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 1 3/4 feet of wood, how many full shelves can he cut from the piece of wood?
- A5 shelves
- B6 shelves
- C7 shelves
- D8 shelves
Show answer & explanationAnswer & explanation
Correct answer: B. 6 shelves
To find out how many shelves can be cut, divide the total length of the wood by the length required for one shelf. Convert both mixed numbers to improper fractions before dividing.
Why the other options are wrong
- A. Incorrect calculation; possibly an error in fraction conversion or division.
- C. Incorrect calculation; likely an error in the division process.
- D. Incorrect calculation; this number is too high, suggesting an overestimation or calculation error.
Dividing with Mixed Numbers
To divide mixed numbers, first convert both mixed numbers into improper fractions. Then, multiply the first fraction by the reciprocal (flipped version) of the second fraction. Simplify the result.
- Convert mixed numbers to improper fractions (whole * denominator + numerator / denominator).
- Change division to multiplication by the reciprocal.
- Simplify before or after multiplying.
Memory trick: Mixed to improper, flip and multiply, simplify your answer, and then you'll fly!