Adding Integers with the Same Sign

Warm UpWrite the integer for each situation.

1. An elevator ride down 27 stories2. A $700.00 profit3. 46 degrees below zero4. A gain of 12 yards

Find the sum or difference.

5. 183 + 78 = 7. 677 – 288 =6. 1188 + 902 = 8. 2647 – 1885 =

• Suppose the temperature is -1◦F and drops by 3◦F? Explain how to use the number line to find the new temperature.

• How would using a number line to find the sum 2 + 5 be different from using a number line to find the sum -2 + (-5)?

• Can you find two different negative integers that have the same sum as -2 + (-5)?

Adding Integers with a Common Sign

• When adding integers with the same sign, add the absolute values of the integers and use the sign of the integers for the sum.

• Absolute value refers to the integer’s distance from zero on a number line.

• Positive integers are always to the right of zero and negative integers are always to the left of zero.

Opposites

Integers that have the same absolute value, but different signs, are known as opposites. They have the same distance from zero, but they are in opposite directions.

Example: 5 and (-5)

Both integers are five units from zero on the number line.

-15 -10 -5 0 5 10 15

Can we use the same method to add two positive integers?

Commutative Property

The commutative property for addition allows us to add integers in any order, if and only if the operational sign stays the same throughout the expression.

7 + 6 = 6 + 7 3 + 5 + 4 = 5 + 4 + 3 13 = 13 12 = 12

Does this property work for adding two negative integers?

Challenge Time

1. Choose any two negative integers.

2. Is the sum of the integers less than or greater than the value of either of the integers?

3. Will this be true no matter which two intgers we choose? Explain.