Grade 8 Integers What You Will Learn n

Grade 8 Integers!

What You Will Learn n n Some definitions related to integers. Rules for multiplying and dividing integers. Are you ready? ?

Definition n Positive number = a number greater than zero. 0 1 2 3 4 5 6

Definition n Negative number = a number less than zero. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Definition n Opposite Numbers = numbers that are the same distance from zero in the opposite direction -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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

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

Negative Numbers Are Used to Measure Temperature

Negative Numbers Are Used to Measure Above and Below Sea Level 30 20 10 0 -10 -20 -30 -40 -50

Negative Numbers Are Used to Show Debt Let’s say your parents bought a car but had to get a loan from the bank for $5, 000. When counting all their money they add in -$5, 000 to show they still owe the bank.

Hint n If you don’t see a negative or positive sign in front of a number it is positive. 9 = +9

Integer Multiplication Rules n Rule #1 – If the signs are the same, pretend the signs aren’t there. Multiply the numbers and then put a positive sign in front of your answer. 9 x 5 = +45 (-9) x (-5) = +45

Solve the Problems -3 x -5 = n 4 x 7 = n (+3) x (+4) = n -6 x -7 = n 5 x 9 = n -9 x -9 = n

Answers -3 x -5 = +15 +28 n 4 x 7 = n (+3) x (+4) = +12 n -6 x -7 = +42 n 5 x 9 = +45 n -9 x -9 = +81 n

Integer Multiplication Rules n Rule #2 – If the signs are different pretend the signs aren’t there. Multiply the numbers and put a negative sign in front of your answer. -9 x 5 = -45

Solve These Problems 3 x -5 = n -4 x 7 = n (+3) x (-4) = n -6 x 7 = n 5 x -9 = n -9 x 9 = n

Answers 3 x -5 = -15 n -4 x 7 = -28 n (+3) x (-4) = -12 n -6 x 7 = -42 n 5 x -9 = -45 n -9 x 9 = -81 n

One Way to Multiply Integers Is With a Number Line When the signs are the same, count to the right. When the signs are opposite, count to the left. 2 x 3=6 + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

One Way to Multiply Integers Is With a Number Line (+3) x (-2) = -6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

What about dividing with integers?

Integer Division Rule Dividing by a negative number is the same as multiplying by a negative number. Same signs result in a positive answer and different signs result in a negative answer. 14 ÷ (-7) is the same as -14 ÷ (+7) = -2

Here are some more examples. 16 ÷ (-8)= -2 -33 ÷ (-11)= 3 16 ÷ (+8)= 2 -33 ÷ (+11)= -3

How do we know that “A negative times (or divided by) a negative equals a positive” is true? The following slides show two ways to think about it…

Think about grammar! Some people think of a negative as meaning “not”. So if I say I’m not going to the store, doesn’t that mean I AM going to the store? (two negatives results in a positive answer? )

Think about patterns: 4 3 2 1 0 x x x 5 5 5 = = = 20 15 10 5 0 Both numbers are going down!

What about this pattern? : 4 x -5 = -20 3 x -5 = -15 2 x -5 = -10 1 x -5 = -5 0 x -5 = 0 The left numbers are going down and the right #s are going up!

But if we continue that pattern: 3 x -5 = -15 2 x -5 = -10 1 x -5 = -5 0 x -5 = 0 -1 x -5 = 5 -2 x -5 = 10 -3 x -5 = 15 -4 x -5 = 20 The left #s are still going down & the right #s are still going up! (Neg x neg = positive)

You have learned lots of things about multiplying and dividing integers. Review what you think you know with a partner!