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Problem 13: What is the missing number in the sequence, given that the top number is the difference between the two bottom numbers?

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.

    612=(6×2)+12=12+12=1326\frac{1}{2} = \frac{(6 \times 2) + 1}{2} = \frac{12 + 1}{2} = \frac{13}{2} 334=(3×4)+34=12+34=1543\frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}

  2. Find a common denominator for the fractions.

    The least common denominator for 2 and 4 is 4.

    132=13×22×2=264\frac{13}{2} = \frac{13 \times 2}{2 \times 2} = \frac{26}{4}

  3. Subtract the smaller fraction from the larger fraction.

    264−154=26−154=114\frac{26}{4} - \frac{15}{4} = \frac{26 - 15}{4} = \frac{11}{4}

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

    114=234\frac{11}{4} = 2\frac{3}{4}

    The missing value for is \boxed{\text{2\frac{3}{4}}}.

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