1. The Equal Sign and Integers

2. It really means the sides of the equation are in Balance.
What does = mean?
5 + 9 = ____
Some might think the Equal Sign means “do the operation.” Like – Add or multiply.
It really means the sides of the equation are in Balance.

3. Balance this equation 4 + 5 = 3 + ? 9 = 3 + ? 9 = 3 + 6 Now check
4 + 5 = 3 + ?
9 = 3 + ?
9 = Now check
9 = 9 This is true! It must be right!

4. Practice
17 – 5 = 3 + ?
42  6 = 10 - ?

5. Answers 17 – 5 = 3 + ? 12 = 3 + ? 12 = 3 + 6 check 12 = 12 It checks!
42  6 = 10 - ?
7 = 10 - ?
7 = 10 – 3
7 = 7

6. Equal means “the same as” or “Balance” not
Remember!
Equal means “the same as” or “Balance” not
do something!

7. Definition
Positive number – a number greater than zero. 1 2 3 4 5 6

8. Definition
Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

9. Definition
Integers – Integers are all the whole numbers and all of their opposites on the negative number line including zero. 7
opposite -7

10. The absolute value of 9 or of –9 is 9. Definition
Absolute Value – The size of a number with or without the negative sign.
The absolute value of
9 or of –9 is 9.

11. It is both. A negative 3 is the same as subtracting a positive 3.
Question?
Is that a -3 or minus 3?
Answer - YES!
It is both. A negative 3 is the same as subtracting a positive 3.

12. Integer Addition Rules
Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer.
9 + 5 = 14
= -14

13. Solve the Problems -8 11 7 -13 14 -18 -3 + -5 = 4 + 7 = (+3) + (+4) ==
5 + 9 = = -8 11 7
-13 14
-18

14. Integer Addition Rules
Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. =
Larger abs. value
Answer = - 4
9 - 5 = 4

15. Solve These Problems -2 3 + -5 = -4 + 7 = (+3) + (-4) = -6 + 7 == =
5 – 3 = 2
7 – 4 = 3 3
4 – 3 = 1 -1
7 – 6 = 1 1
9 – 5 = 4 -4
9 – 9 = 0

16. Integer Subtraction Rule
Subtracting a negative number is the same as adding a positive. Change the signs and add.
2 – (-7)
is the same as
2 + (+7)
2 + 7 = 9!

17. Examples
12 – (-8)
12 + (+8)
= 20
-3 – (-11)
-3 + (+11)
= 8

18. Integer Multiplication Rule
If the signs are the same, the answer is positive. If the signs are different the answer is negative.
3 x 3 = 9
-3 x -3 = 9
4 x -5 = -20
-7 x 6 = -42

19. (does this look familiar?)
Integer Division Rule
If the signs are the same, the answer is positive. If the signs are different the answer is negative.
(does this look familiar?)

20. The Hard Part
Integers are easy but the hard part is Subtracting negatives. Can you think of a way that helps you see it in your head?
Please share.