Integers How We add and Subtract LIVE A. Gilleran This Photo by Unknown Author is licensed under CC BY-SA-NC

What will You Learn LIVE What Integers are Rules for adding and subtracting Integers A way to show that a rule is true What will You Learn A. Gilleran

Integers include positive and negative whole numbers What is an Integer Integers include positive and negative whole numbers NEWS A. Gilleran

1 2 3 4 5 6 Positive number – a number greater than zero. Positive Numbers A. Gilleran

1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 Negative Numbers 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 Negative number – a number less than 0 Negative Numbers A. Gilleran

What are negative numbers used for? Negative numbers are used to measure temperature Used to measure under sea level Negative numbers used to show debt Negative Numbers A. Gilleran

Temperature A. Gilleran This Photo by Unknown Author is licensed under CC BY-SA

Sea Level 10 20 -10 -20 -30 -40 A. Gilleran

Debt If you owe your friend €20, you would add in -20 to your budget show that you still owe money. A. Gilleran

Question 5 6 7 8 9 10 11 12 13 If it was -3 Degrees in the morning, but by lunch it was +6 degrees. How much did the temperature go up? Clue: If you do not see a negative or positive sign in front of the number, it is positive A. Gilleran This Photo by Unknown Author is licensed under CC BY-SA

Question 5 6 7 8 9 10 11 12 13 If it was -3 Degrees in the morning, but by lunch it was +6 degrees. How much did the temperature go up? A. Gilleran This Photo by Unknown Author is licensed under CC BY-SA

Integer Addition Rules LIVE Rule # 1 – Same Signs If the signs are the same, pretend the signs are not there. Add the numbers, then put the signs that the number had in front of your answer. 10 + 5 = 15 - 10 + - 5 = -15 Integer Addition Rules A. Gilleran

You Try A. Gilleran

(+8) (+13) = ? 5 21 -5 +5 A. Gilleran

(-22) + (-11) = ? +33 -11 +11 -33 A. Gilleran

(-12) + (+6) = ? +6 -6 +18 -18 A. Gilleran

(-16) + (+5) = ? 11 21 -21 -11 A. Gilleran

-9 + +5 = 9 - 5 = 4 Larger . value Answer = - 4 LIVE Rule # 2 – Different Signs If the signs are different, pretend they are not there. Subtract the smaller from the bigger and put the sign of the bigger number in front of your answer. 10 + 5 = 15 - 10 + - 5 = -15 -9 + +5 = Larger . value Answer = - 4 9 - 5 = 4 Integer Addition Rules A. Gilleran

One Way to Add Integers Is With a Number Line When the number is positive, count to the right. When the number is negative, count to the left. - + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 A. Gilleran

One Way to Add Integers Is With a Number Line +3 + -5 = -2 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 - A. Gilleran

One Way to Add Integers Is With a Number Line +6 + -4 = +2 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 - A. Gilleran

One Way to Add Integers Is With a Number Line +3 + -7 = -4 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 - A. Gilleran

One Way to Add Integers Is With a Number Line -3 + +7 = +4 - 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 + A. Gilleran

2 – (-7) is the same as 2 + (+7) 2 + 7 = 9! 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! Integer Subtraction Rules A. Gilleran

You Try A. Gilleran

12 – (-8) 12 + (+8) 12 + 8 = 20 -3 – (-11) -3 + (+11) -3 + 11 = 8 A. Gilleran

(+12) – (-8) = ? 4 -4 20 -20 Answer Now A. Gilleran

(-3) – (-11) = ? 14 -14 8 -8 Answer Now A. Gilleran

(+12) - (+8) = ? -4 +4 20 -20 Answer Now A. Gilleran

(-3) – (+11) = ? 8 -8 11 +11 Answer Now A. Gilleran

How can we check “Subtracting a negative number is the same as adding a positive” is true? We can use the same method we use to check our answers when we subtract. A. Gilleran

Suppose you subtract a – b and it equals c: a – b = c 5 – 2 = 3 To check if your answer is correct, add b and c: a = b + c 5 = 2 + 3 A. Gilleran

You Try A. Gilleran

a – b = c a = b + c 9 – 5 = 4 9 = 5 + 4 20 – 3 = 17 20 = 3 + 17 A. Gilleran

If the method for checking subtraction works, it should also work for subtracting negative numbers. A. Gilleran

Then let’s check with the negative numbers to see if it’s true… If a – b = c, and…. 2 – (-5) is the same as 2 + (+5), which equals 7, Then let’s check with the negative numbers to see if it’s true… A. Gilleran

a – b = c a = b + c 2 – (-5) = 7 2 = -5 + 7 It works! 2 – (-5) = 7 2 = -5 + 7 It works! a – b = c a = b + c -11 – (-3) = -8 -11 = -3 + -8 YES! A. Gilleran

Check Your Answers 1. Solve: 3 – 10 = 7 Check: 3 = 10 + (-7) A. Gilleran

Check Your Answers 1. Solve: 20 – ( 5) = 25 Check: 20 = -5 + 25 A. Gilleran

Review You have learned a lot about adding and subtracting integers Let’s Review Review A. Gilleran

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 numbers in front of your answer. 9 + 5 = 14 -9 + -5 = -14 A. Gilleran

Integer Addition Rules If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one Put the sign of the one with the larger value in front of your answer. -9 + +5 = Larger value Answer = - 4 9 - 5 = 4 A. Gilleran

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! A. Gilleran

6 – (-9) = 15 Discuss with a partner ways that you know that this problem is solved correctly. 6 – (-9) = 15 A. Gilleran