A concert audience of 600 people has 3/10 males and 5/6 older than 10. Calculate the fraction of females, fraction younger than 10, number of females, and number younger than 10.

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Asked on May 21, 2026Mathematics

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.

Accepted Answer · 2026-05-21T19:23:45.846Z

You're on a roll — here are the solutions to the problems from the image. Exercise 4.11 1. There are 600 people in a concert audience. (3)/(10) are male and (5)/(6) older than 10 years of age. a) What fraction of the audience is female? Step 1: The total audience is represented by the fraction 1. If (3)/(10) are male, the rest are female. Fraction female = 1 - (3)/(10) Fraction female = (10)/(10) - (3)/(10) = (7)/(10) The fraction of the audience that is female is (7)/(10). b) What fraction of the audience is younger than 10 years of age? Step 1: The total audience is represented by the fraction 1. If (5)/(6) are older than 10, the rest are younger than 10. Fraction younger than 10 = 1 - (5)/(6) Fraction younger than 10 = (6)/(6) - (5)/(6) = (1)/(6) The fraction of the audience younger than 10 years of age is (1)/(6). c) How many people in the audience are female? Step 1: Use the fraction of females from part (a) and the total number of people. Number of females = (7)/(10) × 600 Number of females = 7 × 60 = 420 There are 420 female people in the audience. d) How many people are younger than 10 years of age? Step 1: Use the fraction of people younger than 10 from part (b) and the total number of people. Number of people younger than 10 = (1)/(6) × 600 Number of people younger than 10 = 1 × 100 = 100 There are 100 people younger than 10 years of age. 2. Jane has walked 2(4)/(5) km from her home towards the shops. She has to walk a further 1(3)/(5) km to get there. What is the total distance from her house to the shops? Step 1: Add the distance already walked and the remaining distance. Total distance = 2(4)/(5) km + 1(3)/(5) km Step 2: Add the whole numbers and the fractions separately. Total distance = (2+1) + ((4)/(5) + (3)/(5)) Total distance = 3 + (7)/(5) Step 3: Convert the improper fraction to a mixed number and add to the whole number. (7)/(5) = 1(2)/(5) Total distance = 3 + 1(2)/(5) = 4(2)/(5) km The total distance from her house to the shops is 4(2)/(5) km. 3. We are erecting safety fencing around our swimming pool. The total length of fencing is 20(3)/(8) m. The builders have already erected two pieces. One is 3(2)/(8) m, the next is 4(5)/(8) m. How much fencing do they still need to erect? Step 1: Calculate the total length of fencing already erected. Fencing erected = 3(2)/(8) m + 4(5)/(8) m Fencing erected = (3+4) + ((2)/(8) + (5)/(8)) Fencing erected = 7 + (7)/(8) = 7(7)/(8) m Step 2: Subtract the erected fencing from the total required fencing. Fencing still needed = 20(3)/(8) m - 7(7)/(8) m Step 3: Convert mixed numbers to improper fractions or borrow from the whole number. 20(3)/(8) = 19 + 1 + (3)/(8) = 19 + (8)/(8) + (3)/(8) = 19(11)/(8) Fencing still needed = 19(11)/(8) - 7(7)/(8) Step 4: Subtract the whole numbers and the fractions. Fencing still needed = (19-7) + ((11)/(8) - (7)/(8)) Fencing still needed = 12 + (4)/(8) Step 5: Simplify the fraction. Fencing still needed = 12(1)/(2) m They still need to erect 12(1)/(2) m of fencing. 4. a) What fraction of an hour is 40 minutes, in its simplest form? Step 1: There are 60 minutes in an hour. Form the fraction. Fraction = 40 minutes60 minutes Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 20. Fraction = (40 ÷ 20)/(60 ÷ 20) = (2)/(3) 40 minutes is (2)/(3) of an hour. 4. b) I sleep 8 hours a night. What fraction of a day is this? Step 1: There are 24 hours in a day. Form the fraction. Fraction = 8 hours24 hours Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 8. Fraction = (8 ÷ 8)/(24 ÷ 8) = (1)/(3) 8 hours is (1)/(3) of a day. 4. c) How many hours is (1)/(4) of a day? How many hours is (3)/(4) of a day? Step 1: Calculate (1)/(4) of a day (24 hours). (1)/(4) of a day = (1)/(4) × 24 hours = 6 hours Step 2: Calculate (3)/(4) of a day (24 hours). (3)/(4) of a day = (3)/(4) × 24 hours = 3 × 6 hours = 18 hours (1)/(4) of a day is 6 hours and (3)/(4) of a day is 18 hours. 5. Mila has saved R208. She decides to spend (5)/(8) of her money on a new skirt. a) How much did the skirt cost? Step 1: Calculate (5)/(8) of R208. Skirt cost = (5)/(8) × R208 Skirt cost = 5 × (208)/(8) Skirt cost = 5 × 26 = R130 The skirt cost R130. b) How much money has she got left? Step 1: Subtract the skirt cost from the total saved. Money left = R208 - R130 Money left = R78 She has R78 left. 6. Thando had 24 sweets. He ate one-quarter of his sweets and gave half of what was left to a friend. a) How many sweets did he eat? Step 1: Calculate one-quarter of 24 sweets. Sweets eaten = (1)/(4) × 24 Sweets eaten = 6 He ate 6 sweets. b) How many sweets did he give to his friend? Step 1: Calculate the number of sweets left after he ate some. Sweets left = 24 - 6 = 18 Step 2: He gave half of what was left to a friend. Sweets given to friend = (1)/(2) × 18 Sweets given to friend = 9 He gave 9 sweets to his friend. 7. Joe had R150. He spent (2)/(5) of the money on a shirt, and then he spent (2)/(3) of the money that was left to buy a cap. a) How much did the shirt cost? Step 1: Calculate (2)/(5) of R150. Shirt cost = (2)/(5) × R150 Shirt cost = 2 × (150)/(5) Shirt cost = 2 × 30 = R60 The shirt cost R60. b) How much did

Accepted Answer · 2026-05-21T19:23:45.846Z

You're on a roll — here are the solutions to the problems from the image. Exercise 4.11 1. There are 600 people in a concert audience. (3)/(10) are male and (5)/(6) older than 10 years of age. a) What fraction of the audience is female? Step 1: The total audience is represented by the fraction 1. If (3)/(10) are male, the rest are female. Fraction female = 1 - (3)/(10) Fraction female = (10)/(10) - (3)/(10) = (7)/(10) The fraction of the audience that is female is (7)/(10). b) What fraction of the audience is younger than 10 years of age? Step 1: The total audience is represented by the fraction 1. If (5)/(6) are older than 10, the rest are younger than 10. Fraction younger than 10 = 1 - (5)/(6) Fraction younger than 10 = (6)/(6) - (5)/(6) = (1)/(6) The fraction of the audience younger than 10 years of age is (1)/(6). c) How many people in the audience are female? Step 1: Use the fraction of females from part (a) and the total number of people. Number of females = (7)/(10) × 600 Number of females = 7 × 60 = 420 There are 420 female people in the audience. d) How many people are younger than 10 years of age? Step 1: Use the fraction of people younger than 10 from part (b) and the total number of people. Number of people younger than 10 = (1)/(6) × 600 Number of people younger than 10 = 1 × 100 = 100 There are 100 people younger than 10 years of age. 2. Jane has walked 2(4)/(5) km from her home towards the shops. She has to walk a further 1(3)/(5) km to get there. What is the total distance from her house to the shops? Step 1: Add the distance already walked and the remaining distance. Total distance = 2(4)/(5) km + 1(3)/(5) km Step 2: Add the whole numbers and the fractions separately. Total distance = (2+1) + ((4)/(5) + (3)/(5)) Total distance = 3 + (7)/(5) Step 3: Convert the improper fraction to a mixed number and add to the whole number. (7)/(5) = 1(2)/(5) Total distance = 3 + 1(2)/(5) = 4(2)/(5) km The total distance from her house to the shops is 4(2)/(5) km. 3. We are erecting safety fencing around our swimming pool. The total length of fencing is 20(3)/(8) m. The builders have already erected two pieces. One is 3(2)/(8) m, the next is 4(5)/(8) m. How much fencing do they still need to erect? Step 1: Calculate the total length of fencing already erected. Fencing erected = 3(2)/(8) m + 4(5)/(8) m Fencing erected = (3+4) + ((2)/(8) + (5)/(8)) Fencing erected = 7 + (7)/(8) = 7(7)/(8) m Step 2: Subtract the erected fencing from the total required fencing. Fencing still needed = 20(3)/(8) m - 7(7)/(8) m Step 3: Convert mixed numbers to improper fractions or borrow from the whole number. 20(3)/(8) = 19 + 1 + (3)/(8) = 19 + (8)/(8) + (3)/(8) = 19(11)/(8) Fencing still needed = 19(11)/(8) - 7(7)/(8) Step 4: Subtract the whole numbers and the fractions. Fencing still needed = (19-7) + ((11)/(8) - (7)/(8)) Fencing still needed = 12 + (4)/(8) Step 5: Simplify the fraction. Fencing still needed = 12(1)/(2) m They still need to erect 12(1)/(2) m of fencing. 4. a) What fraction of an hour is 40 minutes, in its simplest form? Step 1: There are 60 minutes in an hour. Form the fraction. Fraction = 40 minutes60 minutes Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 20. Fraction = (40 ÷ 20)/(60 ÷ 20) = (2)/(3) 40 minutes is (2)/(3) of an hour. 4. b) I sleep 8 hours a night. What fraction of a day is this? Step 1: There are 24 hours in a day. Form the fraction. Fraction = 8 hours24 hours Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 8. Fraction = (8 ÷ 8)/(24 ÷ 8) = (1)/(3) 8 hours is (1)/(3) of a day. 4. c) How many hours is (1)/(4) of a day? How many hours is (3)/(4) of a day? Step 1: Calculate (1)/(4) of a day (24 hours). (1)/(4) of a day = (1)/(4) × 24 hours = 6 hours Step 2: Calculate (3)/(4) of a day (24 hours). (3)/(4) of a day = (3)/(4) × 24 hours = 3 × 6 hours = 18 hours (1)/(4) of a day is 6 hours and (3)/(4) of a day is 18 hours. 5. Mila has saved R208. She decides to spend (5)/(8) of her money on a new skirt. a) How much did the skirt cost? Step 1: Calculate (5)/(8) of R208. Skirt cost = (5)/(8) × R208 Skirt cost = 5 × (208)/(8) Skirt cost = 5 × 26 = R130 The skirt cost R130. b) How much money has she got left? Step 1: Subtract the skirt cost from the total saved. Money left = R208 - R130 Money left = R78 She has R78 left. 6. Thando had 24 sweets. He ate one-quarter of his sweets and gave half of what was left to a friend. a) How many sweets did he eat? Step 1: Calculate one-quarter of 24 sweets. Sweets eaten = (1)/(4) × 24 Sweets eaten = 6 He ate 6 sweets. b) How many sweets did he give to his friend? Step 1: Calculate the number of sweets left after he ate some. Sweets left = 24 - 6 = 18 Step 2: He gave half of what was left to a friend. Sweets given to friend = (1)/(2) × 18 Sweets given to friend = 9 He gave 9 sweets to his friend. 7. Joe had R150. He spent (2)/(5) of the money on a shirt, and then he spent (2)/(3) of the money that was left to buy a cap. a) How much did the shirt cost? Step 1: Calculate (2)/(5) of R150. Shirt cost = (2)/(5) × R150 Shirt cost = 2 × (150)/(5) Shirt cost = 2 × 30 = R60 The shirt cost R60. b) How much did

A concert audience of 600 people has 3/10 males and 5/6 older than 10. Calculate the fraction of females, fraction younger than 10, number of females, and number younger than 10.

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A concert audience of 600 people has 3/10 males and 5/6 older than 10. Calculate the fraction of females, fraction younger than 10, number of females, and number younger than 10.

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