Question

Perform the indicated operation. \(7 \frac{3}{8}-4 \frac{1}{4}\)

Short answer

Answer: The result of subtracting \(4 \frac{1}{4}\) from \(7 \frac{3}{8}\) is \(3 \frac{1}{8}\).

Step-by-step solution

Convert mixed numbers to improper fractions

To convert the mixed numbers to improper fractions, use the following formula: \((Whole \ Number \times Denominator) + Numerator\) For \(7 \frac{3}{8}\): \(Whole \ Number = 7\) \(Denominator = 8\) \(Numerator = 3\) \(7 \frac{3}{8}\) as an improper fraction: \((7 \times 8) + 3 = 56 + 3 = 59\) So, \(7 \frac{3}{8} = \frac{59}{8}\) For \(4 \frac{1}{4}\): \(Whole \ Number = 4\) \(Denominator = 4\) \(Numerator = 1\) \(4 \frac{1}{4}\) as an improper fraction: \((4 \times 4) + 1 = 16 + 1 = 17\) So, \(4 \frac{1}{4} = \frac{17}{4}\)

Find the common denominator

To subtract the two fractions, we need to find a common denominator. The Least Common Multiple (LCM) of 8 and 4 is 8. So, the common denominator is 8.

Change both fractions to the common denominator, if needed.

The fraction \(\frac{59}{8}\) already has the common denominator of 8, so we don't need to change it. However, we need to change \(\frac{17}{4}\) so that it has a denominator of 8. To do this, multiply both the numerator and the denominator by the same number to achieve the desired denominator: \(\frac{17}{4} = \frac{17 \times 2}{4 \times 2} = \frac{34}{8}\)

Subtract the fractions

Now, we can subtract the fractions: \(\frac{59}{8} - \frac{34}{8} = \frac{59 - 34}{8} = \frac{25}{8}\)

Convert the improper fraction back to a mixed number (optional)

If desired, we can convert the improper fraction back to a mixed number: \(\frac{25}{8} = 3 \frac{1}{8}\) So, the result of the subtraction is: \(7 \frac{3}{8} - 4 \frac{1}{4} = 3 \frac{1}{8}\)