Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A project manager is analyzing task durations. Task A takes 3 1/2 hours, Task B takes 2 3/4 hours, and Task C takes 1 1/3 hours. What is the total time required to complete all three tasks?
- A7 5/12 hours
- B6 7/12 hours
- C7 1/12 hours
- D6 1/4 hours
Show answer & explanationAnswer & explanation
Correct answer: A. 7 5/12 hours
Convert mixed numbers to improper fractions or add whole numbers and fractions separately. Whole numbers: 3 + 2 + 1 = 6. Fractions: 1/2 + 3/4 + 1/3. Find a common denominator, which is 12. 6/12 + 9/12 + 4/12 = 19/12. Convert 19/12 to a mixed number: 1 7/12. Add to the whole numbers: 6 + 1 7/12 = 7 7/12 hours.
Why the other options are wrong
- B. This results from an error in adding the fractions or whole numbers.
- C. This results from an error in calculating the sum of the fractions, possibly 1/2 + 3/4 + 1/3 = (6+9+4)/12 = 19/12 = 1 and 7/12. Then 6+1 and 7/12 = 7 and 7/12. This is the correct answer.
- D. This results from a significant error in finding a common denominator or adding the fractions.
Adding Mixed Numbers
To add mixed numbers, you can either add the whole number parts and fractional parts separately (finding a common denominator for the fractions), or convert all mixed numbers to improper fractions, add them, and then convert back to a mixed number.
- Option 1: Add whole parts, add fractional parts (with common denominator), combine.
- Option 2: Convert to improper fractions, add, convert back.
- Always simplify fractional part at the end.
Memory trick: Mixed: Whole and part, combine with common ground.