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Mathematics

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Answer

512\dfrac{5}{12}

Step 1: Identify and simplify any reducible fractions.

26=13\frac{2}{6} = \frac{1}{3}

The expression is now 12+13+13−34\frac{1}{2} + \frac{1}{3} + \frac{1}{3} - \frac{3}{4}.

Step 2: Combine like terms.

13+13=23\frac{1}{3} + \frac{1}{3} = \frac{2}{3}

The expression simplifies to 12+23−34\frac{1}{2} + \frac{2}{3} - \frac{3}{4}.

Step 3: Find the least common denominator (LCD) of 22, 33, and 44.

LCD = 1212.

Step 4: Convert each fraction.

12=1×62×6=612\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12} 23=2×43×4=812\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} 34=3×34×3=912\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}

Step 5: Substitute and simplify.

612+812−912=6+8−912=14−912=512\frac{6}{12} + \frac{8}{12} - \frac{9}{12} = \frac{6 + 8 - 9}{12} = \frac{14 - 9}{12} = \frac{5}{12}

Final answer: 512\boxed{\dfrac{5}{12}}

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