Questions: Adding Fractions with Unlike Denominators
3 questions to test your understanding
Score: 0 / 3
Question 1 Multiple Choice
What is 1/2 + 1/3?
A2/5
B2/6
C5/6
D1/6
The least common denominator of 2 and 3 is 6. Rewrite: 1/2 = 3/6 and 1/3 = 2/6. Add: 3/6 + 2/6 = 5/6. The answer 2/5 is the classic 'add across' error — adding numerators (1+1=2) and denominators (2+3=5) separately, which is always wrong.
Question 2 True / False
When finding a common denominator for 1/4 + 1/6, you is expected to use 24 as the denominator.
TTrue
FFalse
Answer: False
Any common multiple of 4 and 6 works. The least common multiple is 12, not 24. Using 12 gives 3/12 + 2/12 = 5/12 directly. Using 24 also works (6/24 + 4/24 = 10/24 = 5/12), but requires simplifying afterward. The LCD is preferred for efficiency, not required for correctness.
Question 3 Short Answer
A student adds 2/3 + 1/4 and writes 3/7. What mistake did they make, and what is the correct answer?
Think about your answer, then reveal below.
Model answer: They added numerators and denominators separately (2+1=3, 3+4=7). The correct answer is 11/12: convert to twelfths (2/3 = 8/12, 1/4 = 3/12), then add numerators: 8/12 + 3/12 = 11/12.
Fractions can only be added when they represent same-sized pieces. The denominator names the size of the piece — thirds and fourths are different sizes. You must first rewrite both fractions with a common denominator before adding. The 3/7 error is the most common fraction mistake and always produces a wrong answer.