New SAT Math Workbook

Be very careful of the minus sign between the

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Unformatted text preview: two fractions, use the same shortcuts used in arithmetic. Remember a c ad + bc a c ad − bc that + = , and that − = . All sums or differences should be simplified to simplest form. b d bd b d bd Example: Add Solution: Add the two cross products and put the sum over the denominator product: Example: Add Solution: 10 a + 12a 22a = 15 15 3b + 2a ab 32 + ab 2a 4a + 5 3 Example: Add Solution: Since both fractions have the same denominator, we must simply add the numerators and put the sum over the same denominator. 5a + 5b 5(a + b) = =5 a+b a+b 5a 5b + a+b a+b Example: Subtract Solution: 4r − s 2r − 7s − 6 6 Since both fractions have the same denominator, we subtract the numerators and place the difference over the same denominator. Be very careful of the minus sign between the fractions as it will change the sign of each term in the second numerator. 4r − s − (2r − 7s) 4r − s − 2r + 7s 2r + 6s 2(r + 3s) r + 3s = = = = 6 6 6 6 3 www.petersons.com 160 Chapter 11 Exercise 2 Work out each problem. Circle the letter that appears before your answer. 1. Subtract (A) (B) (C) (D) (E) 2. Add (A) (B) (C) (D) (E) 3. 6x + 5y 4 x + y − 2x 2x x+4 1 + 6 2 x+7 (A) 6 x +5 (B) 8 x+4 (C) 12 x +5 (D) 12 x +5 (E) 6 4. Add 1 + 4y 4y 1 + 2y x + 2y x x + 3y x 3c 3d + c+d c+d 6cd c+d 3cd c+d 3 2 5. Subtract (A) (B) (C) (D) (E) − 3b 7b − 4 10 2b 3 3 9cd c+d b 5 b 20 b 2b 3 a 3a Add + 5 10 (A) (B) (C) (D) (E) 4a 15 a 2 3a 2 50 2a 25 3a 2 15 www.petersons.com Factoring and Algebraic Fractions 161 3. MULTIPLICATION OR DIVISION OF FRACTIONS In multiplying or dividing fractions, we must first factor all numerators and denominators and may then divide all factors common to any numerator and any denominator. Remember always to invert the fraction following the division sign. Where exponents are involved, they are added in multiplication and subtracted in division. Example: Find the product of Solution: Factors common to both numerator and denominator are x2 in the first numerator and second denominator and y2 in the first denominator and secon...
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