Math
Grades 6–8 · Ratios & Proportions

How to solve a proportion.

Most proportion mistakes happen before any math does, in how the ratio gets set up. Study Butler spends the time there, making sure the units line up, because once the proportion is set up right, solving it is the easy part.

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Here is what that looks like.

Study Butler will not print the answer. It points at the next step and lets your kid take it.

An example. The butler answers the question with a question.

3 apples cost 2 dollars, how much for 12 apples.

set it up so the same things line up. apples over dollars on both sides. what goes where.

3 over 2 equals 12 over x?

perfect setup. now cross-multiply and solve for x.

Where students get stuck.

The same few mistakes come up again and again. Here is where the butler slows things down.

01Setting up the ratio with units mismatched

If apples are on top on one side, apples must be on top on the other. Study Butler checks the setup before any cross-multiplying happens.

02Cross-multiplying in the wrong direction

Students multiply along the wrong diagonal. The butler ties cross-multiplication to keeping the equation balanced, not to a memorized X shape.

03Forgetting to solve for the variable after

Cross-multiplying gives an equation, not the answer. Study Butler asks what is still left to do once the products are written down.

Bring the problem they're stuck on.

Type it, say it, or snap a photo. Study Butler walks your kid to the answer one question at a time, so they learn it instead of copying it.

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Questions parents ask.

What does cross-multiplying actually do?
It clears the fractions on both sides so you are left with a simple equation. Study Butler connects it to keeping both sides equal, rather than a trick shape.
How do you know if a problem is a proportion?
When two ratios are set equal, usually a known rate compared to an unknown one. Study Butler helps your kid spot that structure in the word problem.