Worksheets · Pre-Algebra

Unit rates and ratios worksheet

A ratio compares two amounts and simplifies like a fraction. A unit rate is a ratio with a 1 underneath: miles per one hour, dollars per one pound. Divide to get there, and the better buy is whichever deal has the smaller unit price.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Ratios and Unit Rates

Date Period

Answer each question.

  1. Write the ratio in simplest form

    Write the ratio 24:4 in simplest form
  2. Write the ratio 42:54 in simplest form
  3. Write the ratio 5:10 in simplest form

  1. Find the unit rate

    Find the unit rate: 528 pages in 12 hours
  2. Find the unit rate: 10 pounds of apples for $65.00
  3. Find the unit rate: 385 miles in 10 hours

  1. Find the better buy

    Which is the better buy: 12 bagels for $18.60 or 7 for $12.60?
  2. Which is the better buy: 3 cans for $2.55 or 8 for $8.88?
  3. Which is the better buy: 7 batteries for $7.70 or 6 for $9.30?

  1. Find a missing amount from a ratio

    The ratio of boys to girls is 3:7. There are 50 students. How many are girls?
  2. The ratio of boys to girls is 3:7. There are 27 boys. How many girls are there?
  3. The ratio of red marbles to blue marbles is 3:8. There are 77 marbles. How many are blue marbles?

  1. Complete the ratio table

    Complete the ratio table. Pages1__3__Hours510__20
  2. Complete the ratio table. Cost ($)4__12__Items714__28

  1. Find unit rates with fractions

    Maria uses 43 gallons of paint every 15 of a wall. How much is that per wall?
  2. Maria walks 54 miles every 23 hour. How much is that per hour?

  1. Compare the rates

    Printer A prints 104 pages in 4 minutes. Printer B prints 60 pages in 3 minutes. Which is faster?
  2. Typist A types 156 words in 3 minutes. Typist B types 248 words in 4 minutes. Which is faster?

  1. Write the ratio three ways

    A group has 8 boys and 4 girls. Write the ratio of girls to all students three ways, in simplest form.
  2. A group has 11 boys and 19 girls. Write the ratio of boys to girls three ways, in simplest form.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Ratios and Unit RatesAnswer keyVersion 1

Date Period

Answer each question.

  1. Write the ratio in simplest form

    Write the ratio 24:4 in simplest form6:1
  2. Write the ratio 42:54 in simplest form7:9
  3. Write the ratio 5:10 in simplest form1:2

  1. Find the unit rate

    Find the unit rate: 528 pages in 12 hours44 pages per hour
  2. Find the unit rate: 10 pounds of apples for $65.00$6.50 per pound
  3. Find the unit rate: 385 miles in 10 hours38.5 miles per hour

  1. Find the better buy

    Which is the better buy: 12 bagels for $18.60 or 7 for $12.60?12 for $18.60, at $1.55 each
  2. Which is the better buy: 3 cans for $2.55 or 8 for $8.88?3 for $2.55, at $0.85 each
  3. Which is the better buy: 7 batteries for $7.70 or 6 for $9.30?7 for $7.70, at $1.10 each

  1. Find a missing amount from a ratio

    The ratio of boys to girls is 3:7. There are 50 students. How many are girls?35
  2. The ratio of boys to girls is 3:7. There are 27 boys. How many girls are there?63
  3. The ratio of red marbles to blue marbles is 3:8. There are 77 marbles. How many are blue marbles?56

  1. Complete the ratio table

    Complete the ratio table. Pages1__3__Hours510__202,15,4
  2. Complete the ratio table. Cost ($)4__12__Items714__288,21,16

  1. Find unit rates with fractions

    Maria uses 43 gallons of paint every 15 of a wall. How much is that per wall?203 gallons of paint per wall
  2. Maria walks 54 miles every 23 hour. How much is that per hour?158 miles per hour

  1. Compare the rates

    Printer A prints 104 pages in 4 minutes. Printer B prints 60 pages in 3 minutes. Which is faster?Printer A: 26 vs 20 pages per minute
  2. Typist A types 156 words in 3 minutes. Typist B types 248 words in 4 minutes. Which is faster?Typist B: 62 vs 52 words per minute

  1. Write the ratio three ways

    A group has 8 boys and 4 girls. Write the ratio of girls to all students three ways, in simplest form.1:3, 1 to 3, 13
  2. A group has 11 boys and 19 girls. Write the ratio of boys to girls three ways, in simplest form.11:19, 11 to 19, 1119

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Find the unit rate: 360 miles in 6 hours

  1. Per hour means divide by the hours.
  2. 360 over 6.

The answer is 60 miles per hour.

Where students go wrong

Dividing the wrong way round. A unit rate is the first quantity per one of the second, so the hours go underneath. 6 over 360 is hours per mile, which nobody asked for.

Also called unit rate, simplifying ratios, better buy or rates and ratios.

What you can put on this worksheet

A ratio in simplest form
Write the ratio 25:30 in simplest form → 5:6
A unit rate
Find the unit rate: 36 laps in 6 minutes → 6 laps per minute
The better buy
Which is the better buy: 7 batteries for $15.75 or 8 for $19.84? → 7 for $15.75, at $2.25 each
Part-part-whole
The ratio of red marbles to blue marbles is 4:7. There are 22 marbles. How many are blue marbles? → 14
Complete a ratio table
Complete the ratio table. Pages4__12__Hours612__24 → 8,18,16
Unit rates with fractions
Maria uses 23 cup of flour every 14 of a batch. How much is that per batch? → 83 cups of flour per batch
Which rate is faster?
Typist A types 88 words in 2 minutes. Typist B types 165 words in 3 minutes. Which is faster? → Typist B: 55 vs 44 words per minute
A ratio three ways
A group has 15 red marbles and 19 blue marbles. Write the ratio of red marbles to blue marbles three ways, in simplest form. → 15:19, 15 to 19, 1519

Questions about these worksheets

Yes. Every unit rates and ratios 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.

Pre-Algebra is usually taken around 7th or 8th 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 unit rates and ratios 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 two 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 8: a ratio in simplest form, a unit rate, the better buy, part-part-whole, complete a ratio table, unit rates with fractions, which rate is faster? and a ratio three ways. Tick as many as you want and set how many of each, or let it spread them evenly.

Dividing the wrong way round. A unit rate is the first quantity per one of the second, so the hours go underneath. 6 over 360 is hours per mile, which nobody asked for.