Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A project manager is analyzing task durations. Task X takes 2 1/2 hours, Task Y takes 1 3/4 hours, and Task Z takes 3/5 of an hour. What is the total time required to complete all three tasks?
- A6 1/20 hours
- B4 13/20 hours
- C5 13/20 hours
- D5 1/20 hours
Show answer & explanationAnswer & explanation
Correct answer: D. 5 1/20 hours
To add these mixed numbers and fractions, first find a common denominator, which is 20. Convert each to a fraction with denominator 20: Task X: 2 1/2 = 5/2 = 50/20 hours. Task Y: 1 3/4 = 7/4 = 35/20 hours. Task Z: 4/5 = 16/20 hours. Add the fractions: 50/20 + 35/20 + 16/20 = (50 + 35 + 16)/20 = 101/20 hours. Convert the improper fraction to a mixed number: 101 ÷ 20 = 5 with a remainder of 1. So, the total time is 5 1/20 hours.
Why the other options are wrong
- A. This might result from an incorrect common denominator or arithmetic error in addition.
- B. This might result from an incorrect common denominator or arithmetic error in addition.
- C. This might result from an arithmetic error or miscalculation during conversion.
Adding Mixed Numbers and Fractions
To add mixed numbers and fractions, convert all to improper fractions with a common denominator. Add the numerators, keep the common denominator, then convert the result back to a mixed number.
- Find the least common denominator (LCD) for all fractions.
- Convert mixed numbers to improper fractions.
- Rewrite all fractions with the LCD.
- Add the numerators, keeping the common denominator.
- Simplify the resulting improper fraction to a mixed number.
Memory trick: Common ground for all, then add 'em all!