Question

Evaluate the expression. $$ \frac{7}{12}-\left(-\frac{3}{4}\right)+\left(-\frac{1}{8}\right) $$

Short answer

The expression simplifies to \( \frac{29}{24} \)

Step-by-step solution

Break down the expression into parts

Express the expression as: \( \frac{7}{12} + \left(\frac{3}{4}\right) - \frac{1}{8} \). This helps to separate the parts of the expression, looking at each fraction separately, and better understanding the influence of the negative signs.

Convert all fractions to equivalent fractions with same denominator

All fractions should have the same denominator for easy addition and subtraction. The least common multiple of 12, 4, and 8 is 24. Convert each fraction to an equivalent fraction with denominator 24: \( \frac{14}{24} + \frac{18}{24} - \frac{3}{24} \).

Add and subtract the fractions

Now that all fractions have the same denominator, they can be added and subtracted. Perform the addition and subtraction to get the answer: \( \frac{14 + 18 - 3}{24} = \frac{29}{24} \).