Six pens cost $9. Find the price per pen.
Incorrect answer: $0.67 per pen
Reversing the division reverses the meaning. Dollars per notebook and notebooks per dollar are both rates, but they answer different questions.
Reversing a unit-rate calculation
The requested unit tells you the division order. Cost per pen is cost divided by pens.
The correction
$1.50 per pen
9 ÷ 6 = 1.50.
- Write the comparison with units in the intended order.
- Divide numerator and denominator by the denominator’s value to make it one.
- Use the unit rate to compare options or scale to a new quantity.
Try the reasoning in another example
A cyclist travels 45 km in 3 hours at a constant speed. Find the speed.
- Divide distance by time: 45 ÷ 3.
- The rate is measured in kilometers per hour.
Answer: 15 km/h
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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