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Subtract the fractions: (2)/(3) - (3)/(2)

Mathematics

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Answer

−56-\frac{5}{6}

Step-by-step solution

5 steps

  1. Identify the fractions in the expression.

    The expression is a subtraction of two fractions: 23−32\frac{2}{3} - \frac{3}{2}.

  2. Find a common denominator for the fractions.

    The denominators are 3 and 2. The least common multiple (LCM) of 3 and 2 is 6.

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

    For the first fraction, 23\frac{2}{3}:
    Multiply the numerator and denominator by 2:

    23=2×23×2=46\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}

    For the second fraction, 32\frac{3}{2}:
    Multiply the numerator and denominator by 3:

    32=3×32×3=96\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}

  4. Perform the subtraction with the equivalent fractions.

    46−96\frac{4}{6} - \frac{9}{6}

  5. Subtract the numerators and keep the common denominator.

    4−96=−56\frac{4 - 9}{6} = \frac{-5}{6}

    The final answer is −56-\frac{5}{6}.

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