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

2. © William James Calhoun To add and subtract rational numbers and to simplify expressions that contain rational numbers. This section is simple. You use the rules from section 2-2 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. © William James Calhoun 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. © William James Calhoun EXAMPLE 1α: Find each sum. a. b. -1.34 + (-0.458)c. 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. -1.34 (+) -0.458 Add the numbers’ strengths and keep the sign. -1.798

5. © William James Calhoun EXAMPLE 1β: Find each sum. a. b. -8.007 + (-5.755)

6. © William James Calhoun EXAMPLE 2α: Find each difference. a. b. -6.24 – 8.52 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. -6.24 (+) -8.52 Add strengths and keep sign. -14.76

7. © William James Calhoun EXAMPLE 2β: Find each difference. a. b. c. 6.32 – (-3.42)

8. © William James Calhoun EXAMPLE 3α: 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. © William James Calhoun EXAMPLE 3β: Evaluate. a. p – 7.1 if p = 5.2 b. if