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March 15, 2026Mathematics

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Answer

\dfrac{5}{12}

5 steps

Identify and simplify any reducible fractions.
$\frac{2}{6} = \frac{1}{3}$
The expression is now $\frac{1}{2} + \frac{1}{3} + \frac{1}{3} - \frac{3}{4}$ .
Combine like terms.
$\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$
The expression simplifies to $\frac{1}{2} + \frac{2}{3} - \frac{3}{4}$ .
Find the least common denominator (LCD) of 2, 3, and 4.
LCD = 12.
Convert each fraction.
$\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}$ $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$ $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$
Substitute and simplify.
$\frac{6}{12} + \frac{8}{12} - \frac{9}{12} = \frac{6 + 8 - 9}{12} = \frac{14 - 9}{12} = \frac{5}{12}$
Final answer: $\boxed{\dfrac{5}{12}}$

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