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 Phatsimo — ready when you are. Here are the solutions to your questions: 1. Find the values of the following: a) (1)/(2) of 16 Step 1: Multiply the fraction by the number. (1)/(2) × 16 = (1 × 16)/(2) = (16)/(2) Step 2: Simplify the fraction. (16)/(2) = 8 The value is 8. b) (1)/(5) of 20 Step 1: Multiply the fraction by the number. (1)/(5) × 20 = (1 × 20)/(5) = (20)/(5) Step 2: Simplify the fraction. (20)/(5) = 4 The value is 4. c) (1)/(7) of 42 Step 1: Multiply the fraction by the number. (1)/(7) × 42 = (1 × 42)/(7) = (42)/(7) Step 2: Simplify the fraction. (42)/(7) = 6 The value is 6. d) (1)/(10) of 40 Step 1: Multiply the fraction by the number. (1)/(10) × 40 = (1 × 40)/(10) = (40)/(10) Step 2: Simplify the fraction. (40)/(10) = 4 The value is 4. e) (4)/(5) of 35 Step 1: Multiply the fraction by the number. (4)/(5) × 35 = (4 × 35)/(5) = (140)/(5) Step 2: Simplify the fraction. (140)/(5) = 28 The value is 28. f) (2)/(3) of 36 Step 1: Multiply the fraction by the number. (2)/(3) × 36 = (2 × 36)/(3) = (72)/(3) Step 2: Simplify the fraction. (72)/(3) = 24 The value is 24. g) (9)/(10) of 100 Step 1: Multiply the fraction by the number. (9)/(10) × 100 = (9 × 100)/(10) = (900)/(10) Step 2: Simplify the fraction. (900)/(10) = 90 The value is 90. h) (6)/(7) of 84 Step 1: Multiply the fraction by the number. (6)/(7) × 84 = (6 × 84)/(7) = (504)/(7) Step 2: Simplify the fraction. (504)/(7) = 72 The value is 72. 2. Work out the following: a) (1)/(3) × 12 Step 1: Multiply the numerator by the whole number and divide by the denominator. (1)/(3) × 12 = (1 × 12)/(3) = (12)/(3) Step 2: Simplify the fraction. (12)/(3) = 4 The product is 4. b) (1)/(4) × 8 Step 1: Multiply the numerator by the whole number and divide by the denominator. (1)/(4) × 8 = (1 × 8)/(4) = (8)/(4) Step 2: Simplify the fraction. (8)/(4) = 2 The product is 2. c) (3)/(4) × 8 Step 1: Multiply the numerator by the whole number and divide by the denominator. (3)/(4) × 8 = (3 × 8)/(4) = (24)/(4) Step 2: Simplify the fraction. (24)/(4) = 6 The product is 6. d) (4)/(5) × 20 Step 1: Multiply the numerator by the whole number and divide by the denominator. (4)/(5) × 20 = (4 × 20)/(5) = (80)/(5) Step 2: Simplify the fraction. (80)/(5) = 16 The product is 16. e) (2)/(3) × 9 Step 1: Multiply the numerator by the whole number and divide by the denominator. (2)/(3) × 9 = (2 × 9)/(3) = (18)/(3) Step 2: Simplify the fraction. (18)/(3) = 6 The product is 6. f) (1)/(6) × 36 Step 1: Multiply the numerator by the whole number and divide by the denominator. (1)/(6) × 36 = (1 × 36)/(6) = (36)/(6) Step 2: Simplify the fraction. (36)/(6) = 6 The product is 6. g) (5)/(6) × 24 Step 1: Multiply the numerator by the whole number and divide by the denominator. (5)/(6) × 24 = (5 × 24)/(6) = (120)/(6) Step 2: Simplify the fraction. (120)/(6) = 20 The product is 20. h) (4)/(9) × 45 Step 1: Multiply the numerator by the whole number and divide by the denominator. (4)/(9) × 45 = (4 × 45)/(9) = (180)/(9) Step 2: Simplify the fraction. (180)/(9) = 20 The product is 20. 3. At 10 years Kgomotso was (1)/(3) the weight of her father. If her father was 108 kg, what was her weight? Step 1: Identify the father's weight and the fraction representing Kgomotso's weight. Father's weight = 108 kg. Kgomotso's weight = (1)/(3) of father's weight. Step 2: Calculate Kgomotso's weight. Kgomotso's weight = (1)/(3) × 108 kg = (108)/(3) kg Step 3: Simplify the expression. (108)/(3) = 36 kg Kgomotso's weight was 36 kg. 4. In a certain month in winter, BMC killed (3)/(4) of its normal number of cattle. If it normally killed 6600 cattle, how many did it kill in this month? Step 1: Identify the normal number of cattle and the fraction killed. Normal cattle killed = 6600. Fraction killed in winter = (3)/(4). Step 2: Calculate the number of cattle killed in winter. Cattle killed = (3)/(4) × 6600 Step 3: Multiply the numerator by the total and divide by the denominator. Cattle killed = (3 × 6600)/(4) = (19800)/(4) Step 4: Simplify the expression. (19800)/(4) = 4950 BMC killed 4950 cattle in that month. 5. A bag contains counters. (3)/(5) of the counters are blue. How many counters are blue if there are 60 counters in the bag? Step 1: Identify the total number of counters and the fraction that are blue. Total counters = 60. Fraction of blue counters = (3)/(5). Step 2: Calculate the number of blue counters. Blue counters = (3)/(5) × 60 Step 3: Multiply the numerator by the total and divide by the denominator. Blue counters = (3 × 60)/(5) = (180)/(5) Step 4: Simplify the expression. (180)/(5) = 36 There are 36 blue counters in the bag. 6. Of the 9380 people tested for HIV, (3)/(20) of them were HIV positive. How many people were HIV positive? Step 1: Identify the total number of people tested and the fraction that were HIV positive. Total people tested = 9380. Fraction HIV positive = (3)/(20). Step 2: Calculate the number of people who were HIV positive. HIV positive people = (3)/(20) × 9380 Step 3: Multiply the numerator by the total and divide by the denominator. HIV positive people = (3 × 9380)/(20) = (28140)/(20) Step 4: Simplify the expression. (28140)/(20) = 1407 There were 1407 people who were HIV positive. Send me the next one 📸