All numbers are real numbers There are rational

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

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.

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 = 0 2) -9 + -11 = -20 3) 13 + (-19) = -6 4) 7 + 5 = 12 5) -12 + 10 = -2 6) -22 + (-16) = -38 7) 18 + (-5) = 13

Class Review First and Last Name November 29, 2017 ÷ 2

Rule for subtracting integers • To subtract integers, add the opposite. • What does this mean? • Keep, Change • Keep the 1 st 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 • 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 • Same sign add the integers and keep the sign. • -4 + (-3) = -7

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

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

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

Time for some practice! 1. 2. 3. 4. 5. 6. -9 – 5 = -9 + -5 = -14 27 – (-8) = 27 + 8 = 35 -3 – (-1) = -3 + 1 = -2 -8 – 9 = -8 + -9 = -17 14 – 17 = 14 + -17 = -3 4 – (-19) = 4 + 19 = 23

Rewrite as an addition problem then solve. 1. 5 – (-4) = 5 + 4 = 9 2. -7 – (-8) = -7 + 8 = 1 2 + -6 = -4 3. 2 – 6 = 4. -12 – 12 = -12 + -12 = -24 5. -14 – (-14) = -14 + 14 = 0

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

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

Ex 2 a: 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. – 2 – 5 = – 2 + -5 = – 7°F

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

Ex 4: Identify the answer as positive, negative or zero. DO NOT SOLVE. • – 0. 8 + -0. 8 negative zero -2. 6 + 3. 6 5. 6 + -6. 7 positive negative