Ratio foundations · grades 5–6
Simplifying Ratios Worksheet Generator
Create fresh ratio-reduction practice where every pair is built from a coprime base ratio and one whole-number scale factor. The answer key therefore always shows the ratio in lowest terms.
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Simplifying Ratios Practice
Simplify ratios · Medium whole numbers · Seed 261401
Simplify 45 : 99 = ____
Simplify 88 : 104 = ____
Simplify 49 : 70 = ____
Simplify 112 : 72 = ____
Simplify 6 : 26 = ____
Simplify 55 : 40 = ____
Simplify 12 : 21 = ____
Simplify 110 : 70 = ____
Simplify 39 : 36 = ____
Simplify 24 : 78 = ____
Simplify 80 : 50 = ____
Simplify 35 : 98 = ____
Simplify 20 : 90 = ____
Simplify 18 : 12 = ____
Simplify 45 : 126 = ____
Simplify 78 : 42 = ____
Simplify 60 : 54 = ____
Simplify 42 : 48 = ____
Simplifying a ratio to lowest terms
To simplify a ratio, divide both numbers by their greatest common factor, the largest number that divides both exactly. A ratio is in lowest terms when the only common factor left is 1. Simplifying keeps the relationship the same while using the smallest whole numbers, and it makes ratios easier to compare. If the two quantities use different units, convert them to the same unit first.
Worked examples
- 12 : 18. The greatest common factor is 6, so divide both by 6 to get 2 : 3.
- 15 : 25. Both numbers divide by 5, giving 3 : 5, and 3 and 5 share no factor other than 1.
- 40 minutes to 2 hours. Change the hours to minutes first: 2 hours is 120 minutes. Then 40 : 120 divides by 40 to give 1 : 3.
- 8 : 8 simplifies to 1 : 1, because any number divided by itself is 1.
Common slips
- Dividing the two numbers by different amounts. Dividing 12 by 6 and 18 by 3 gives 2 : 6, which is a different ratio.
- Stopping too early. 6 : 9 is not finished, because both numbers still divide by 3 to give 2 : 3.
- Simplifying without matching units. 40 minutes to 2 hours is not 20 : 1.
- Swapping the order. 12 : 18 simplifies to 2 : 3, not 3 : 2.
How to use this worksheet
Ask students to write the common factor beside each ratio before dividing. The answer key lists the simplified ratio, so it is quick to check whether a mistake came from the factor or from the division.
Common Core connection
- 6.RP.A.1 · Describe ratios and use ratio language to compare two quantities.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Treat a ratio like a fraction for reduction: divide both terms by the same greatest common factor.
Ask students to check that the simplified terms have no common factor greater than 1 before moving on.
Use the small set for structure first, then move to medium or large numbers after the reduction process is secure.
Model a full reduction: 18:24 divides by 6 to give 3:4. Dividing by 2 first (9:12) and then by 3 reaches the same lowest terms.
Watch for students who subtract the same number from both terms (18:24 becoming 12:18). Ratios reduce only by division, exactly like fractions.
Mix simplifying, tables, unit rates, proportions, and percent proportions in one generator.
Connect ratios to percents →Practice part / whole = percent / 100 after equivalent ratios are secure.
More skills in this set
Quick answers
Are simplified answers always in lowest terms?
Yes. Each problem starts from a coprime base pair and scales both terms by the same factor.
Which standard does this practice?
CCSS 6.RP.A.1 and 6.RP.A.3a: understand ratio language and generate equivalent ratios, including reducing to a simplest form.
Is 3:4 the same ratio as 4:3?
No. Order carries meaning. 3:4 means 3 of the first quantity for every 4 of the second, so reversing the terms describes a different relationship.
Can I increase the number size?
Yes. Small, medium, and large sets increase both the base terms and possible scale factors.
Can I make another version?
Yes. New problems changes the seed while keeping the selected skill and number range.
Is an answer key available?
Yes. The direct PDF can append a separate answer-key page.