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 fraction problems from the image. Exercise 4.9 1. Fill in the < or > symbol: a) (2)/(7) < (6)/(7) b) (9)/(10) > (7)/(10) c) (11)/(100) < (17)/(100) d) (99)/(100) > (89)/(100) 2. First make sure the fractions have the same denominator and then compare them by filling in <, > or = symbols: a) (4)/(5) ___ (9)/(10) Step 1: Convert (4)/(5) to have a denominator of 10. (4)/(5) = (4 × 2)/(5 × 2) = (8)/(10) Step 2: Compare (8)/(10) and (9)/(10). (8)/(10) < (9)/(10) So, (4)/(5) < (9)/(10) b) (3)/(8) ___ (5)/(16) Step 1: Convert (3)/(8) to have a denominator of 16. (3)/(8) = (3 × 2)/(8 × 2) = (6)/(16) Step 2: Compare (6)/(16) and (5)/(16). (6)/(16) > (5)/(16) So, (3)/(8) > (5)/(16) c) (5)/(6) ___ (11)/(12) Step 1: Convert (5)/(6) to have a denominator of 12. (5)/(6) = (5 × 2)/(6 × 2) = (10)/(12) Step 2: Compare (10)/(12) and (11)/(12). (10)/(12) < (11)/(12) So, (5)/(6) < (11)/(12) d) (13)/(18) ___ (2)/(3) Step 1: Convert (2)/(3) to have a denominator of 18. (2)/(3) = (2 × 6)/(3 × 6) = (12)/(18) Step 2: Compare (13)/(18) and (12)/(18). (13)/(18) > (12)/(18) So, (13)/(18) > (2)/(3) e) (9)/(21) ___ (3)/(7) Step 1: Convert (3)/(7) to have a denominator of 21. (3)/(7) = (3 × 3)/(7 × 3) = (9)/(21) Step 2: Compare (9)/(21) and (9)/(21). (9)/(21) = (9)/(21) So, (9)/(21) = (3)/(7) f) (6)/(11) ___ (12)/(33) Step 1: Convert (6)/(11) to have a denominator of 33. (6)/(11) = (6 × 3)/(11 × 3) = (18)/(33) Step 2: Compare (18)/(33) and (12)/(33). (18)/(33) > (12)/(33) So, (6)/(11) > (12)/(33) 3. Arrange these fractions in descending order, by first writing them all with a denominator of 48: The fractions are: (5)/(6), (1)/(3), (11)/(12), (19)/(24), (3)/(4), (7)/(8), (11)/(24), (12)/(24). Step 1: Convert each fraction to have a denominator of 48. (5)/(6) = (5 × 8)/(6 × 8) = (40)/(48) (1)/(3) = (1 × 16)/(3 × 16) = (16)/(48) (11)/(12) = (11 × 4)/(12 × 4) = (44)/(48) (19)/(24) = (19 × 2)/(24 × 2) = (38)/(48) (3)/(4) = (3 × 12)/(4 × 12) = (36)/(48) (7)/(8) = (7 × 6)/(8 × 6) = (42)/(48) (11)/(24) = (11 × 2)/(24 × 2) = (22)/(48) (12)/(24) = (12 × 2)/(24 × 2) = (24)/(48) Step 2: Arrange the fractions with denominator 48 in descending order (largest to smallest). (44)/(48), (42)/(48), (40)/(48), (38)/(48), (36)/(48), (24)/(48), (22)/(48), (16)/(48) Step 3: Write the original fractions in descending order. (11)/(12), (7)/(8), (5)/(6), (19)/(24), (3)/(4), (12)/(24), (11)/(24), (1)/(3) 3 done, 2 left today. You're making progress.