Question

Perform the indicated operation. \(2 \frac{2}{7}-\left(-3 \frac{3}{8}\right)\)

Short answer

Question: Subtract the mixed numbers 2 2/7 and -3 3/8. Answer: The result of subtracting the mixed numbers 2 2/7 and -3 3/8 is 275/56.

Step-by-step solution

Convert the mixed numbers to improper fractions

To convert the mixed numbers into improper fractions, first multiply each whole number by its denominator and then add it to the numerator. The result will become the new numerator, and the denominator remains unchanged: \(2 \frac{2}{7} = \frac{14+2}{7} = \frac{16}{7}\) \(-3 \frac{3}{8} = \frac{-24+3}{8} = \frac{-21}{8}\) Now our expression is \(\frac{16}{7}-\left(-\frac{21}{8}\right)\).

Change subtraction to addition

To simplify the expression, we can replace subtraction with adding the opposite. So we will change the subtraction to addition by changing the sign of the second fraction: \(\frac{16}{7} - \left(-\frac{21}{8}\right) = \frac{16}{7} + \frac{21}{8}\)

Find a common denominator

In order to add the fractions, we need a common denominator. We find the least common multiple (LCM) of 7 and 8, which is 56. Now, we will rewrite both fractions with a denominator of 56: \(\frac{16}{7} \times \frac{8}{8} = \frac{128}{56}\) \(\frac{21}{8} \times \frac{7}{7} = \frac{147}{56}\) Now, the expression becomes \(\frac{128}{56} + \frac{147}{56}\).

Add the fractions

Now that both fractions have the same denominator, we can add their numerators: \(\frac{128}{56} + \frac{147}{56} = \frac{128+147}{56} = \frac{275}{56}\)

Simplify, if necessary

The fraction \(\frac{275}{56}\) cannot be simplified further, so this is our final answer: \(\frac{275}{56}\)