Divide Fractional Distances by Fractional Times
A unit rate asks how much of one quantity corresponds to one whole unit of another.
About 20 minutes, plus any extended practice
Supplied materials
- Paper or a browser scratch area; a calculator is optional unless rounding is requested.
- Supplied teaching case: A model cart travels 1 kilometers in 3/4 hours at constant speed. What is its unit rate? Candidate answers: (A) 3.3333 km/hour (B) 3/4 km/hour (C) 4/3 km/hour (D) 7/4 km/hour.
- Independent check inputs: A model cart travels 3/2 kilometers in 1 hour at constant speed. What is its unit rate? Candidate answers: (A) 2/3 km/hour (B) 3.5 km/hour (C) 3/2 km/hour (D) 5/2 km/hour.
Learn the idea
Proportional relationships compare multiplicative changes rather than fixed additions. Rates connect two labeled quantities, and a proportional graph must be consistent with a zero starting amount as well as a constant ratio. A unit rate asks how much of one quantity corresponds to one whole unit of another. Dividing fractions requires multiplying by the reciprocal of the divisor.
Here is the method on the supplied teaching case. Divide distance by time: (1)÷(3/4)=4/3. The denominator is hours, so the rate is kilometers per hour.
Keep distance over time when finding speed. Switching the order produces hours per kilometer, which answers a different question; label the result so its meaning remains visible.
- Write or sketch the supplied teaching case, labeling its quantities and restrictions.
- Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
- Solve the independent check with its changed inputs before revealing feedback.
- Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
See the method in action
Teaching case: A model cart travels 1 kilometers in 3/4 hours at constant speed. What is its unit rate? Candidate answers: (A) 3.3333 km/hour (B) 3/4 km/hour (C) 4/3 km/hour (D) 7/4 km/hour. Solution: Divide distance by time: (1)÷(3/4)=4/3. The denominator is hours, so the rate is kilometers per hour. The final answer is 4/3 km/hour. Keep distance over time when finding speed. Switching the order produces hours per kilometer, which answers a different question; label the result so its meaning remains visible.
Check your reasoning
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Helpful tips
- A unit rate asks how much of one quantity corresponds to one whole unit of another.
- Keep distance over time when finding speed.
See the answer and explanation
3/2 km/hour
Divide distance by time: (3/2)÷(1)=3/2. The denominator is hours, so the rate is kilometers per hour.
Take it further
Changed-input task: A model cart travels 9/2 kilometers in 5/2 hours at constant speed. What is its unit rate? Candidate answers: (A) 45/4 km/hour (B) 5/9 km/hour (C) 7 km/hour (D) 9/5 km/hour. Show the mathematical reason, not only the selected answer. Expected result: 9/5 km/hour. Divide distance by time: (9/2)÷(5/2)=9/5. The denominator is hours, so the rate is kilometers per hour.
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More practice: try new cases
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Check the subject sources
- California Department of Education: adopted mathematics standards
- OpenStax: Real numbers and algebra essentials
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