:Q 1. Reduce 125/375 to lowest terms. (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2 (e) 2/5 :RCA 1. (a) 1/3 Ans. 125 1 125 1 --- = - x --- = - Ans. 375 3 125 3 :RA :Q 2 35a b 2. Reduce ----- 2 50ab (a) 6a/10b (b) a/10b (c) 7a/10b (d) a/5a (e) 8b/9a :RCC 2. (c) 7a/10b Ans. Divide numerator and denominator by 5 ab, the highest common factor of both. :RA :Q 3. Arrange 1/2, .1/2, 1/.2, in order from smallest to largest. (a) 1/.2, 1/2, .1/2 (b) 1/2, .1/2, 1/.2 (c) .1/2, 1/2, 1/.2 (d) .1/2, 1/.2, 1/2 (e) It cannot be determined from the information given. :RCC 3. (c) .1/2, 1/2, 1/.2 Ans. To compare the values of arithmetic fractions, compare their decimal equivalents. 1 1 5 5 - = - x - = -- = .5 = .50 2 2 5 10 .1 .10 -- = --- = .05 2 2 :RA In 1/.2, multiply numerator and denominator by 10 to convert the denominator .2 to a whole number: 1 1 10 10 -- = -- x -- = -- = 5 .2 .2 10 2 .1 1 1 --, -, -- Ans. 2 2 .2 :RA :Q 4. If n and d represent positive whole numbers (d not equal to 0, 1, -1), arrange the following in descending order. (1) n/d (2) (n + 1)/d (3) (n - 1)/d (4) (n - 1)/(d + 1) (5) (n + 1)/(d - 1) (a) 5,2,1,3,4 (b) 2,1,3,4,5 (c) 5,3,4,1,2 (d) 3,5,4,1,2 (e) 1,3,2,5,4 :RCA 4. (a) 5,2,1,3,4 Ans. To compare the size of fractions apply the following principles: a. If two fractions have the same denominator, the one with the larger numerator has the greater value. (4/5 is greater than 3/5) b. If two fractions have the same numerator, the one with the smaller denominator has the greater value. (3/4 is greater than 3/5) :RA Therefore: (5) is greater than (2) by principle (b). (2) is greater than (1) by principle (a). (1) is greater than (3) by principle (a). (3) is greater than (4) by principle (b). 5,2,1,3,4 Ans. :RA :Q 5. 3/8 - 1/8 = (a) 1/2 (b) 1/3 (c) 1/8 (d) 1/5 (e) 1/4 :RCE 5. (e) 1/4 Ans. Note: Both fractions have the same denominator 3 1 3 - 1 2 1 - - - = ----- = - = - Ans. 8 8 8 8 4 :RA :Q 6. 3/4 - 1/5 = (a) 1/4 (b) 1/2 (c) 11/12 (d) 11/20 (e) 11/21 :RCD 6. (d) 11/20 Ans. LCD of 4 and 5 is 20. 3 x 5 15 1 x 4 4 ----- = -- ----- = -- 4 x 5 20 5 x 4 20 3 1 15 4 11 - - - = -- - -- = -- Ans. 4 5 20 20 20 :RA :Q 7. 4/5 + 7/20 - 1/30 = (a) 1 6/60 (b) 1 7/60 (c) 1 6/90 (d) 2 8/30 (e) 2 1/5 :RCB 7. (b) 1 7/60 Ans. Denominators must be converted to LCD which is 60. 60 x 4/5 = 48 60 x 7/20 = 21 60 x 1/30 = 2 :RA Thus: 4/5 + 7/20 - 1/30 = 48/60 + 21/60 - 2/60 = 48 + 21 - 2 ------------ = 60 67 7 -- = 1 -- Ans. 60 60 :RA :Q 8. Combine: a/b - 1 + b/a 2 2 2 2 a - ab + b a - ab - b (a) ------------ (b) ------------ ab ab a - ab - b a + ab + b (c) ---------- (d) ---------- ab ab 2 a + ab - b (e) ----------- ab :RCA 2 2 a - ab + b 8. (a) ------------ Ans. ab a x a 1 x ab b x b LCD is ab: ----- - ------ + ----- b x a 1 x ab a x b 2 2 a ab b Simplify: -- - -- + -- ab ab ab 2 2 a - ab + b Combine: ----------- Ans. ab :RA :Q 9. 5/8 x 4/15 = (a) 1/7 (b) 1/3 (c) 1/6 (d) 1/2 (e) 1/4 :RCC 9. (c) 1/6 Ans. 5/8 x 4/15 = 20/120 20/120 = 1/6 Ans. :RA :Q 10. Multiply a/b x c/d ac ca ab bc dc (a) -- (b) -- (c) -- (d) -- (e) -- bd db cd ad ab :RCA ac 10. (a) -- Ans. bd Put the product of the numerator over the product of the denominator: ac -- Ans. bd :RA :Q 11. Simplify the complex fraction: 2/3 + 5/6 --------- 3/8 (a) 8 (b) 9 (c) 6 (d) 4 (e) 1 :RCD 11. (d) 4 Ans. Multiply the numerator and denominator by 24, (LCD). (2/3 + 5/6) x 24 ---------------- (3/8) x 24 2/3 x 24 + 5/6 x 24 ------------------- 3/8 x 24 16 + 20 36 ------- = -- = 4 Ans. 9 9 :RA :Q 5 + 4 12. Evaluate ----- 5 (a) 1 1/2 (b) 2 1/2 (c) 1 4/5 (d) 4 (e) 2 4/5 :RCC 12. (c) 1 4/5 Ans. Combine numerator: 9/5 Simplify: 1 4/5 Ans. :RA :Q 2 a a 5 1 13. Simplify -- / - x - - - 10 2 a 2 (a) 1/2 (b) 1/3 (c) 1/4 (d) 1 (e) 0 :RCA 13. (a) 1/2 Ans. Note: Invert the fraction after the division sign. 2 a 2 5 1 -- x - x - - - 10 a a 2 Do the multiplication and division first. 1 1 1 - - = - Ans. 2 2 :RA :Q 14. A tank 3/8 full contains 12 gallons of water. What is the capacity of the tank? (a) 20 gal. (b) 10 gal. (c) l5 gal. (d) 32 gal. (e) It cannot be determined from the information given. :RCD 14. (d) = 32 gal. Ans. Let C = Tank capacity in gallons. 3/8 C = 12 C = 12 x 8/3 C = 32 gal. Ans. :RA :Q 15. Mr. Jordan owns 3/5 of the stock of a corporation. He sells 2/5 of his shares for $16,800. What is the total value of the corporation's stock? (a) $170,000 (b) $80,000 (c) $60,000 (d) $70,000 (e) $160,000 :RCD 15. (d) $70,000 Ans. Let y = value of the stock 2/5 x 3/5y = $16,800 6/25y = 16,800 y = $70,000 Ans. :RA :Q 16. A tank 1/4 full requires 10 gallons to make it 7/8 full. What is the capacity of the tank in gallons? (a) 20 (b) 10 (c) 16 (d) 15 (e) 13 :RCC 16. (c) 16 Ans. Let C = capacity in gallons gallons in tank originally + gallons added = gallons in tank at end (1/4)C + 10 = 7/8 C :RA Multiply both sides of the equation by 8, the LCD, to eliminate the denominators. C 7 8- + 10 = 8-C 4 8 2C + 80 = 7C 80 = 5C 16 = C Ans. :ET :ET
