $\frac{1}{3} + \frac{1}{4} + \frac{5}{6}$ . Give your answer as a mixed number.
[2 marks]
Answer
C2
Find the missing number. $\frac{2}{3} + □ = 1 \frac{1}{4}$
[2 marks]
Answer

C3
Work out each one. Give your answers as simply as possible.
(a) $4 \frac{1}{6} - 1 \frac{2}{3}$
(b) $8 - 3 \frac{5}{9}$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$
C4
A ribbon is $5 \frac{1}{3}$ m long. Pieces of $1 \frac{3}{4}$ m and $2 \frac{1}{6}$ m are cut off. How much ribbon is left?
[3 marks]
Answer $\dots\dots$ m
C5
Which is bigger, $\frac{3}{4} + \frac{1}{5}$ or $\frac{2}{3} + \frac{3}{10}$ ? Show how you decide.
[2 marks]
Answer $\dots\dots$

Exam-style questions

GCSE Foundation

D1
Tom says, " $\frac{2}{5} + \frac{1}{3} = \frac{3}{8}$ ."
Tom is wrong. Explain his mistake and work out the correct answer.
[2 marks]

D2
Meg walks $2 \frac{3}{4}$ km to the park, then $1 \frac{2}{3}$ km to the shop, then home. She walks $6 \frac{1}{2}$ km in total. How far is it from the shop to her home?
[3 marks]
Answer $\dots\dots$ km
D3
This isosceles triangle has a perimeter of $12 \frac{1}{4}$ cm. Its base is $3 \frac{3}{4}$ cm.
Not drawn accurately
(a)
Work out the length of one of the two equal sides.
[3 marks]
Answer $\dots\dots$ cm
(b)
The base is made $1 \frac{1}{3}$ cm longer. The perimeter stays the same. Work out the new length of each equal side.
[3 marks]
Answer $\dots\dots$ cm
Total for D3: 6 marks
D4
On a school day Sam spends $\frac{1}{3}$ of the day asleep, $\frac{1}{4}$ of the day at school and $\frac{1}{8}$ of the day eating.
(a)
What fraction of the day is left?
[3 marks]
Answer
(b)
A day has $24$ hours. How many hours is this?
[1 mark]
Answer $\dots\dots$ hours
Total for D4: 4 marks
D5
Two mixed numbers add up to $8 \frac{1}{3}$ . Their difference is $2 \frac{1}{2}$ . Work out the two numbers.
[4 marks]
Answer $\dots\dots$ and $\dots\dots$

Extension

Stretch

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

E1
A unit fraction has $1$ on top, such as $\frac{1}{5}$ .
Find three different unit fractions that add up to $1$ . Explain why there is only one way to do it.
[4 marks]
Hint 1 · What to try
If none of the three is $\frac{1}{2}$ , the biggest they can be is $\frac{1}{3} + \frac{1}{4} + \frac{1}{5}$ . Is that enough?
Hint 2 · The first line
So one of them is $\frac{1}{2}$ , and the other two add up to $\frac{1}{2}$ . Try $\frac{1}{3}$ next.
Hint 3 · The full method
$\frac{1}{2} + \frac{1}{3} + \frac{1}{6} = 1$ . With $\frac{1}{4}$ the third would also be $\frac{1}{4}$ , which is not different.

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.
I can subtract when the fraction part is too small.
I can solve problems with fractions in words and shapes.

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