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 Master, good to see you again. Here are the solutions to your fraction problems. Exercise 4.9 1. Fill in the < or > symbol: a) (3)/(4) < (6)/(4) 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 > 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)/(2) ___ (5)/(16) Step 1: Convert (3)/(2) to have a denominator of 16. (3)/(2) = (3 × 8)/(2 × 8) = (24)/(16) Step 2: Compare (24)/(16) and (5)/(16). (24)/(16) > (5)/(16) So, (3)/(2) > (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: Simplify (9)/(21). (9)/(21) = (9 ÷ 3)/(21 ÷ 3) = (3)/(7) Step 2: Compare (3)/(7) and (3)/(7). (3)/(7) = (3)/(7) So, (9)/(21) = (3)/(7) f) (6)/(11) ___ (12)/(55) Step 1: Convert (6)/(11) to have a denominator of 55. (6)/(11) = (6 × 5)/(11 × 5) = (30)/(55) Step 2: Compare (30)/(55) and (12)/(55). (30)/(55) > (12)/(55) So, (6)/(11) > (12)/(55) 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) Exercise 4.11 1. There are 600 people in a concert audience. (3)/(10) are male and 45% are older than 10 years of age. The question is incomplete, but I can calculate the number of males and the number of people older than 10 years. Step 1: Calculate the number of males. Number of males = (3)/(10) × 600 Number of males = 3 × 60 = 180 There are 180 males. Step 2: Calculate the number of people older than 10 years of age. Number of people older than 10 = 45\% of 600 Number of people older than 10 = (45)/(100) × 600 Number of people older than 10 = 45 × 6 = 270 There are 270 people older than 10 years of age. Send me the next one 📸