This document provides instruction on adding and subtracting rational numbers. It outlines the key rules for combining like terms with the same or different signs. Examples are provided to demonstrate rewriting mixed numbers as improper fractions, finding common denominators, and performing the arithmetic operations accordingly. Practice problems are assigned for homework.

1. Chapter 02 – Section 02 Adding and Subtracting Rational Numbers

2. To add and subtract rational numbers and to simplify expressions that contain rational numbers. OBJECTIVES 2-2 ADDING AND SUBTRACTING RATIONAL NUMBERS This section is simple. You use the rules from section 2-3 about adding and subtracting integers. Only in this section, you will need to find common denominators before adding and subtracting. Your calculator will be a big help for you in this section. On the next slide is a review of the rules of adding and subtracting. After that, its just examples.

3. 2-2 ADDING AND SUBTRACTING RATIONAL NUMBERS To add or subtract integers and rational numbers, follow these rules: 1) If the statement is a subtract statement, change it to an add statement by adding the opposite of what is being subtracted. Example: 2 – (-4) => 2 + 4 2) If the two terms being added have the same sign, combine their absolute values (strengths) and keep the sign. Example: 2 + 8 = 10; and -2 + (-8) = -10 3) If the two terms being added have different signs, subtract their absolute values (strengths) and keep the sign of the stronger. Example: -2 + 8 = 6; and 2 + (-8) = -6 You must have these rules committed to memory as of right… NOW!!!

4. EXAMPLE 1 α : Find each sum. a. b. -1.34 + (-0.458) c. 2-2 ADDING AND SUBTRACTING RATIONAL NUMBERS Rewrite mixed numbers as improper fractions. Get a common denominator. Add. Rewrite mixed numbers as improper fractions. Get a common denominator. Add. Line up the decimal places. Add the numbers’ strengths and keep the sign. -1.798 EX1 β -1.34 (+) -0.458

5. EXAMPLE 1 β : Find each sum. a. b. -8.007 + (-5.755) 2- 2 ADDING AND SUBTRACTING RATIONAL NUMBERS

6. EXAMPLE 2 α : Find each difference. a. b. -6.24 – 8.52 2-2 ADDING AND SUBTRACTING RATIONAL NUMBERS EX2 β Get a common denominator. Negative negative yields a positive. Subtract the strengths and keep the sign of the stronger number. Remember subtracting is the same as adding the additive inverse. -6.24 + (-8.52) Line up the decimals. Add strengths and keep sign. -14.76 -6.24 (+) -8.52

7. EXAMPLE 2 β : Find each difference. a. b. c. 6.32 – (-3.42) 2-2 ADDING AND SUBTRACTING RATIONAL NUMBERS

8. 2-2 ADDING AND SUBTRACTING RATIONAL NUMBERS EX3 β EXAMPLE 3 α : a. Evaluate p - 3.5 if p = 2.8. b. Evaluate if Plug in 2.8 for p. (2.8) - 3.5 Subtract strengths and take the sign of the stronger. -0.7 Plug in the value of x. Get a common denominator. Subtract strengths and take sign of the stronger.

9. 2-2 ADDING AND SUBTRACTING RATIONAL NUMBERS EXAMPLE 3 β : Evaluate. a. p – 7.1 if p = 5.2 b. if

10. HOMEWORK #17 – 33 odd 37 – 53 odd 2-2 ADDING AND SUBTRACTING RATIONAL NUMBERS