Unit 8 Section 1 : Mental Division of Whole Numbers

The process of division is just multiplication in reverse.

This means that if 4 3 = 12 then 12 3 = 4 and 12 4 = 3

If you know your multiplication tables well, you should find it reasonably easy to do simple divisions in your head.

For example: you want to work out 42 7, and you remember that 6 7 = 42, so the answer is 6.

When there is more than one operation in a question, you need to remember the order in which operations are carried out. This can be summarised by BODMAS:

If you see two of the same operation you just do them in the order they appear (left to right).

Example Question

Below are three examples of BODMAS used in a question.
(a) 3 + 4 5 = 3 + 20 = 23 (Multiply before Add)
(b) 10 ( 2 + 3 ) = 10 5 = 2 (Brackets before Division)
(c) 20 2 2 = 10 2 = 5 (do operations left to right)

Practice Questions
Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.

(a) What is 3 + 16 2 ?

(b) What is 15 (2 + 3) ?

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

Question 1
Use mental arithmetic to answer these questions (do not use a calculator).

(a) 16 4
(b) 12 6
(c) 15 5
(d) 20 4
(e) 18 9
(f) 40 8
(g) 36 9
(h) 15 3
(i) 64 8
(j) 42 7
(k) 24 6
(l) 32 8
(m) 49 7
(n) 56 8
(o) 45 5

Question 2
Use BODMAS to work out whether these statements are TRUE or FALSE.

(a) 10 2 = 2 10
(b) 12 + 8 2 = 10
(c) 3 + 12 4 = 6
(d) 6 2 + 3 = 6

Question 3
Work out the answers to the following questions (without a calculator).

(a) 3 + 4 8
(b) 8 + 3 6
(c) 8 6 - 4
(d) 12 2 + 5
(e) 5 - 12 3
(f) 14 2 + 8
(g) 3 2 + 8 4
(h) 3 6 - 15 3
(i) 42 7 + 3
(j) 16 4 + 24 6
(k) 8 2 + 5 3
(l) 8 6 - 45 5

Question 4
A pupil works out 200 4 by this method:

200 2 = 100
100 2 = 50

So 200 4 = 50. This works because doing (2) twice is the same as doing (4).
Use similar methods to find the answers to these questions (not a calculator).

(a) 500 4
(b) 52 4
(c) 68 4
(d) 128 4
(e) 224 4
(f) 104 8
(g) 80 16
(h) 112 16
(i) 128 8


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Produced by A.J. Reynolds January 2001