Chapter 22: Fractions - Operations and Problem Solving > HARD QUESTIONS (Questions 15-20)HARD QUESTIONS (Questions 15-20)Previous Question 1 of 61 / 6NextReveal all steps Step 1: Convert mixed numbers to improper fractions. 3 1/2 = (3 × 2 + 1)/2 = 7/2 2 2/5 = (2 × 5 + 2)/5 = 12/5 Step 2: Multiply the fractions. 7/2 × 12/5 = (7 × 12)/(2 × 5) = 84/10 Step 3: Simplify and convert to mixed number. 84/10 = 42/5 (dividing both by 2) 42/5 = 8 2/5 Therefore, 3 1/2 × 2 2/5 = 8 2/5. Step 1: Convert mixed numbers to improper fractions. 4 1/3 = (4 × 3 + 1)/3 = 13/3 1 5/6 = (1 × 6 + 5)/6 = 11/6 Step 2: Divide by flipping and multiplying. 13/3 ÷ 11/6 = 13/3 × 6/11 = (13 × 6)/(3 × 11) = 78/33 Step 3: Simplify. 78/33 = 26/11 (dividing both by 3) = 2 4/11 Therefore, 4 1/3 ÷ 1 5/6 = 2 4/11. Step 1: Convert 2 1/4 to an improper fraction. 2 1/4 = (2 × 4 + 1)/4 = 9/4 Step 2: Find 2/3 of 9/4. 2/3 × 9/4 = (2 × 9)/(3 × 4) = 18/12 Step 3: Simplify. 18/12 = 3/2 (dividing both by 6) = 1 1/2 Therefore, you need 1 1/2 cups of flour. Step 1: Find how much water was used. Water used = 1/4 of 3/5 = 1/4 × 3/5 = 3/20 of the tank Step 2: Subtract from the original amount. Water remaining = 3/5 - 3/20 Convert 3/5 to twentieths: 3/5 = 12/20 = 12/20 - 3/20 = 9/20 Therefore, 9/20 of the tank is now full. Step 1: Find the LCM of 3 and 4. LCM = 12 Step 2: Rewrite fractions with common denominator. x/3 = 4x/12 x/4 = 3x/12 Step 3: Add the fractions. 4x/12 + 3x/12 = 7 7x/12 = 7 Step 4: Solve for x. 7x = 7 × 12 7x = 84 x = 84 ÷ 7 x = 12 Check: 12/3 + 12/4 = 4 + 3 = 7 ✓ Therefore, x = 12. Step 1: Find the number of boys and girls. Boys = 3/7 of 840 = 3/7 × 840 = 2520/7 = 360 boys Girls = 840 - 360 = 480 girls Or: Girls = 4/7 of 840 = 4/7 × 840 = 480 girls Part (a): Boys who play football Football boys = 2/5 of 360 = 2/5 × 360 = 720/5 = 144 boys Part (b): Girls who play netball Netball girls = 1/4 of 480 = 1/4 × 480 = 120 girls Part (c): Fraction playing football or netball Total playing = 144 + 120 = 264 students Fraction = 264/840 Simplify: 264/840 = 33/105 = 11/35 (dividing by 8, then 3) Check: HCF(264, 840) = 24, so 264/840 = 11/35 Answers: (a) 144 boys play football, (b) 120 girls play netball, (c) 11/35 of all students.
