Chapter 22: Fractions - Operations and Problem Solving > MODERATE QUESTIONS (Questions 8-14)MODERATE QUESTIONS (Questions 8-14)Previous Question 1 of 71 / 7NextReveal all steps Step 1: Find the LCM of the denominators (3 and 4). LCM of 3 and 4 = 12 Step 2: Convert each fraction to equivalent fractions with denominator 12. 2/3 = (2 × 4)/(3 × 4) = 8/12 3/4 = (3 × 3)/(4 × 3) = 9/12 Step 3: Add the fractions. 8/12 + 9/12 = 17/12 Step 4: Convert to mixed number. 17/12 = 1 5/12 Therefore, 2/3 + 3/4 = 1 5/12. Step 1: Find the LCM of the denominators (6 and 4). LCM of 6 and 4 = 12 Step 2: Convert each fraction. 5/6 = (5 × 2)/(6 × 2) = 10/12 1/4 = (1 × 3)/(4 × 3) = 3/12 Step 3: Subtract the fractions. 10/12 - 3/12 = 7/12 Therefore, 5/6 - 1/4 = 7/12. To multiply fractions: Multiply the numerators together. Multiply the denominators together. 3/5 × 4/7 = (3 × 4)/(5 × 7) = 12/35 Check if it can be simplified: HCF(12, 35) = 1 Therefore, 3/5 × 4/7 = 12/35. To divide fractions: Keep, Change, Flip (KCF) Keep the first fraction, change ÷ to ×, flip the second fraction. 4/5 ÷ 2/3 = 4/5 × 3/2 = (4 × 3)/(5 × 2) = 12/10 Simplify by dividing both by 2: = 6/5 Convert to mixed number: 6/5 = 1 1/5 Therefore, 4/5 ÷ 2/3 = 6/5 or 1 1/5. "Of" means multiply. 3/4 of 56 = 3/4 × 56 Method 1: Divide first, then multiply. 56 ÷ 4 = 14 14 × 3 = 42 Method 2: Multiply then simplify. 3/4 × 56/1 = (3 × 56)/(4 × 1) = 168/4 = 42 Therefore, 3/4 of 56 = 42. Method 1: Convert to improper fractions first. 2 1/3 = 7/3 1 3/4 = 7/4 Find LCM of 3 and 4 = 12 7/3 = 28/12 7/4 = 21/12 28/12 + 21/12 = 49/12 = 4 1/12 Method 2: Add whole numbers and fractions separately. Whole numbers: 2 + 1 = 3 Fractions: 1/3 + 3/4 = 4/12 + 9/12 = 13/12 = 1 1/12 Total: 3 + 1 1/12 = 4 1/12 Therefore, 2 1/3 + 1 3/4 = 4 1/12. Step 1: Find the LCM of all denominators (3, 8, 4, 12). LCM = 24 Step 2: Convert all fractions to equivalent fractions with denominator 24. 2/3 = (2 × 8)/(3 × 8) = 16/24 5/8 = (5 × 3)/(8 × 3) = 15/24 3/4 = (3 × 6)/(4 × 6) = 18/24 7/12 = (7 × 2)/(12 × 2) = 14/24 Step 3: Order by numerator (ascending). 14/24 < 15/24 < 16/24 < 18/24 Step 4: Write in original form. Ascending order: 7/12, 5/8, 2/3, 3/4
