Simplify the expression 2 5/8 x 3 1/7 into an improper fraction and a mixed number: 33/4 ; 8 1/4 What is the product of 2 3/8 and 2/3? 19/12 ; 17/12 What is the quotient of 5/3 + 4/15? 25/4 ; 6 1/4
The Correct Answer and Explanation is:
Let’s tackle each question with accuracy and clarity, and correct any mistakes along the way.
1. Simplify 2 5/8 × 3 1/7
Convert to improper fractions: 2 5/8 = 21/8 3 1/7 = 22/7
Multiply: (21 × 22) / (8 × 7) = 462 / 56 Simplify: 462 ÷ 14 = 33, 56 ÷ 14 = 4 Result: 33/4 or 8 1/4
✔ This is correct.
2. Product of 2 3/8 × 2/3
Convert 2 3/8 to improper: 2 3/8 = 19/8
Multiply: (19 × 2) / (8 × 3) = 38 / 24 Simplify: 38 ÷ 2 = 19, 24 ÷ 2 = 12 Result: 19/12 or 1 7/12
✔ This is correct. The 17/12 given is incorrect.
3. Quotient of 5/3 ÷ 4/15
To divide, multiply by the reciprocal: (5/3) × (15/4) = (5 × 15) / (3 × 4) = 75 / 12
Simplify: 75 ÷ 3 = 25, 12 ÷ 3 = 4 Result: 25/4 or 6 1/4
✔ This is correct.
Summary of corrections and explanations:
The first problem demonstrates how multiplying two mixed numbers involves converting them into improper fractions, multiplying the numerators and denominators, and then simplifying.
The second problem highlights a calculation error: 17/12 is incorrect; the correct answer is 19/12. This mistake likely came from mismanaging either the numerator multiplication or simplifying the result too early.
The third problem requires understanding that dividing by a fraction means multiplying by its reciprocal. This step can be conceptually tricky but follows consistent rules.
Being careful with conversions and simplification preserves accuracy. With fractions, precision at every step is essential.
