The Equal Sign and Integers

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.

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

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

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

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

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

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

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

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.

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.

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 -9 + -5 = -14

Solve the Problems -8 11 7 -13 14 -18 -3 + -5 = 4 + 7 = (+3) + (+4) = -6 + -7 = 5 + 9 = -9 + -9 = -8 11 7 -13 14 -18

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. -9 + +5 = Larger abs. value Answer = - 4 9 - 5 = 4

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

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!

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

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

(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?)

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.