Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A carpenter is building a custom bookshelf. He has a piece of wood that is 10 1/2 feet long. If each shelf requires 2 3/4 feet of wood, how many full shelves can he cut from the piece of wood?
- A6 shelves
- B4 shelves
- C3 shelves
- D5 shelves
Show answer & explanationAnswer & explanation
Correct answer: C. 3 shelves
To solve this, convert the mixed numbers to improper fractions, then divide the total length of wood by the length required for one shelf. The answer must be a whole number representing full shelves.
Why the other options are wrong
- A. This would require approximately 16.5 feet of wood (6 * 2.75).
- B. This would require approximately 11 feet of wood (4 * 2.75).
- D. This would require approximately 13.75 feet of wood (5 * 2.75).
Dividing Mixed Numbers
To divide mixed numbers, first convert them into improper fractions. Then, multiply the first fraction by the reciprocal of the second fraction. Finally, simplify the result if necessary.
- Convert mixed numbers to improper fractions: a b/c = (ac + b)/c.
- Dividing by a fraction is equivalent to multiplying by its reciprocal.
- The reciprocal of a/b is b/a.
Memory trick: Improper Flip Multiply!