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Simplify the expression: 3 rac12 + ((3)/(4) of 3 rac12) + 1 rac18

Mathematics

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Answer

7147\frac{1}{4}

Step-by-step solution

6 steps

  1. Convert all mixed numbers to improper fractions.

    312=(3×2)+12=723\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2} 118=(1×8)+18=981\frac{1}{8} = \frac{(1 \times 8) + 1}{8} = \frac{9}{8}

  2. Substitute these into the expression and perform the multiplication ("of") first.

    312+(34 of 312)+118=72+(34×72)+983\frac{1}{2} + \left(\frac{3}{4} \text{ of } 3\frac{1}{2}\right) + 1\frac{1}{8} = \frac{7}{2} + \left(\frac{3}{4} \times \frac{7}{2}\right) + \frac{9}{8} 72+(3×74×2)+98=72+218+98\frac{7}{2} + \left(\frac{3 \times 7}{4 \times 2}\right) + \frac{9}{8} = \frac{7}{2} + \frac{21}{8} + \frac{9}{8}

  3. Find a common denominator for all fractions, which is 8.

    Convert 72\frac{7}{2} to have a denominator of 8.

    72=7×42×4=288\frac{7}{2} = \frac{7 \times 4}{2 \times 4} = \frac{28}{8}

  4. Add the fractions.

    288+218+98=28+21+98\frac{28}{8} + \frac{21}{8} + \frac{9}{8} = \frac{28 + 21 + 9}{8} 588\frac{58}{8}

  5. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2.

    58÷28÷2=294\frac{58 \div 2}{8 \div 2} = \frac{29}{4}

  6. Convert the improper fraction to a mixed number.

    294=714\frac{29}{4} = 7\frac{1}{4}

    The simplified expression is 7147\frac{1}{4}.

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