Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
An architect is designing a staircase. Each step needs to be 7 3/4 inches high. If the total rise of the staircase is 93 inches, how many steps are needed?
- A10 steps
- B11 steps
- C12 steps
- D13 steps
Show answer & explanationAnswer & explanation
Correct answer: C. 12 steps
First, convert the mixed number to an improper fraction: 7 3/4 = (7*4 + 3)/4 = 31/4 inches. To find the number of steps, divide the total rise by the height of each step: 93 inches / (31/4 inches/step). This is equivalent to 93 * (4/31). 93 divided by 31 is 3. So, 3 * 4 = 12 steps.
Why the other options are wrong
- A. Incorrect calculation, perhaps from rounding or misinterpreting the fraction.
- B. Incorrect calculation, possibly from an error in division or fraction conversion.
- D. Incorrect calculation, likely from an arithmetic error.
Dividing with Mixed Numbers
To divide by a mixed number, first convert the mixed number into an improper fraction. Then, multiply the dividend by the reciprocal of the improper fraction.
- Mixed numbers must be converted to improper fractions first.
- Division by a fraction is equivalent to multiplication by its reciprocal.
- Simplify before multiplying for easier calculation.
Memory trick: Mixed to improper, flip and multiply, then simplify to get your reply!