Simplify the expression (5 - 15/16) × 1 12/13.

Question

Accepted Answer

Step 1: Simplify the first bracket (5 - 15/16).
- Convert 5 to a fraction with denominator 16: 5 = 80/16.
- Subtract: 80/16 - 15/16 = (80 - 15)/16 = 65/16.

Step 2: Convert the mixed number 1 12/13 to an improper fraction.
- 1 12/13 = (1 × 13 + 12)/13 = (13 + 12)/13 = 25/13.

Step 3: Multiply the two fractions.
- (65/16) × (25/13) = (65 × 25) / (16 × 13) = 1625 / 208.

Step 4: Simplify the fraction 1625/208.
- Divide numerator and denominator by their GCD if possible. Here, GCD is 1.
- Convert to mixed number: 208 × 7 = 1456, remainder = 1625 - 1456 = 169.
- So, 1625/208 = 7 169/208.

Step 5: Simplify the fractional part 169/208.
- Find GCD of 169 and 208.
- 169 = 13 × 13, 208 = 13 × 16, so GCD = 13.
- Divide numerator and denominator by 13: 169/13 = 13, 208/13 = 16.
- Fraction simplifies to 13/16.

Final answer: 7 13/16.

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