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
