Complete 3/4 = __/12.
Incorrect answer: 3
Adding the same number to the top and bottom does not preserve a fraction. For example, 1/2 and 2/3 are different amounts.
Changing only one part of a fraction
Multiplying numerator and denominator by the same nonzero value preserves the fraction. Subtracting the same number does not.
The correction
9
Multiply numerator and denominator by 3.
- Think of repartitioning the same whole, not changing its size.
- Multiply both numerator and denominator by the same factor to generate an equivalent fraction.
- To simplify, divide both by a common factor until no common factor greater than one remains.
Try the reasoning in another example
Simplify 6/8.
- Both 6 and 8 are divisible by 2.
- Divide both parts by 2.
Answer: 3/4
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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