This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the exercises. 1. Reduce these fractions to their lowest terms. a) Step 1: Find the greatest common divisor (GCD) of 5 and 20, which is 5. Step 2: Divide the numerator and the denominator by 5. (5)/(20) = (5 ÷ 5)/(20 ÷ 5) = (1)/(4) b) Step 1: Find the GCD of 16 and 24, which is 8. Step 2: Divide the numerator and the denominator by 8. (16)/(24) = (16 ÷ 8)/(24 ÷ 8) = (2)/(3) c) Step 1: Find the GCD of 56 and 280, which is 56. Step 2: Divide the numerator and the denominator by 56. (56)/(280) = (56 ÷ 56)/(280 ÷ 56) = (1)/(5) d) Step 1: Find the GCD of 7 and 322. Since 322 = 7 × 46, the GCD is 7. Step 2: Divide the numerator and the denominator by 7. (7)/(322) = (7 ÷ 7)/(322 ÷ 7) = (1)/(46) e) Step 1: Find the GCD of 21 and 35, which is 7. Step 2: Divide the numerator and the denominator by 7. (21)/(35) = (21 ÷ 7)/(35 ÷ 7) = (3)/(5) f) Step 1: Find the GCD of 24 and 54, which is 6. Step 2: Divide the numerator and the denominator by 6. (24)/(54) = (24 ÷ 6)/(54 ÷ 6) = (4)/(9) g) Step 1: Find the GCD of 90 and 126, which is 18. Step 2: Divide the numerator and the denominator by 18. (90)/(126) = (90 ÷ 18)/(126 ÷ 18) = (5)/(7) h) Step 1: Find the GCD of 128 and 176, which is 16. Step 2: Divide the numerator and the denominator by 16. (128)/(176) = (128 ÷ 16)/(176 ÷ 16) = (8)/(11) i) Step 1: Find the GCD of 5 and 100, which is 5. Step 2: Divide the numerator and the denominator by 5. (5)/(100) = (5 ÷ 5)/(100 ÷ 5) = (1)/(20) j) Step 1: Find the GCD of 30 and 36, which is 6. Step 2: Divide the numerator and the denominator by 6. (30)/(36) = (30 ÷ 6)/(36 ÷ 6) = (5)/(6) 2. Find the numbers represented by (?) a) Step 1: Observe that the denominator 7 is multiplied by 3 to get 21 (7 × 3 = 21). Step 2: Multiply the numerator 3 by the same factor. (3)/(7) = (3 × 3)/(7 × 3) = (9)/(21) The missing number is 9. b) Step 1: Observe that the numerator 24 is divided by 8 to get 3 (24 ÷ 8 = 3). Step 2: Divide the denominator 56 by the same factor. (3)/(?) = (24 ÷ 8)/(56 ÷ 8) = (3)/(7) The missing number is 7. c) Step 1: Observe that the numerator 28 is divided by 4 to get 7 (28 ÷ 4 = 7). Step 2: Divide the denominator 36 by the same factor. (28)/(36) = (28 ÷ 4)/(36 ÷ 4) = (7)/(9) The missing number is 9. d) Step 1: Observe that the numerator 42 is divided by 2 to get 21 (42 ÷ 2 = 21). Step 2: Divide the denominator 56 by the same factor. (42)/(56) = (42 ÷ 2)/(56 ÷ 2) = (21)/(28) The missing number is 28. e) Step 1: Observe that the numerator 25 is divided by 25 to get 1 (25 ÷ 25 = 1). Step 2: Divide the denominator 100 by the same factor. (1)/(?) = (25 ÷ 25)/(100 ÷ 25) = (1)/(4) The missing number is 4. f) Step 1: Observe that the numerator 12 is divided by 3 to get 4 (12 ÷ 3 = 4). Step 2: Divide the denominator 21 by the same factor. (12)/(21) = (12 ÷ 3)/(21 ÷ 3) = (4)/(7) The missing number is 7.