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MF.PR.8 Challenge MF-022-A12-V01

Use proportional reasoning to solve percent problems without relying on memorized templates alone.

Identify all valid percent setups for one problem

Problem

For “\(27\) is what percent of \(45\)?” which complete response correctly evaluates the candidate proportions?

A. \(27/45~=~x/100\)
B. \(45/27~=~100/x\)
C. \(27/x~=~45/100\)
D. \(x/45~=~27/100\)
E. \(100/45~=~x/27\)
F. \(45/100~=~27/x\)

Question-support diagram for the problem 27 is what percent of 45. The visual shows three labeled quantity boxes with part 27, whole 45, and percent x, a reference relationship part divided by whole equals percent divided by 100, and a two-column grid listing candidate setups A through F for comparison. Open full size
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What this problem is really about

Anchor the meaning first: twenty-seven is the part, forty-five is the whole, and x names the percent out of one hundred. Different-looking proportions can still be equivalent if their cross products reproduce the same relationship; reversing both ratios is harmless, but changing only one role is not. Test every candidate this way, then solve one shared equation and check it against the reduced part-whole ratio.

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Four variants of this problem type
Curriculum context
Standard
MF.PR.8
Category
Proportional Reasoning
Domain
Percents
Objective
Use proportional reasoning to solve percent problems without relying on memorized templates alone.
Problem type
Identify all valid percent setups for one problem