Solving proportions worksheet for Algebra 1

Two fractions set equal. Cross-multiply, then solve what is left. Half the questions put a whole expression on top, so the cross-multiplication has to be distributed; hard puts the variable on the bottom, which can give two answers.

Also taught in Geometry and Pre-Algebra, each at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets Name Solving Proportions Date Period Solve each proportion. Solve by cross-multiplying $\frac{8}{a} = \frac{112}{- 112}$ $\frac{p}{5} = \frac{48}{20}$ $\frac{2}{y} = \frac{28}{196}$ $\frac{x}{14} = \frac{- 6}{84}$ $\frac{x + 5}{5} = \frac{33}{15}$ $\frac{v - 3}{13} = \frac{7}{91}$ $\frac{b + 4}{13} = \frac{- 33}{39}$ $\frac{3}{m} = \frac{18}{- 18}$ $\frac{x}{4} = \frac{18}{8}$ $\frac{x - 8}{5} = \frac{- 126}{45}$ Solve proportions with binomials $\frac{x - 9}{4} = \frac{x - 10}{3}$ $\frac{x + 7}{2} = \frac{x + 17}{6}$ $\frac{x}{4} = \frac{x + 20}{9}$ $\frac{x - 4}{3} = \frac{x}{5}$ $\frac{x + 2}{7} = \frac{x - 13}{2}$ $\frac{x - 1}{4} = \frac{x + 4}{6}$ $\frac{x - 3}{3} = \frac{x + 5}{9}$ $\frac{x + 5}{8} = \frac{x}{4}$ $\frac{x + 3}{3} = \frac{x + 23}{6}$ $\frac{x + 4}{4} = \frac{x - 2}{3}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Solving Proportions

Date Period

Solve each proportion.

Solve by cross-multiplying
$\frac{8}{a} = \frac{112}{- 112}$
$\frac{p}{5} = \frac{48}{20}$
$\frac{2}{y} = \frac{28}{196}$
$\frac{x}{14} = \frac{- 6}{84}$
$\frac{x + 5}{5} = \frac{33}{15}$
$\frac{v - 3}{13} = \frac{7}{91}$
$\frac{b + 4}{13} = \frac{- 33}{39}$
$\frac{3}{m} = \frac{18}{- 18}$
$\frac{x}{4} = \frac{18}{8}$
$\frac{x - 8}{5} = \frac{- 126}{45}$

Solve proportions with binomials
$\frac{x - 9}{4} = \frac{x - 10}{3}$
$\frac{x + 7}{2} = \frac{x + 17}{6}$
$\frac{x}{4} = \frac{x + 20}{9}$
$\frac{x - 4}{3} = \frac{x}{5}$
$\frac{x + 2}{7} = \frac{x - 13}{2}$
$\frac{x - 1}{4} = \frac{x + 4}{6}$
$\frac{x - 3}{3} = \frac{x + 5}{9}$
$\frac{x + 5}{8} = \frac{x}{4}$
$\frac{x + 3}{3} = \frac{x + 23}{6}$
$\frac{x + 4}{4} = \frac{x - 2}{3}$



Sigma Prep · sigmaprep.io/worksheets Name Solving ProportionsAnswer keyVersion 1 Date Period Solve each proportion. Solve by cross-multiplying $\frac{8}{a} = \frac{112}{- 112}$ ${- 8}$ $\frac{p}{5} = \frac{48}{20}$ ${12}$ $\frac{2}{y} = \frac{28}{196}$ ${14}$ $\frac{x}{14} = \frac{- 6}{84}$ ${- 1}$ $\frac{x + 5}{5} = \frac{33}{15}$ ${6}$ $\frac{v - 3}{13} = \frac{7}{91}$ ${4}$ $\frac{b + 4}{13} = \frac{- 33}{39}$ ${- 15}$ $\frac{3}{m} = \frac{18}{- 18}$ ${- 3}$ $\frac{x}{4} = \frac{18}{8}$ ${9}$ $\frac{x - 8}{5} = \frac{- 126}{45}$ ${- 6}$ Solve proportions with binomials $\frac{x - 9}{4} = \frac{x - 10}{3}$ ${13}$ $\frac{x + 7}{2} = \frac{x + 17}{6}$ ${- 2}$ $\frac{x}{4} = \frac{x + 20}{9}$ ${16}$ $\frac{x - 4}{3} = \frac{x}{5}$ ${10}$ $\frac{x + 2}{7} = \frac{x - 13}{2}$ ${19}$ $\frac{x - 1}{4} = \frac{x + 4}{6}$ ${11}$ $\frac{x - 3}{3} = \frac{x + 5}{9}$ ${7}$ $\frac{x + 5}{8} = \frac{x}{4}$ ${5}$ $\frac{x + 3}{3} = \frac{x + 23}{6}$ ${17}$ $\frac{x + 4}{4} = \frac{x - 2}{3}$ ${20}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Solving ProportionsAnswer keyVersion 1

Date Period

Solve each proportion.

Solve by cross-multiplying
$\frac{8}{a} = \frac{112}{- 112}$ ${- 8}$
$\frac{p}{5} = \frac{48}{20}$ ${12}$
$\frac{2}{y} = \frac{28}{196}$ ${14}$
$\frac{x}{14} = \frac{- 6}{84}$ ${- 1}$
$\frac{x + 5}{5} = \frac{33}{15}$ ${6}$
$\frac{v - 3}{13} = \frac{7}{91}$ ${4}$
$\frac{b + 4}{13} = \frac{- 33}{39}$ ${- 15}$
$\frac{3}{m} = \frac{18}{- 18}$ ${- 3}$
$\frac{x}{4} = \frac{18}{8}$ ${9}$
$\frac{x - 8}{5} = \frac{- 126}{45}$ ${- 6}$

Solve proportions with binomials
$\frac{x - 9}{4} = \frac{x - 10}{3}$ ${13}$
$\frac{x + 7}{2} = \frac{x + 17}{6}$ ${- 2}$
$\frac{x}{4} = \frac{x + 20}{9}$ ${16}$
$\frac{x - 4}{3} = \frac{x}{5}$ ${10}$
$\frac{x + 2}{7} = \frac{x - 13}{2}$ ${19}$
$\frac{x - 1}{4} = \frac{x + 4}{6}$ ${11}$
$\frac{x - 3}{3} = \frac{x + 5}{9}$ ${7}$
$\frac{x + 5}{8} = \frac{x}{4}$ ${5}$
$\frac{x + 3}{3} = \frac{x + 23}{6}$ ${17}$
$\frac{x + 4}{4} = \frac{x - 2}{3}$ ${20}$

How to do these

$\frac{x}{4} = \frac{15}{20}$

Cross-multiply: 20x = 60.
Divide both sides by 20.

The answer is ${3}$ .

Where students go wrong

Multiplying straight across instead of diagonally. The rule is top-left times bottom-right equals top-right times bottom-left, and getting it the other way round gives an answer that looks fine and is not.

Also called cross multiplying or ratio and proportion.

What you can put on this worksheet

Cross-multiply: $\frac{v}{7} = \frac{12}{14}$ → ${6}$
Do two ratios form a proportion: Does $\frac{5}{9}$ equal $\frac{20}{36}$ ? Check with cross products. → Yes
Binomials on both sides: $\frac{x + 3}{7} = \frac{x}{4}$ → ${4}$
Fraction answers, and the variable underneath: $\frac{v}{10} = \frac{2}{7}$ → ${\frac{20}{7}}$
Decimals, rounded to hundredths: Solve. Round to the nearest hundredth. $\frac{6}{7.6} = \frac{v}{1.7}$ → $1.34$
A binomial on the bottom: $\frac{4}{k + 7} = \frac{2}{5}$ → ${3}$

Questions about these worksheets

Yes. Every solving proportions sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the solving proportions questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 6: cross-multiply, do two ratios form a proportion, binomials on both sides, fraction answers, and the variable underneath, decimals, rounded to hundredths and a binomial on the bottom. Tick as many as you want and set how many of each, or let it spread them evenly.

Solving proportions worksheet for Algebra 1

Select your difficulty

Solve by cross-multiplying

Solve proportions with binomials

Solve by cross-multiplying

Solve proportions with binomials

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

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