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Grade 7 · unit review

Review: Fractional Rates and Proportional Relationships

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.

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Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. A model cart travels 7/2 kilometers in 2 hours at constant speed. What is its unit rate?
Need a hint?
  • A unit rate asks how much of one quantity corresponds to one whole unit of another.
  • Keep distance over time when finding speed.
2. For candidate multiplier 7, which supplied (x,y) table is proportional?
Need a hint?
  • A proportional rule has the form y=kx.
  • Check every supplied nonzero row, and check that a stated row with input zero has output zero.
3. A proportional graph passes through (0,0) and (7,56). What is y when x=9?
Need a hint?
  • The point (1,k) on a proportional graph describes its constant.
  • A rising line is not automatically proportional.
4. Printer A makes 21 pages in 7 minutes; B makes 36 in 10 minutes. Which statement follows from these constant-rate models?
Need a hint?
  • Rates can be compared fairly after both are expressed per one identical unit.
  • Use the same time unit and the same output unit for both processes.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. 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. 2. For candidate multiplier 9, which supplied (x,y) table is proportional? Candidate answers: (A) (0,1), (1,9), (2,18) (B) (1,9), (2,18), (4,36) (C) (1,9), (2,19), (4,36) (D) (1,9), (2,9), (4,9). 3. A proportional graph passes through (0,0) and (9,90). What is y when x=11? Candidate answers: (A) 109 (B) 110 (C) 111 (D) 220. 4. Printer A makes 27 pages in 9 minutes; B makes 44 in 12 minutes. Which statement follows from these constant-rate models? Candidate answers: (A) A is faster because its time is smaller (B) B is faster: 11/3 versus 3 pages/minute (C) The page totals alone determine the faster rate (D) The rates are equal.

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. 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. 2. (1,9), (2,18), (4,36). The correct table has y/x=9 for every nonzero x. The other tables either change this ratio or imply a nonzero value at x=0. 3. 110. The constant of proportionality is y/x=90/9=10. Use y=10x, so y=10×11=110. 4. B is faster: 11/3 versus 3 pages/minute. A has 27/9=3 pages/minute. B has 44/12=11/3, which exceeds 3. Comparing equally labeled unit rates supports B as faster.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.