CHAPTER 1

Whole Numbers

Place Value In Whole Numbers

The position a digit has in a number is called its PLACE

VALUE. For WHOLE NUMBERS the PLACE VALUES

are as follows:

Millions Hundred Thousands

Ten Thousands

Thousands Hundreds Tens Units

1 000 000 100 000 10 000 1000 100 10 1

Non-Calculator Methods for Addition and Subtraction

When adding or subtracting numbers without a calculator

make sure that the columns for each place value are

carefully lined up in the number you are working with.

eg 1 1 8 7 eg 2 1 7 5 4

5 4 - 4 7 0

+ 3 2 1 0 1 2 8 4

3 4 5 1

Multiplying a Whole Number by 10, 100, 1000 …. When you multiply a whole number by 10 you add 1 zero. When you multiply a whole number by 100 you add 2 zeroes. When you multiply a whole number by 1000 you add 3

zeroes.and so on …...

Multiplying a Whole Number by Multiples of 10 (20, 30, 40..)

Multiply by the number of tens and then multiply by 10.

eg 1 eg 2

537 x 20 412 x 30

537 x 2 = 1074 412 x 3 = 1236

1074 x 10 = 10740 1236 x 10 = 12360

Dividing a Whole Number by 10, 100, 1000 …. When you divide a whole number by 10 all digits get moved

1 place to the right. When you divide a whole number by 100 all digits get moved

2 places to the right. When you divide a whole number by 1000 all digits get

moved 3 places to the right. and so on …...

Dividing a Whole Number by Multiples of 10 (20, 30, 40..)Divide by ten and then divide by the number of tens.Eg 1 Eg 27350 ÷ 50 840 ÷ 207350 ÷ 10 = 735 840 ÷ 10 = 84735 ÷ 5 = 147 84 ÷ 2 = 42

Long Multiplication

Example 1Work out, without a calculator

417 x 238

Answer 14 1 7

x 2 3 8 3 3 3 6 1 2 5 1 0 Because we are really multiplying by 30

+ 8 3 4 0 0 Because we are really multiplying by 200

9 9 2 4 6

Long Division

Example 2Work out, without a calculator

16422 ÷ 34

Answer 2 0 0 4 8 33 4 1 6 4 2 2

34 x 1 = 34 34 x 4 = 136 34 x 7 = 23834 x 2 = 68 34 x 5 = 170 34 x 8 = 27234 x 3 = 102 34 x 6 = 204 34 x 9 = 306

Order of Operations in a Calculation

A useful way to remember the order to do mathematical

operations in, is:

B racket

O ver (powers)

D ivide

A dd

S ubtract