Problem 44 - Prealgebra and Introductory Algebra

Question

What is \(-\frac{7}{12}\) minus \(\frac{7}{9} ?\)

Step-by-Step Solution

Answer

The answer is \(-\frac{49}{36}\).

Step 1: Find a common denominator

A common denominator between 12 and 9 is 36 (since both 12 and 9 divide evenly into 36).

Step 2: Convert fractions to equivalent fractions with the common denominator

To convert \(-\frac{7}{12}\) to a fraction with a denominator of 36, multiply both the numerator and the denominator by 3, resulting in \(-\frac{21}{36}\). To convert \(\frac{7}{9}\) to a fraction with a denominator of 36, multiply both the numerator and the denominator by 4, resulting in \(\frac{28}{36}\).

Step 3: Subtract the fractions

Now that the fractions have the same denominator, subtract the numerators. So, \(-\frac{21}{36} - \frac{28}{36} = -\frac{49}{36}\).