Adding and Subtracting Integers

•What rules can you come up with that can sum up adding & subtracting integers?

•Remember, rules must apply at all times, and must be clear.

5 – 3 = 2-7 – (-4) = -35 – (-10) = 15-10 – 5 = -15

5 + 2 = 7-5 + (-2) = -7-10 + 12 = 28 + (-10) = -2

Add Integers with the Same Sign

Add Integers with the Same Sign

Find –6 + (–3).

Use a number line.

Answer: So, –6 + (–3) = –9.

From there, move 3 units left to show –3.

Move 6 units left to show –6.

Start at 0.

Add Integers with the Same Sign

Find –34 + (–21).

–34 + (–21) = –55 Both integers are negative, so the sum is negative.

Answer: –55

Add Integers with Different Signs

Add Integers with Different Signs

Find 8 + (–7).

Answer: So, 8 + (–7) = 1.

Use a number line.

Then move 7 units left.

Move 8 units right.

Start at zero.

Find –5 + 4.

Answer: So, –5 + 4 = -1.

Add Integers with Different Signs

Use a number line.

Then move 4 units right.

Move 5 units left.

Start at 0.

Add: 18 + (–27).

Add Integers with Different Signs

Find 5 + (–19) + (–5).

Subtraction of Integers

Subtract Positive Integers

Find 2 – 15.

2 – 15 = 2 + (–15) To subtract 15, add –15.

= –13 Simplify.

Answer: –13

Subtract Positive Integers

Find –13 – 8.

Answer: –21

–13 – 8 = –13 + (–8) To subtract 8, add –8.

= –21 Simplify.

Subtract Negative Integers

Find 12 – (–6).

Answer: 18

12 – (–6) = 12 + 6 To subtract –6, add 6.

= 18 Simplify.

Let’s model 12 – (-6) in a different way:

First, use 12 positive counters to model the number 12.

Now ask yourself, do I have 6 negative counters I can take away? No

Let’s use “zero pairs” to create the negatives that we need.

Reminder: a “zero pair” is a positive and negative counter that cancels each other out, leaving you with a sum of zero.

Now we have -6 to take away!

That’s right! 12 - (-6) = 18

Which is the same as 12 + 6 = 18What’s left?

Find –21 – (–8).

Answer: –13

Subtract Negative Integers

–21 – (–8) = –21 + 8 To subtract –8, add 8.

= –13 Simplify.

ALGEBRA Evaluate g – h if g = –2 and h = –7.

Answer: 5

Evaluate an Expression

g – h = –2 – (–7) Replace g with –2 and h with –7.

= –2 + 7 To subtract –7, add 7.

= 5 Simplify.

Write an addition expression to describe the situation. Then

find each sum and explain its meaning.

SKATEBOARDING Hakeem starts at the top of a half pipe 8 feet above street level. He descends 14 feet to the lowest point in his run.

Write an addition expression to describe the situation. Then

find each sum and explain its meaning.

SUBMARINE A submarine dives 106 feet below the water. Then it rises 63 feet.

FIND THE ERROR  Alicia and Mitsu are finding -16 - (-19) . Who is correct? Explain your reasoning.

SPACE  The temperatures on the moon vary from -173ºC to 127ºC. Find the difference in temperatures.

MONEY  Camilia owes her brother $25, so she gives her brother the $18 she earned dog-sitting for the neighbors. Write an addition sentence to describe this situation. Then find the sum and explain its meaning.