Integers

Green counters = positive numbers = + 3 Red counters = negative numbers = -3

1 green counter and 1 red counter together – cancel each other out x x x x x x

Subtracting Integers

x x + 4 - + 2 +4 - +2 = +2 Subtracting Integers To subtract, remove 2 green + 4 - 2 green (2 positive) remain + 2 +4 - +2 = +2

x x x - 4 - - 3 -4 - -3 = -1 Subtracting Integers To subtract, remove 3 red - 4 - 1 red (1 negative) remains - 3 -4 - -3 = -1

x x x + 2 - + 3 +2 - +3 = -1 Subtracting Integers To subtract, remove 3 green + 2 There aren’t enough green counters to subtract, so we will need to add one - To add a green, we also need to add a red (we add 1 “zero pair” + 3 Now we can remove the final green 1 red (1 negative) remains +2 - +3 = -1

x x x - 2 - - 3 -2 - -3 = +1 Subtracting Integers To subtract, remove 3 red - 2 There aren’t enough red counters to subtract, so we will need to add one - To add a red, we also need to add a green (we add 1 “zero pair” - 3 Now we can remove the final red 1 green (1 positive remains -2 - -3 = +1

x x x - 2 - + 3 -2 - +3 = -5 Subtracting Integers To subtract, remove 3 green - 2 There aren’t any green counters to subtract, so we will need to add 3 x x x - To add 3 greens, we also need to add 3 reds (we add 3 “zero pairs” + 3 Now we can remove 3 greens 5 red (5 negative) remain -2 - +3 = -5

x x + 3 - - 2 +3 - -2 = +5 Subtracting Integers To subtract, remove 2 red + 3 There aren’t any red counters to subtract, so we will need to add 2 x x - To add 2 red, we also need to add 2 green (we add 2 “zero pairs” - 2 Now we can remove 2 red 5 green (5 positive) remain +3 - -2 = +5

Subtracting is adding the opposite Subtracting Integers Subtracting is adding the opposite 10 – 5 = 5 10 + -5 = 5 +

Now, follow the rules for addition: Subtracting integers + -3 - 2 = Subtracting is adding the opposite - - -3 + + 2 = Now, follow the rules for addition: Same signs, add and keep -3 + -2 = -5

Now, follow the rules for addition: Subtracting integers + -4 - 8 = Subtracting is adding the opposite - - -4 + + 8 = Now, follow the rules for addition: Same signs, add and keep -4 + -8 = -12

Now, follow the rules for addition: Subtracting integers + -6 - 9 = Subtracting is adding the opposite - - -6 + + 9 = Now, follow the rules for addition: Same signs, add and keep -6 + -9 = -15

+ + - - + + 7 = Subtracting integers 5 - 7 = +5 +5 + -7 = -2 5 - 7 = Subtracting is adding the opposite +5 - - + + 7 = Now, follow the rules for addition: Different signs, subtract, keep the sign of the higher one +5 + -7 = -2

+ + - - + + 9 = Subtracting integers 6 - 9 = +6 +6 + -9 = -3 6 - 9 = Subtracting is adding the opposite +6 - - + + 9 = Now, follow the rules for addition: Different signs, subtract, keep the sign of the higher one +6 + -9 = -3

Now, follow the rules for addition: Subtracting integers + - 2 - 9 = Subtracting is adding the opposite +2 - - + + 9 = Now, follow the rules for addition: Same signs, add and keep +2 + +9 = +11

Now, follow the rules for addition: Subtracting integers + - 1 - 6 = Subtracting is adding the opposite +1 - - + + 6 = Now, follow the rules for addition: Same signs, add and keep +1 + +6 = +7

Now, follow the rules for addition: Subtracting integers + - 5 - 4 = Subtracting is adding the opposite +5 - - + + 4 = Now, follow the rules for addition: Same signs, add and keep +5 + +4 = +9

- - - - - + + 6 = Subtracting integers 3 - 6 = 3 -3 + +6 = +3 3 - 6 = Subtracting is adding the opposite - 3 - - + + 6 = Now, follow the rules for addition: Different signs, subtract Keep the sign of the higher one -3 + +6 = +3

- - - - - + + 9 = Subtracting integers 2 - 9 = 2 -2 + +9 = +7 2 - 9 = Subtracting is adding the opposite - 2 - - + + 9 = Now, follow the rules for addition: Different signs, subtract Keep the sign of the higher one -2 + +9 = +7

- - - - - + + 3 = Subtracting integers 7 - 3 = 7 -7 + +3 = -4 7 - 3 = Subtracting is adding the opposite - 7 - - + + 3 = Now, follow the rules for addition: Different signs, subtract Keep the sign of the higher one -7 + +3 = -4

- - - - - + + 1 = Subtracting integers 10 - 1 = 10 -10 + +1 = -9 10 - 1 = Subtracting is adding the opposite 10 - - - + + 1 = Now, follow the rules for addition: Different signs, subtract Keep the sign of the higher one -10 + +1 = -9

Rule: KEEP, SWITCH, CHANGE Keep the sign of the first number, switch the subtraction sign to addition and change the sign of the second number