2.2 Adding and Subtracting Rational Numbers• Use a number line to find each sum.

a. -3 + (- 4)

Step 1 – Draw an arrow from 0 to -3.

Step 2 – Draw a second arrow 4 units to the left to represent adding -4.

Step 3 – The second arrow ends at the sum of -7, so -3 + (-4) = -7.

Adding and Subtracting Rational Numbers• Use a number line to find each sum.

b. 2.5 + (-3.5)

Step 1 – Draw an arrow from 0 to 2.5.

Step 2 – Draw a second arrow 3.5 units to the left.

Step 3 – The second arrow ends at the sum of -1, so 2.5 + (-3.5) = -1.

Addition of Rational Numbers

• To add rational numbers with the same sign, add their absolute values. The sum has the same sign as the addends.

• To add rational numbers with different signs, subtract the lesser absolute value from the greater absolute value. The sum has the same sign as the number with the greater absolute value.

Add Rational Numbers• Find each sum.

a. -11 + (-7)

= -18

b. 7 3

16 8

7 6

16 16

1

16

Subtract Rational Numbers

• Every positive rational number can be paired with a negative rational number. These pairs are called opposites.

• A number and its opposite are additive inverses of each other.– When you add two opposites, the sum is

always 0.

Additive Inverse Property

• The sum of a number and its additive inverse is 0.

• For every number a, a + (-a) = 0.

• Examples:

2 + (-2) = 0 -4.25 + 4.25 = 0

Subtraction of Rational Numbers

• To subtract a rational number, add its additive inverse.

• For any numbers a and b, a – b = a + (-b).

• Examples:

8 – 15 = 8 + (-15) = -7

-7.6 – 12.3 = -7.6 + (-12.3) = -19.9

Subtract Rational Numbers to Solve a Problem• During a five-day period, a telecommunications

company’s stock price went from $17.82 to $15.36 per share. Find the change in the price of the stock.

15.36 – 17.82

= -2.46

The price of the stock changed by -$2.46.

The problem asks for the change in a stock’s price from the beginning of a week to the end. Since the change was negative, the price dropped. This makes sense since the ending price is less than the beginning price.

More Practice!!!!!

• Textbook p. 76 – 77 #17 – 36, 39 – 56.