Question

Perform the indicated operation. \(12 \frac{1}{4}-7 \frac{1}{8}\)

Short answer

Answer: The result of the subtraction is 5 1/8.

Step-by-step solution

Convert mixed fractions to improper fractions

To convert a mixed fraction to an improper fraction, we use the formula: \(\text{improper}_\text{numerator}= \text{whole part} \times \text{denominator}+\text{numerator}\). Then, put that result over the original denominator to get the improper fraction. For the first fraction: \(12 \frac{1}{4}= \frac{(12\times 4)+1}{4}= \frac{49}{4}\) For the second fraction: \(7 \frac{1}{8}= \frac{(7\times 8)+1}{8}= \frac{57}{8}\) So, the subtraction problem becomes: \(\frac{49}{4} - \frac{57}{8}\)

Find a common denominator and subtract the numerators

The least common multiple (LCM) of 4 and 8 is 8. So, we will convert the first fraction to have a denominator of 8. \(\frac{49}{4} \times \frac{2}{2}= \frac{98}{8}\) Now we can perform the subtraction: \(\frac{98}{8} - \frac{57}{8}= \frac{98-57}{8}= \frac{41}{8}\)

Convert the resulting improper fraction to a mixed fraction

To convert an improper fraction to a mixed fraction, divide the numerator by the denominator and write the remainder as a fraction. In this case, \(41 \div 8 = 5 \text{ R } 1\). So, our mixed fraction is: \(5 \frac{1}{8}\) Therefore, the result of the subtraction \(12 \frac{1}{4}-7 \frac{1}{8}\) is \(5 \frac{1}{8}\).