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 comparisons for each pair of fractions: a) (1)/(2) > (1)/(4) Step 1: To compare, convert (1)/(2) to an equivalent fraction with a denominator of 4. (1)/(2) = (1 × 2)/(2 × 2) = (2)/(4) Step 2: Compare (2)/(4) and (1)/(4). Since 2 > 1, (2)/(4) > (1)/(4). b) (1)/(2) = (2)/(8) Step 1: To compare, convert (1)/(2) to an equivalent fraction with a denominator of 8. (1)/(2) = (1 × 4)/(2 × 4) = (4)/(8) Step 2: Compare (4)/(8) and (2)/(8). Since 4 > 2, (4)/(8) > (2)/(8). Correction: The student's answer in the image is =. Let's re-evaluate. Step 1: Simplify (2)/(8). (2)/(8) = (2 ÷ 2)/(8 ÷ 2) = (1)/(4) Step 2: Compare (1)/(2) and (1)/(4). Since (1)/(2) is larger than (1)/(4), the correct symbol is >. (1)/(2) > (2)/(8) c) (1)/(4) < (3)/(8) Step 1: To compare, convert (1)/(4) to an equivalent fraction with a denominator of 8. (1)/(4) = (1 × 2)/(4 × 2) = (2)/(8) Step 2: Compare (2)/(8) and (3)/(8). Since 2 < 3, (2)/(8) < (3)/(8). d) (1)/(2) = (2)/(4) Step 1: Simplify (2)/(4). (2)/(4) = (2 ÷ 2)/(4 ÷ 2) = (1)/(2) Step 2: Compare (1)/(2) and (1)/(2). They are equal. e) (2)/(2) > (1)/(8) Step 1: Simplify (2)/(2). (2)/(2) = 1 Step 2: Compare 1 and (1)/(8). Since 1 is greater than any proper fraction, 1 > (1)/(8). f) (5)/(8) > (2)/(4) Step 1: To compare, convert (2)/(4) to an equivalent fraction with a denominator of 8. (2)/(4) = (2 × 2)/(4 × 2) = (4)/(8) Step 2: Compare (5)/(8) and (4)/(8). Since 5 > 4, (5)/(8) > (4)/(8). g) (2)/(4) < (8)/(8) Step 1: Simplify both fractions. (2)/(4) = (1)/(2) (8)/(8) = 1 Step 2: Compare (1)/(2) and 1. Since (1)/(2) < 1. h) (1)/(4) < (4)/(8) Step 1: Simplify (4)/(8). (4)/(8) = (4 ÷ 4)/(8 ÷ 4) = (1)/(2) Step 2: Compare (1)/(4) and (1)/(2). Since (1)/(4) is smaller than (1)/(2), (1)/(4) < (1)/(2). i) (4)/(8) = (1)/(2) Step 1: Simplify (4)/(8). (4)/(8) = (4 ÷ 4)/(8 ÷ 4) = (1)/(2) Step 2: Compare (1)/(2) and (1)/(2). They are equal. j) (1)/(2) < (4)/(4) Step 1: Simplify (4)/(4). (4)/(4) = 1 Step 2: Compare (1)/(2) and 1. Since (1)/(2) < 1. k) (1)/(2) > (1)/(8) Step 1: To compare, convert (1)/(2) to an equivalent fraction with a denominator of 8. (1)/(2) = (1 × 4)/(2 × 4) = (4)/(8) Step 2: Compare (4)/(8) and (1)/(8). Since 4 > 1, (4)/(8) > (1)/(8). l) (5)/(8) > (1)/(2) Step 1: To compare, convert (1)/(2) to an equivalent fraction with a denominator of 8. (1)/(2) = (1 × 4)/(2 × 4) = (4)/(8) Step 2: Compare (5)/(8) and (4)/(8). Since 5 > 4, (5)/(8) > (4)/(8). m) (1)/(2) < (7)/(8) Step 1: To compare, convert (1)/(2) to an equivalent fraction with a denominator of 8. (1)/(2) = (1 × 4)/(2 × 4) = (4)/(8) Step 2: Compare (4)/(8) and (7)/(8). Since 4 < 7, (4)/(8) < (7)/(8). n) (3)/(4) > (1)/(8) Step 1: To compare, convert (3)/(4) to an equivalent fraction with a denominator of 8. (3)/(4) = (3 × 2)/(4 × 2) = (6)/(8) Step 2: Compare (6)/(8) and (1)/(8). Since 6 > 1, (6)/(8) > (1)/(8). o) (1)/(4) < (6)/(8) Step 1: To compare, convert (1)/(4) to an equivalent fraction with a denominator of 8. (1)/(4) = (1 × 2)/(4 × 2) = (2)/(8) Step 2: Compare (2)/(8) and (6)/(8). Since 2 < 6, (2)/(8) < (6)/(8). 3 done, 2 left today. You're making progress.