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Evaluate 5 1/3 - 2 1/4 - 1 7/8

Mathematics

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Answer

1524\mathbf{1\frac{5}{24}}

Step-by-step solution

6 steps

  1. Convert the mixed numbers to improper fractions.

    513=(5×3)+13=1635\frac{1}{3} = \frac{(5 \times 3) + 1}{3} = \frac{16}{3} 214=(2×4)+14=942\frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{9}{4} 178=(1×8)+78=1581\frac{7}{8} = \frac{(1 \times 8) + 7}{8} = \frac{15}{8}

    The expression becomes:

    163−94−158\frac{16}{3} - \frac{9}{4} - \frac{15}{8}

  2. Find the least common multiple (LCM) of the denominators 3, 4, and 8.

    The LCM of 3, 4, and 8 is 24.

  3. Convert each fraction to an equivalent fraction with a denominator of 24.

    163=16×83×8=12824\frac{16}{3} = \frac{16 \times 8}{3 \times 8} = \frac{128}{24} 94=9×64×6=5424\frac{9}{4} = \frac{9 \times 6}{4 \times 6} = \frac{54}{24} 158=15×38×3=4524\frac{15}{8} = \frac{15 \times 3}{8 \times 3} = \frac{45}{24}

  4. Perform the subtraction with the common denominator.

    12824−5424−4524=128−54−4524\frac{128}{24} - \frac{54}{24} - \frac{45}{24} = \frac{128 - 54 - 45}{24}

  5. Calculate the numerator.

    128−54−45=74−45=29128 - 54 - 45 = 74 - 45 = 29

  6. Write the result as an improper fraction and then convert it to a mixed number.

    2924=1524\frac{29}{24} = 1\frac{5}{24}

    The evaluated expression is:

    1524\mathbf{1\frac{5}{24}}
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