1. Positive and Negative numbers

2. Negative numbers A positive or negative whole number, including zero, is called an integer. For example, –3 is an integer. This can also be written as – 3. It is 3 less than 0. 0 – 3 =–3 Here the ‘–’ sign means minus 3 or subtract 3. Here the ‘–’ sign means negative 3.

3. Positive and negative integers can be shown on a number line. Positive integersNegative integers We can use the number line to compare integers. For example, –3–8 –3 ‘is greater than’ –8 Integers on a number line

4. Adding integers We can use a number line to help us add positive and negative integers. –2 + 5 = -23 = 3 To add a positive integer we move forwards up the number line.

5. 5-3 Subtracting integers We can use a number line to help us subtract positive and negative integers. 5 – 8 == –3 To subtract a positive integer we move backwards down the number line. 5 – 8is the same as5 – +8

7. We can use a number line to help us add positive and negative integers. To add a negative integer we move backwards down the number line. –3 + –4 = = –7 -3-7 –3 + –4is the same as–3 – 4 Adding integers

8. 3 – –6 = 39 = 9 We can use a number line to help us subtract positive and negative integers. To subtract a negative integer we move forwards up the number line. 3 – –6is the same as3 + 6 Subtracting integers

9. We can use a number line to help us subtract positive and negative integers. –4 – –7 = -43 = 3 To subtract a negative integer we move forwards up the number line. –4 – –7is the same as–4 + 7 Subtracting integers

10. Adding and subtracting integers To add a positive integer we move forwards up the number line. To add a negative integer we move backwards down the number line. To subtract a positive integer we move backwards down the number line. To subtract a negative integer we move forwards up the number line. a + – b is the same as a – b. a – – b is the same as a + b.

11. Integer circle sums

12. When multiplying negative numbers remember: Rules for multiplying and dividing Dividing is the inverse operation to multiplying. When we are dividing negative numbers similar rules apply: +×+=+ –+×= – –+×=– –+×=– +÷+=+ –+÷= – –+÷=– –+÷=–

13. Multiplying and dividing integers Complete the following: –3 × 8 = 42 ÷ = –6 × –8 = 96 47 × = –141 –72 ÷ –6 = –36 ÷ = –4 ÷ –90 = –6 –7 × = 175 –4 × –5 × –8 = 3 × –8 ÷ = 1.5 –24 –7 –12 –3–3 12 9 540 –25 –160 –16

14. Using a calculator We can enter negative numbers into a calculator by using the sign change key: (–)(–) For example: –456 ÷ –6 can be entered as: (–)(–)456 ÷ (–)(–) 6 = The answer will be displayed as 76. Always make sure that answers given by a calculator are sensible.

15. What two integers have a sum of 2 and a product of –8? Sums and products Start by writing down all of the pairs of numbers that multiply together to make –8. Since –8 is negative, one of the numbers must be positive and one of the numbers must be negative. We can have: –1 × 8 = –81 × –8 = –8–2 × 4 = –8or 2 × –4 = –8 –1 + 8 = 71 + –8 = –7–2 + 4 = 22 + –4 = –2 The two integers are –2 and 4.

16. Sums and products