Adding Integers

Mrs. YoungEMC 1

Problem

• George owes his friend Jeanne $3. If he borrows another $6, how much will he owe her altogether?– Now I know that you are thinking this is

simple, but just wait!

Solution

• Actually, this problem is quite simple: just add $3 and $6 and the result is $9.

• However, the problem can be solved using addition of integers. – Owing $3 can be represented by -3 and

owing $6 can be represented by -6. • The problem becomes:

-3 + -6 = -9

Let’s Use A Number Line!

• Look at the number line below: – Start at 0– Move to the left 3 spaces (why left???)– Move 6 more spaces to the left (why???)– We end at -9

• So -3 + -6 = -9

Let’s Try Another!

• How can we solve +5 + -3???– Simple! Use a number line!

• Start at 0• Move to the right 5 spaces (why right??)• Now move 3 spaces to the left (why left??)

– You can see that +5 + -3 = +2

Let’s Try One More!

• Solve -5 + 3– Start at 0– Move to the left 5 spaces (why??)– Now move 3 spaces to the right (why?)

• You can see that we end up at -2!

Let’s Check Out Some Rules!

• When adding integers that have the same sign, the answer will have the same sign.– For example: The sum of two negative

integers is a negative integer.

Adding Negative Integers

Integers Sum

-2 + -9 = -11

-5 + -8 = -13

-13 + -7 = -20

Rules Continued…

• Also, when adding two positive integers, the answer will be a positive integer.

Adding Positive Integers

Integers Sum

+2 + +9 = +11

+17 + +5 = +22

+29 + +16 = +45

Uh oh! Wait!

• But, what if I want to add a positive integer and a negative integer… what should I do??

• It’s simple!• Follow these steps:

1.  Find the absolute value of each integer.

2. Subtract the smaller number from the larger number you get in Step 1.

3. The result from Step 2 takes the sign of the integer with the greater absolute value.

Let’s Try It!

• We can use a number line, or you don’t have to!– Solve +7 + -3

• Always start at 0• Move to the ____________ 7 spaces• Then move to the ________ 3 spaces

Let’s do it without the number line!

1. Find the absolute value of -7 and the absolute value of +3 (7 and 3)

2. Subtract the smaller number from the larger number in the Step 1 (7 – 3)

3. The result from Step 2 takes the sign of the integer with the greater absolute value.

• The answer would be -4 because the integer with the greater absolute value is negative!

Try this one!

• Solve -9 and +5. • Use a number line or not!1. Find the absolute value of -9 and the

absolute value of +52. Subtract the smaller number from the

larger number in the Step 13. The result from Step 2 takes the sign of

the integer with the greater absolute value.

• And the answer is……

Yep! You’re right!

-4

Here’s a Song For You!

(to the tune of “Row, row, row your boat”)

"Same Sign, Add and keep,Different sign, subtract.

Take the sign of the higher number

Then it'll be exact!"