1. ALGEBRA READINESS
Chapter 5 Section 2

2. 5.2: Add and Subtract Rational Numbers
To add two rational numbers with the same sign, add them together and keep the same sign. To add two rational numbers with different signs, subtract them and keep the sign of the “bigger” number. To subtract two rational numbers you add the opposite.

3. Example 1 a. b. Adding and Subtracting Rational Numbers Subtract. Add.4 a. + –
Rule of different signs 5 5 = 5 3 –
Subtract. b.
1.3 – +
5.8 ( )
Rule of same signs
Add.
7.1 = –

4. Example 1 c. Adding and Subtracting Rational Numbers Subtraction rule4 3 2 1 –
Subtraction rule = + 4 3 1 2 – = 4 1 2 –
Add. Write as a mixed number. 4

5. Find the sum or difference.
Practice for Example 1
Find the sum or difference. 1. 9 –
5.3 + ( )
ANSWER –
3.7 2.
0.6 –
0.2 + ( )
ANSWER –
0.8 3.
14.6 –
11.2 ( )
ANSWER
3.4 4. 8 7 + 3 1 –
ANSWER 24 13

6. Find the sum or difference.
Practice for Example 1
Find the sum or difference. 5. 5 2 + 3 – 1
ANSWER 5 4 6. 2 1 – 9 4 3
ANSWER 4 1 13 –

7. Evaluate the expression x 5.1 y when x 3.7 and y 2.3.
Example 2
Evaluating an Algebraic Expression
Evaluate the expression x y when x and y – – = = –
SOLUTION x
5.1 = – ( )
2.3 y
3.7
Substitute 3.7 for x and for y. = ( – )
5.1
3.7 +
2.3
Add the opposites of 5.1 and =
0.9
Add.

8. Evaluate the expression when and .
Practice for Example 2 = 8 3 – x = 2 1 y
Evaluate the expression when and 1
ANSWER – 24 5 7. x + y – 3 8. x 4 3 y –
ANSWER 8 5 9. x – 3 1 y 2
ANSWER – 24 53 or 5 2

9. A man was at the top of a mountain at an elevation of
Example 3
Evaluating Change
A man was at the top of a mountain at an elevation of
513.4 meters. He rappelled down to an elevation of
485.9 meters. What was the change in elevation?
SOLUTION
STEP 1 Write a verbal model.
STEP 2 Find the change in elevation. =
485.9
Substitute values.
Change in elevation –
513.4

10. The change in elevation was 27.5 meters.
Example 3
Evaluating Change =
485.9 + ( –
513.4 )
Subtraction rule
Add. = –
27.5
ANSWER
The change in elevation was meters. – 10

11. Find the change in temperature.
Practice for Example 3
Find the change in temperature.
10. From 12.5°C to 2.1°C –
ANSWER –
14.6°C 4 3
11. From °F to 51°F –
ANSWER °F 4 1 –
12. From 57.7 °C to 49.4°C
ANSWER –
8.3°C 5 1
13. From °F to °F – 2
ANSWER °F 10 3 – 13