real rational irrational rational Real Numbers All numbers are numbers. There are two types of real numbers; they are numbers and numbers. Natural numbers, whole numbers, integers are all numbers. rational irrational rational

Adding Integers We can use positive and negative counters to model the addition of integers. Positive Integer Negative Integer A positive integer paired with a negative integer form a zero pair. The value of a zero pair is 0.

Add -2 + (-4) = -6

Add 5 + 6 = 11

Add -3 + (-5) = -8

Add -3 + -2 = -5

Do you notice a pattern or rule? Adding Integers with like signs. - When the signs are the same, add the numbers together and keep the sign.

Add -5 + 3 = -2 Remove all the zero pairs.

Add 4 + (-1) = 3 Remove all the zero pairs.

Add -6 + 5 = -1 Remove all the zero pairs.

Add 3 + (-7) = -4 Remove all the zero pairs.

Did you notice a pattern or rule? Adding integers with unlike signs. - When the signs are different, subtract the integers and keep the sign of the larger digit.

Summary Adding Integers with like signs. - When the signs are the same, add the numbers together and keep the sign. -9 + -3 = -12 Adding integers with unlike signs. - When the signs are different, subtract the integers and keep the sign of the larger integer. -9 + 3 = -6

Let’s try a few examples using the rules for adding integers. 1) -8 + 8 = 2) -9 + -11 = 3) 13 + (-19) = 4) 7 + 5 = 5) -12 + 10 = 6) -22 + (-16) = 7) 18 + (-5) = -20 -6 12 -2 -38 13

−6 14 + −4 14 = Simplify. −7 11 + 2 11 = −𝟕+𝟐 𝟏𝟏 = −𝟔+−𝟒 𝟏𝟒 = −𝟓 𝟏𝟏 Class Review First and Last Name November 29, 2017 Simplify. −7 11 + 2 11 = −6 14 + −4 14 = −𝟓 𝟏𝟏 −𝟕+𝟐 𝟏𝟏 = −𝟔+−𝟒 𝟏𝟒 = −𝟏𝟎 𝟏𝟒 ÷ 2 −𝟓 𝟕 ÷ 2

Rule for subtracting integers To subtract integers, add the opposite. What does this mean? Keep, Change, Change Keep the 1st integer the same Change the subtraction sign to addition. Change the sign of the second integer. Then follow the rules for addition.

Let’s try an example. -5 – (-2) -5 + 2 keep, change, change Opposite sign subtract and keep the sign of the larger digit. -5 + 2 = -3

Let’s try an example -4 – 3 -4 + (-3) keep, change, change Same sign add the integers and keep the sign. -4 + (-3) = -7

10 Example + 6 – (-4) 6 4 Keep, Change, Change Now follow the rules for adding integers! 10

-13 Example + -5 – 8 -5 -8 Keep, Change, Change Now follow the rules for adding integers! -13

-2 Example + 18 – 20 18 -20 Keep, Change, Change Now follow the rules for adding integers! -2

Time for some practice! -9 + -5 = -14 -9 – 5 = 27 – (-8) = -3 – (-1) = -8 – 9 = 14 – 17 = 4 – (-19) = 35 27 + 8 = -3 + 1 = -2 -8 + -9 = -17 14 + -17 = -3 4 + 19 = 23

Rewrite as an addition problem then solve. 5 – (-4) = -7 – (-8) = 2 – 6 = -12 – 12 = -14 – (-14) = 5 + 4 = 9 -7 + 8 = 1 2 + -6 = -4 -12 + -12 = -24 -14 + 14 =

-2 – 3 -2 + – 3 Subtraction Addition Ex 1a: Write an equivalent subtraction and addition expressions for the model below. • • Subtraction -2 – 3 -2 + – 3 Addition

3 – 4 3 + – 4 Subtraction Addition Ex 1b: Write an equivalent subtraction and addition expressions for the model below. • • Subtraction 3 – 4 3 + – 4 Addition

8 – 10 = 8 + -10 = – 2°F – 7°F – 2 – 5 = – 2 + -5 = Temp at 5:00 P.M. Ex 2a: Between 6:00 A.M. and noon, the temperature rose from 0°F to 8°F. By 5:00 P.M., the temperature had dropped by 10°F. By 8:00 P.M., the temperature dropped another 5°F. Write and simplify a subtraction expression for the temperature at 5:00 P.M. and 8:00 P.M. Temp at 5:00 P.M. 8 – 10 = 8 + -10 = – 2°F Temp at 8:00 P.M. – 7°F – 2 – 5 = – 2 + -5 =

Ex 3: Rewrite as an addition problem then solve. To subtract an integer, add it’s opposite. Keep, Change, Change 6 – (-1) = + = -4 – (-3) = + = 1 – 6 = + = -3 – (-4) = + = -3 – 5 = + = 6 1 7 -4 3 -1 1 -6 -5 -3 4 1 -3 -5 -8

Ex 4: Identify the answer as positive, negative or zero. DO NOT SOLVE. – 0.8 + -0.8 negative -0.8 – 0.8 -5 - 𝟑 𝟑 𝟒 −𝟑 𝟏 𝟐 – (−𝟑 𝟏 𝟐 ) 𝟏 𝟐 −(− 𝟏 𝟒 ) −2.6 – (–3.6) 5.6 – 6.7 -5 + - 3 3 4 negative - 3 1 2 + 3 1 2 zero 1 2 + 1 4 positive -2.6 + 3.6 positive 5.6 + -6.7 negative