Algebra 1 proportion problems are solved by writing an equation with a variable and cross-multiplying, so the setup matters more than the arithmetic. The situations include recipes with fractions, map scales, speeds, prices and shadows.
Also taught in Pre-Algebra, at its own level and with its own examples.
Select your difficulty
Pick more than one for a sheet that mixes them.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
A car travels 150 miles in 3 hours. At the same speed, how far does it travel in 5 hours?
Miles over hours on both sides: 150/3 = x/5.
Cross-multiply: 3x = 750.
Divide: x = 250.
The answer is 250 miles.
Where students go wrong
Adding the difference instead of scaling. Going from 3 people to 8 is not 5 more cups of rice; the amount grows by the same factor as the people, which is why the two ratios are set equal.
Also called proportion word problems, ratio word problems, similar figures word problems or shadow problems.
What you can put on this worksheet
Proportion word problems
A person 6 feet tall casts a shadow 9 feet long. At the same moment a tree casts a shadow 18 feet long. How tall is the tree?→ 12 ft
With fractions
A recipe uses 65 teaspoon of salt for 5 servings. How much is needed for 6 servings?→ 1 teaspoon
Exchange rates, resizing, and shadows
A 12 ft lamppost casts a 21 ft shadow. At the same time, how long is the shadow of an 8 ft post?→ 14 ft
Questions about these worksheets
Yes. Every proportion word problems 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 proportion word problems 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 3: proportion word problems, with fractions and exchange rates, resizing, and shadows. Tick as many as you want and set how many of each, or let it spread them evenly.
Flipping one ratio. Cups over people on one side and people over cups on the other gives a wrong answer that still looks reasonable.