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In problem 17, the top number is the difference between the two bottom numbers. Convert the mixed numbers 8 rac12 and 5 rac25 to improper fractions, find their difference, and express it as a mixed nu

Mathematics

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The pattern for these problems is that the top number is the difference between the two bottom numbers.

  1. Convert the mixed numbers to improper fractions.

    812=(8×2)+12=16+12=1728\frac{1}{2} = \frac{(8 \times 2) + 1}{2} = \frac{16 + 1}{2} = \frac{17}{2} 525=(5×5)+25=25+25=2755\frac{2}{5} = \frac{(5 \times 5) + 2}{5} = \frac{25 + 2}{5} = \frac{27}{5}

  2. Find a common denominator for the fractions.

    The least common denominator for 2 and 5 is 10.

    172=17×52×5=8510\frac{17}{2} = \frac{17 \times 5}{2 \times 5} = \frac{85}{10} 275=27×25×2=5410\frac{27}{5} = \frac{27 \times 2}{5 \times 2} = \frac{54}{10}

  3. Subtract the smaller fraction from the larger fraction to find the difference.

    8510−5410=85−5410=3110\frac{85}{10} - \frac{54}{10} = \frac{85 - 54}{10} = \frac{31}{10}

  4. Convert the improper fraction back to a mixed number.

    3110=3110\frac{31}{10} = 3\frac{1}{10}

    The missing value for is \boxed{\text{3\frac{1}{10}}}.

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