Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium

A construction crew is pouring concrete for a foundation. They have 3 1/2 cubic yards of concrete remaining. If each section of the foundation requires 1/4 cubic yard of concrete, how many full sections can they pour?

  1. A15
  2. B14
  3. C13
  4. D12
Show answer & explanation

Correct answer: B. 14

First, convert the mixed number 3 1/2 to an improper fraction, which is 7/2. Then, divide 7/2 by 1/4. Dividing by a fraction is the same as multiplying by its reciprocal: (7/2) * (4/1) = 28/2 = 14. So, they can pour 14 full sections.

Why the other options are wrong

  • A. This would be the result if 3 3/4 was divided by 1/4.
  • C. This is close but incorrect, possibly from a rounding error or slight miscalculation.
  • D. This would be the result if 3 1/2 was divided by 5/12.

Dividing Mixed Numbers by Fractions

To divide a mixed number by a fraction, first convert the mixed number to an improper fraction. Then, multiply the improper fraction by the reciprocal of the divisor fraction.

  • A mixed number combines a whole number and a fraction.
  • An improper fraction has a numerator greater than or equal to its denominator.
  • The reciprocal of a fraction a/b is b/a.

Memory trick: Keep, Change, Flip (KCF): Keep the first, change to multiply, flip the second.

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