**Whole Numbers**

All the positive numbers 1; 2; 3; 4; … are called the set of natural numbers. If we include 0 in the set of natural numbers, we get the set of counting numbers or whole numbers. We use numbers to add, subtract, multiply and divide. We can also write numbers in a particular order, from largest to smallest, e.g., 124; 1124; 5124; 9124. When we need to estimate, we can round off numbers to the nearest 5, 10, 100 or 1000. **Whole numbers** – or counting numbers are the numbers, 0; 1; 2; 3; 4; … and are represented by the symbol Nₒ. **Natural numbers** – are whole numbers greater than or equal to 1: (1; 2; 3; 4; …) and are represented by the symbol N.

**Rounding off to the nearest 5:**

Look at the last digit of the number (the units digit) and round the number off to the closest number that 5 divides into.

1; 2 – “Move back to number ending in 0”

3; 4 – “Move forward to the number ending in 5”

6; 7 - “Move back to number ending in 5”

8; 9 - “Move forward to the number ending in 0”

**Round off a number to the nearest 10:**

When rounding off to the nearest 10, look at the units- digit.

Underline the Tens digit - 5**8**6

Look at the digit to the RIGHT of the Tens digit - 58**6**

If this digit is 0, 1, 2, 3, or 4, the Tens stay the same. This is called rounding down. If this digit is 5, 6, 7, 8 or 9, round up. This is called rounding up.

586 rounded to the nearest 10 is 590. **We use the same method to round off to 100 (look at the tens digit) and 1000 (look at the hundreds digit)**

For example: 465 78**4** rounded off to the nearest 10 is 465 780.

465 7**8**4 rounded to the nearest 100 is 465 800.

465 **7**84 rounded to the nearest 1000 is 466 000.

Try this: **Round off 987 516 to:**

- The nearest 5
- The nearest 10
- The nearest 100
- The nearest 1000

**Properties Of Whole Numbers**

Adding numbers is called finding the **sum**, and subtracting numbers is called finding the **difference**. Multiplying numbers is called finding the **product** and dividing numbers is called finding the **quotient**.

When you add or multiply numbers, the order of the numbers does not matter, for example: 4 + 5 = 5 + 4 and 4 x 5 = 5 x 4. This is called the **commutative property** of addition and multiplication.

The order in which you add or multiply numbers also does not matter, for example: (4+5) +6 = 4 + (5+6) and (4x5) x6 = 4 x (5x6). This is called the** associative property** of addition and multiplication.

**Distributive, Associative And Commutative Property**

- 2 x 5 + 2 x 6 – 2 x 7

= 2 x (5 + 6 - 7)

= 2 x 4

**= 8** - 123 x 7

=(100 + 20 + 3) x 7

=(100 x 7)+(20 x 7)+(3 x 7)

= 700 + 140 + 21

**= 861** - 12(6 + 7)

= 12 x 6 + 12 x 7

= 72 + 84

**= 156**

When numbers in brackets are multiplied by a number in front of the brackets, each number inside the brackets is affected. This property of numbers works for addition and subtraction, for example: 4(5 + 6) = (4 x 5) + (4 x 6) or 6(5 – 4) = (6 x 5) - (6 x 4). This property is called the **distributive property** of multiplication.

**Distributive property**

**What is the answer to 2(4 + 3)?****The "2" outside the brackets is multiplied onto everything that is inside the brackets.**

Addition and subtraction are called **inverse operations**. If you add and subtract the same amount from a number, you end up back where you started. These operations have an effect on each other, for example: 856 + 12 – 12 = 856.

Multiplication and division are called **inverse operations.** If you multiply and divide a number by the same amount, you end up back where you started as the operations have an inverse effect on each other, for example: 524 x 12 ÷ 12 = 524.

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