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Simplify.\newline17−521517-5\frac{2}{15}

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Full solution

Q. Simplify.\newline17−521517-5\frac{2}{15}
  1. Convert to Improper Fraction: First, let's convert the mixed number to an improper fraction. 52155 \frac{2}{15} is the same as (5×15+2)/15(5 \times 15 + 2)/15, which is (75+2)/15(75 + 2)/15.\newlineCalculation: 5×15+2=775 \times 15 + 2 = 77, so 5215=77155 \frac{2}{15} = \frac{77}{15}.
  2. Subtract Whole Number: Now, we need to subtract the fraction from the whole number. To do this, we can convert 1717 to a fraction with the same denominator as 7715\frac{77}{15}. So, 1717 becomes 17×151517 \times \frac{15}{15}.\newlineCalculation: 17×15=25517 \times 15 = 255, so 17=2551517 = \frac{255}{15}.
  3. Subtract Fractions: Next, we subtract the two fractions. We have 25515−7715\frac{255}{15} - \frac{77}{15}.\newlineCalculation: 255−77=178255 - 77 = 178, so 25515−7715=17815\frac{255}{15} - \frac{77}{15} = \frac{178}{15}.
  4. Simplify Fraction: Finally, we can simplify the fraction 17815\frac{178}{15} by dividing both the numerator and the denominator by their greatest common divisor, which is 11 in this case. So, the fraction remains 17815\frac{178}{15}.\newlineCalculation: 178÷1=178178 \div 1 = 178, 15÷1=1515 \div 1 = 15, so 17815\frac{178}{15} is already in its simplest form.

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