KS3 Maths · Year 7 · Chapter 12: Fractions and decimals · Lesson 5

Division with large and small numbers

Year 7About 75 minutesNo calculator47 marks

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Date

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Quick questions to start.

A1
Last lesson
Work out $0.6 \times 0.07$ .
[1 mark]
Answer
A2
Needed today
Work out $4.8 \div 6$ .
[1 mark]
Answer
A3
Needed today
Work out $270 \div 9$ .
[1 mark]
Answer
A4
From chapter 10
Work out $5 a - b$ when $a = 3$ and $b = 4$ .
[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 (a) $36 \div 0.4$ (b) $15 \div 0.03$ .

Hint Multiply both numbers by

10

100

until you divide by a whole number. The answer does not change.

B1
Work out each one.
(a) $24 \div 0.6$
(b) $63 \div 0.09$
(c) $5 \div 0.2$
[3 marks]
Answer(a) $\dots$ (b) $\dots$ (c) $\dots$

Example 2

Work out (a) $0.48 \div 60$ (b) $90 \div 3000$ .

Hint Divide both numbers by

10

100

1000

until you divide by a single digit.

B2
Work out each one.
(a) $0.35 \div 70$
(b) $42 \div 600$
(c) $8 \div 400$
[3 marks]
Answer(a) $\dots$ (b) $\dots$ (c) $\dots$

Example 3

Work out (a) $2.4 \div 0.08$ (b) $0.56 \div 0.7$ .

Hint Multiply both by

100

in (a) and by

10

in (b), so you divide by a whole number.

B3
Work out each one.
(a) $3.6 \div 0.04$
(b) $0.81 \div 0.9$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 4

A ribbon $7.5$ m long is cut into pieces $0.25$ m long. How many pieces are there?

Hint Work out

7.5 \div 0.25

. Multiply both by

100

. Check your answer by multiplying.

B4
A jug holds $1.8$ litres. How many glasses holding $0.15$ litres each can it fill? Check your answer by multiplying.
[2 marks]
Answer $\dots\dots$ glasses

Practice

Year 7

C1
$391 \div 17 = 23$ . Use this fact to work out
(a) $39.1 \div 17$
(b) $391 \div 1.7$
(c) $3.91 \div 0.17$
[3 marks]
Answer(a) $\dots$ (b) $\dots$ (c) $\dots$
C2
Solve each equation.
(a) $0.5 t = 14$
(b) $20 x = 0.6$
[2 marks]
Answer(a) $t = \dots$ (b) $x = \dots$

C3
Which of these have the same answer as $12 \div 3$ ?
$A 1.2 \div 0.3$ $B 120 \div 0.3$
$C 0.12 \div 0.03$ $D 1.2 \div 3$
[2 marks]
Answer $\dots\dots$
C4
Find each missing number.
(a) $4.5 \div □ = 90$
(b) $□ \div 0.3 = 70$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$
C5
$a = 1.2$ , $b = 0.04$ and $c = 300$ . Work out
(a) $a \div b$
(b) $a \div c$
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Exam-style questions

GCSE Foundation

D1
Ava says, " $5 \div 0.5 = 2.5$ , because dividing always makes a number smaller."
Ava is wrong. Explain why and give the correct answer.
[2 marks]

D2
A water cooler holds $18$ litres.
(a)
How many cups holding $0.25$ litres can be filled from the cooler?
[2 marks]
Answer $\dots\dots$ cups
(b)
On Monday each person drinks $0.3$ litres. The cooler is emptied. How many people drank from it?
[2 marks]
Answer $\dots\dots$ people
(c)
The $18$ litres cost $£2.70$ . Work out the cost of $1$ litre.
[2 marks]
Answer $£ \dots\dots$
Total for D2: 6 marks
D3
This rectangle has an area of $4.2$ m². Its width is $0.7$ m.
Not drawn accurately
(a)
Work out its length.
[2 marks]
Answer $\dots\dots$ m
(b)
Work out its perimeter.
[2 marks]
Answer $\dots\dots$ m
Total for D3: 4 marks
D4
Work out each of these. Then put them in order of size, smallest first.
$6 \div 0.3 0.6 \div 3060 \div 0.03 0.06 \div 0.3$
[3 marks]
Answer $\dots\dots$ , $\dots\dots$ , $\dots\dots$ , $\dots\dots$
D5
A $0.4$ kg bag of seeds costs $£3.20$ . A $0.25$ kg bag of the same seeds costs $£2.10$ .
Which bag is better value? Show your working.
[3 marks]

Extension

Stretch

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

E1
Put $0.2$ , $0.5$ , $4$ and $20$ in the boxes, one number in each box, to make the answer as big as possible.
$□ \div □ + □ \div □$
What is the biggest answer?
[4 marks]
Hint 1 · What to try
Put big numbers on top of a division and small numbers underneath.
Hint 2 · The first line
$20 \div 0.2 = 100$ is the biggest single division you can make.
Hint 3 · The full method
Then compare $4 \div 0.5$ with $0.5 \div 4$ .
Answer $\dots\dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can divide by a decimal by first making it a whole number.
I can divide by a large number by making it a single digit.
I can use division with decimals to solve problems.

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