Find 1/2 + 1/3.
Incorrect answer: 2/5
Do not add denominators: 1/3 + 1/4 is not 2/7. The denominator names the size of the pieces, and equivalent fractions let both quantities use that same size.
Adding or subtracting the denominators
A denominator names a part size. Adding differently sized pieces requires a common size first.
The correction
5/6
Rewrite as 3/6 + 2/6.
- Find a common multiple of the denominators; the least common multiple often keeps numbers small.
- Multiply the numerator and denominator of each fraction by the same factor.
- Add or subtract numerators, keep the common denominator, and reduce if possible.
Try the reasoning in another example
Find 5/6 − 1/4.
- Use denominator 12: 5/6 = 10/12 and 1/4 = 3/12.
- Subtract: 10/12 − 3/12 = 7/12.
Answer: 7/12
Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.
The short check below reuses the first example as a retrieval question and adds a second question. It checks this method; it does not establish a grade level.
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