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
Hey Haniya, good to see you again. Here are the solutions to the problems: 1. Fill in the boxes to make equivalent fractions. a) (4)/(8) = ()/(16) Step 1: Find the factor by which the denominator was multiplied. 16 ÷ 8 = 2 Step 2: Multiply the numerator by the same factor. 4 × 2 = 8 The missing number is 8. b) (3)/(7) = ()/(28) Step 1: Find the factor by which the denominator was multiplied. 28 ÷ 7 = 4 Step 2: Multiply the numerator by the same factor. 3 × 4 = 12 The missing number is 12. c) (2)/(5) = (10)/() Step 1: Find the factor by which the numerator was multiplied. 10 ÷ 2 = 5 Step 2: Multiply the denominator by the same factor. 5 × 5 = 25 The missing number is 25. d) (8)/(7) = (32)/() Step 1: Find the factor by which the numerator was multiplied. 32 ÷ 8 = 4 Step 2: Multiply the denominator by the same factor. 7 × 4 = 28 The missing number is 28. 2. Write the first five equivalent fractions for the following. a) (6)/(12) To find equivalent fractions, multiply the numerator and denominator by 2, 3, 4, 5, and 6. (6 × 2)/(12 × 2) = (12)/(24) (6 × 3)/(12 × 3) = (18)/(36) (6 × 4)/(12 × 4) = (24)/(48) (6 × 5)/(12 × 5) = (30)/(60) (6 × 6)/(12 × 6) = (36)/(72) The first five equivalent fractions are (12)/(24), (18)/(36), (24)/(48), (30)/(60), (36)/(72). b) (5)/(6) To find equivalent fractions, multiply the numerator and denominator by 2, 3, 4, 5, and 6. (5 × 2)/(6 × 2) = (10)/(12) (5 × 3)/(6 × 3) = (15)/(18) (5 × 4)/(6 × 4) = (20)/(24) (5 × 5)/(6 × 5) = (25)/(30) (5 × 6)/(6 × 6) = (30)/(36) The first five equivalent fractions are (10)/(12), (15)/(18), (20)/(24), (25)/(30), (30)/(36). c) (3)/(6) To find equivalent fractions, multiply the numerator and denominator by 2, 3, 4, 5, and 6. (3 × 2)/(6 × 2) = (6)/(12) (3 × 3)/(6 × 3) = (9)/(18) (3 × 4)/(6 × 4) = (12)/(24) (3 × 5)/(6 × 5) = (15)/(30) (3 × 6)/(6 × 6) = (18)/(36) The first five equivalent fractions are (6)/(12), (9)/(18), (12)/(24), (15)/(30), (18)/(36). d) (7)/(10) To find equivalent fractions, multiply the numerator and denominator by 2, 3, 4, 5, and 6. (7 × 2)/(10 × 2) = (14)/(20) (7 × 3)/(10 × 3) = (21)/(30) (7 × 4)/(10 × 4) = (28)/(40) (7 × 5)/(10 × 5) = (35)/(50) (7 × 6)/(10 × 6) = (42)/(60) The first five equivalent fractions are (14)/(20), (21)/(30), (28)/(40), (35)/(50), (42)/(60). e) (2)/(5) To find equivalent fractions, multiply the numerator and denominator by 2, 3, 4, 5, and 6. (2 × 2)/(5 × 2) = (4)/(10) (2 × 3)/(5 × 3) = (6)/(15) (2 × 4)/(5 × 4) =