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Evaluate the expression 2/4 + 6/3 - 7/6.

Mathematics

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Answer

43\frac{4}{3}

Step-by-step solution

5 steps

To evaluate the expression 24+63−76\frac{2}{4} + \frac{6}{3} - \frac{7}{6}:

  1. Simplify the fractions.

    24=12\frac{2}{4} = \frac{1}{2} 63=2\frac{6}{3} = 2

    The expression becomes:

    12+2−76\frac{1}{2} + 2 - \frac{7}{6}

  2. Find a common denominator for all terms.

    The denominators are 2, 1 (for the integer 2), and 6. The least common multiple (LCM) of 2, 1, and 6 is 6.

  3. Convert each term to an equivalent fraction with the common denominator of 6.

    12=1×32×3=36\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} 2=2×61×6=1262 = \frac{2 \times 6}{1 \times 6} = \frac{12}{6} 76 remains as 76\frac{7}{6} \text{ remains as } \frac{7}{6}

  4. Perform the addition and subtraction with the common denominator.

    36+126−76=3+12−76\frac{3}{6} + \frac{12}{6} - \frac{7}{6} = \frac{3 + 12 - 7}{6} =15−76= \frac{15 - 7}{6} =86= \frac{8}{6}

  5. Simplify the resulting fraction.

    86=8÷26÷2=43\frac{8}{6} = \frac{8 \div 2}{6 \div 2} = \frac{4}{3} =43= \boxed{\frac{4}{3}}
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