Whole numbers GCSE AQA Maths

Whole numbers

Sophies Tutoring Caithness
GCSE (AQA) Mathematics

​Writing whole numbers as words

Each digit in a number has a place value. A place value shows the position of a digit in a number.

​Millions	Hundred Thousands​	Ten thousands​	Thousands​	Hundreds​	Tens​	Units​
​	​7,	​7,6	​7,65	​7,654,	​7,654,3	​7,654,32

​When writing a whole number as words, putting a comma every three digits from the right breaks the numbers up, making it easier to say and write.

Open Ended

How do you write 68,542 in words?

​Ordering whole numbers

Place values are used to order whole numbers.
1. Put each number in the question into a place value table
2. Look at each column in turn from the left.

You will be able to work out the order using this method.

Reorder

Put the following numbers in order from smallest to largest

• 42,250

• 42,300

• 42,350

• 43,200

• 43,2

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

​Inequality symbols

Inequality symbols are used to compare the size of numbers.

​Example...

4,000>3,900 means 4,000 is greater than 3,900

Adding and Subtracting whole numbers

Column Addition

Numbers can be added together using the column method which involves writing one number underneath the other

​Column addition - example

​1. Start with the units column. 3 + 5 = 8

​2. Then move to the tens column 40 + 10 = 50

​3. Then move to the hundreds column 300+300 = 600

​4. The finished sum = 658

​If the two numbers in a place value column add up to a number greater than 9, you must carry a digit

​1. Start from the units column: 8-5=3

​2. In the tens column: 40-20=20. 2 is written in tens column as this is worth 20.

​3. In the hundreds column: 500-100=400. 4 is written in the hundreds column as this is worth 400.

​4. The finished substraction

Multiplying whole numbers

Grid method for multiplication

The grid method is a visual way of multiplying two numbers. Each digit in the number is put into its place value column.

​Grid method - example

​46 = 40 (four tens) plus 6 (6 units)
35 = 30 (three tens) plus 5 (5 units)

​X	40 (tens) ​	6 (units​)	Total​
30 (tens)​	​30 x 40 = 1200	​30 x 6 = 180	1200 + 180 =1380​
5 (units) ​	4 x 40 = 200​	5 x 6 = 30 ​	200 + 30 = 230 ​
​	​	​	​1380 + 230 = 1610

​Therefore, 46 x 35 = 1610

Dividing whole numbers

Short division

Small numbers can be divided using knowledge of times tables. Larger numbers can be divided using short division. Short division is a written method that uses mental arithmetic to divide a number in stages. It is ideal when the divisor is less than 10.

​Short division - example

Order of Operations

Mathematical operations must be carried out in the correct order. BODMAS and BIDMAS are ways of remembering this order.

​B	O/I​	DM​	AS​
​Brackets	Powers/Indices​	Divide or Multiply (work from left to right) ​	Add or Subtract (work from left to right) ​

Negative numbers

Negative numbers are numbers that are less than zero.

A number line can be used to order negative and positive numbers.

Rules for adding and subtracting negative numbers

When two signs are written next to each other, the rules for adding and subtracting numbers are:

• ​two signs that are different become a negative sign

• two signs that are the same become a positive sign

Rules for multiplying and dividing negative numbers

The rules for multiplying and dividing numbers are:

• ​two signs that are different become a negative sign

• two signs that are the same become a positive sign