HOW TO THINK ABOUT

1. HOW TO THINK ABOUT DIRECTED NUMBERS JW Hick

2. An integer is a “positive or negative whole number”. This can be represented on the number line Examples of integers are 2, 1 and -3

3. Numbers that are “further to the right” on the number line are “greater” than a number on its left. Likewise a number is less than another number if it is to the left on the number line. Example: is -2 greater or less than 1?

4. Well if we recall the number line, -2 is to the left of 1 so -2 is less than 1.

5. BODMAS Bodmas tells you the order in which to compute arithmetic. Brackets are done first Division and multiplication are done second Addition and subtraction are done last

6. EXAMPLE: Compute Well have to do the brackets first, so 6 + 1 give 7. Now we do the multiplication and division second. 2 times 5 gives 10 Now we add and subtract them, in any order and get 6 as our final answer.

7. ADDITION AND SUBTRACTION OF INTEGERS Whenever you do addition and subtraction of directed numbers think in terms of money. Negative numbers mean “you owe money” and positive numbers mean “you have money”. The only real trick is “if two negative signs are next to each other, turn them into a plus”

8. EXAMPLES: Solve the following 2 – – 3 = 5 + 2 – 3 = – 3 – 4 = – 10 + 5 = – 3 + (–1) =

9. 2 – – 3 = • Here we have two negative signs touching each other so we turn them into a plus. • 2 + 3 = 5 • 2) 5 + 2 – 3 = • Think in terms of money. You have $5, you get another $2 and then lose $3 (as it is -3). • 5 + 2 – 3 = 4

10. 3) – 3 – 4 = If you owe $3 and then borrow another $4, you will owe $7. – 3 – 4 = – 7 4) – 10 + 5 = If you owe $10 and then repay $5 you owe $5 – 10 + 5 = – 5

11. 5) – 3 + (–1) = If you owe $3 and then add on more borrowing of another $1, you will owe $4 – 3 + (–1) = – 4

12. MULTIPLICATION AND DIVISION OF INTEGERS When we multiply and divide, “mixed equals minus” If the signs of the integers are “mixed” then you will generate a “minus” answer.

13. EXAMPLES: 1) Here we have one negative number, and one positive number. Hence “the signs are mixed”. Mixed signs mean a minus answer.

14. 2) Again, we have one positive number and one negative number, so the signs are mixed. Mixed signs means minus answer. 3) Both signs are the same, so they are not mixed. This means no negative answer.