1. Order of Operations REVIEW CONCEPTS

2. Why is order important?

3. Remember… BEDMAS Brackets Exponents Division/Multiplication Addition/Subtraction

4. Brackets NOTE: Once every operation inside the brackets is solved, you can drop the brackets.

5. Brackets NOTE: Square brackets are often used to make it easier to locate pairs of brackets.

6. Exponents

9. Multiplying and Dividing

10. Adding and Subtracting

11. Putting it All Together

15. Putting it All Together – Word Problem NOTE: In this word problem, multiplication must be done before addition, but because multiplication has a higher order, it does not matter which order it is written in.

16. Integers Integers are like whole numbers, but they also include negative numbers... but still no fractions allowed! So, integers can be negative {-1, -2,-3, -4, -5,... }, positive {1, 2, 3, 4, 5,... }, or zero {0} We can put that all together like this: Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,... }

17. Examples: These are all integers: -16, -3, 0, 1, 198 But numbers like ½, 1.1 and -3.5 are not integers Note: if there is no sign on a whole number, it is assumed it is positive

18. Adding Positive Numbers Adding positive numbers is just simple addition: Example: 2 + 3 = 5 is really saying “positive two plus positive three is equal to positive five” This could also be written as (+2) + (+3) = +5

19. Subtracting Positive Numbers Subtracting positive numbers is really just simple subtraction Example: 6 – 3 = 3 is really saying positive six subtract positive three equals positive three You could write it as (+6) – (+3) = +3

20. Other Rules Two like signs become a positive sign +(+) 3+(+2) = 3 + 2 = 5 −(−) 6−(−3) = 6 + 3 = 9 Two unlike signs become a negative sign +(−) 7+(−2) = 7 − 2 = 5 −(+) 8−(+2) = 8 − 2 = 6

21. So all you have to remember is Two like signs become a positive sign (the same) Two unlike signs become a negative sign (different)

22. Example: What is 5+(−2) ? +(−) are unlike signs (they are not the same), so they become a negative sign. 5+(−2) = 5 − 2 = 3

23. Example: What is 25−(−4) ? −(−) are like signs, so they become a positive sign. 25−(−4) = 25 + 4 = 29

24. Example: What is −6 + (+3) ? +(+) are like signs, so they become a positive sign. −6 + (+3) = −6 + 3 = -3

25. Multiplying Integers x Two positives make a positive: 3 x 2 = 6 x Two negatives make a positive: (-3) x (-2) = 6 x A negative and a positive (-3) x 2 = -6 make a negative: x A positive and a negative 3 x (-2) = -6 make a negative:

26. Example: (−2) × (+5) The signs are − and + (a negative sign and a positive sign), so they are unlike signs (they are different to each other) So the result must be negative: (−2) × (+5) = -10

27. Example: (−4) × (−3) The signs are − and − (they are both negative signs), so they are like signs (like each other) So the result must be positive: (−4) × (−3) = +12

28. Aside Why does multiplying two negative numbers make a positive? When I say eat, I am encouraging you to eat (positive) When I say don’t eat, I am encouraging you not to eat (negative) So when I say do not NOT eat, I am telling you to eat (positive)

29. What is the value of (-3) × (-5) ?

30. What is the value of (-4) × (+7) ?

31. Dividing Integers When you divide two integers with the same sign, the result is always positive. Negative ÷ Negative = Positive Positive ÷ Positive = Positive When you divide two integers with different signs, the result is always negative. Positive ÷ Negative = Negative Negative ÷ Positive = Negative

32. What is (-10) / 5 ?

33. What is (-12) / (-3)