Simplifying Ratios with Decimals or Fractions: Step-by-Step Method

The problem

Ratios should be expressed in whole numbers. But sometimes you end up with a ratio like 0.5 : 1.5 or 1/3 : 2/5. You cannot leave them like that. You need to convert them into the simplest whole-number ratio.

Method for decimal ratios

Step 1 — Multiply both sides by a power of 10 to eliminate decimals

Choose the power of 10 that removes all decimal places.

Step 2 — Simplify by dividing by the GCF

Worked example 1

Simplify 0.4 : 0.6.

Step 1: Both have one decimal place. Multiply both by 10:

0.4 × 10 = 4, 0.6 × 10 = 6.

Ratio: 4:6.

Step 2: GCF of 4 and 6 is 2. Divide: 2:3.

Answer: 0.4 : 0.6 = 2:3.

Worked example 2

Simplify 1.5 : 2.25.

Step 1: The most decimal places is 2 (in 2.25). Multiply both by 100:

1.5 × 100 = 150, 2.25 × 100 = 225.

Ratio: 150:225.

Step 2: GCF of 150 and 225.

150 = 2 × 3 × 5², 225 = 3² × 5². GCF = 3 × 5² = 75.

150 ÷ 75 = 2, 225 ÷ 75 = 3.

Answer: 1.5 : 2.25 = 2:3.

Worked example 3

Simplify 0.75 : 1.

Step 1: Multiply both by 100: 75 : 100.

Step 2: GCF of 75 and 100 is 25. Divide: 3 : 4.

Answer: 0.75 : 1 = 3:4.

Method for fraction ratios

Step 1 — Find the LCM of all the denominators

Step 2 — Multiply every part of the ratio by that LCM

This clears all the fractions in one move.

Step 3 — Simplify if needed

Worked example 4

Simplify 1/3 : 1/2.

Step 1: LCM of 3 and 2 is 6.

Step 2: 1/3 × 6 = 2, 1/2 × 6 = 3.

Ratio: 2:3.

Answer: 1/3 : 1/2 = 2:3.

Worked example 5

Simplify 2/5 : 3/4.

Step 1: LCM of 5 and 4 is 20.

Step 2: 2/5 × 20 = 8, 3/4 × 20 = 15.

Ratio: 8:15.

Step 3: 8 and 15 share no common factor. Already simplest form.

Answer: 2/5 : 3/4 = 8:15.

Worked example 6

Simplify 3/4 : 1 1/2.

First convert the mixed number: 1 1/2 = 3/2.

Step 1: LCM of 4 and 2 is 4.

Step 2: 3/4 × 4 = 3, 3/2 × 4 = 6.

Ratio: 3:6.

Step 3: GCF = 3. Divide: 1:2.

Answer: 3/4 : 1 1/2 = 1:2.

Method for mixed ratios (decimals and fractions together)

Convert everything to fractions first, then apply the fraction method.

Worked example 7

Simplify 0.5 : 2/3.

Convert 0.5 to a fraction: 1/2.

Now: 1/2 : 2/3.

LCM of 2 and 3 = 6.

1/2 × 6 = 3, 2/3 × 6 = 4.

Answer: 0.5 : 2/3 = 3:4.

Three-part ratios

The same methods work. Just apply the multiplication to all three parts.

Worked example 8

Simplify 1/2 : 1/3 : 1/4.

LCM of 2, 3, and 4 = 12.

1/2 × 12 = 6, 1/3 × 12 = 4, 1/4 × 12 = 3.

Answer: 1/2 : 1/3 : 1/4 = 6:4:3.

Why not just divide one by the other?

For a two-part ratio, you could divide both sides by the smaller value:

0.4 : 0.6 → divide both by 0.4 → 1 : 1.5 → multiply both by 2 → 2:3.

This works but can leave you with awkward decimals. The multiply-then-simplify method is usually cleaner. For automated simplification, try the Ratio Simplifier.

Common mistakes

Multiplying by different numbers. You must multiply every part of the ratio by the same number. Using different multipliers changes the relationship.

Forgetting to simplify after clearing decimals. 150:225 is correct but not in simplest form. Always check for a common factor.

Converting mixed numbers incorrectly. Always convert to improper fractions before applying the method. 1 1/2 is 3/2, not 1/2.

Not finding the LCM correctly for fractions. If you use a common multiple that is not the LCM, the numbers will be bigger but the final simplified ratio will be the same. The LCM just keeps the working easier.

Use the Reducing Fractions Calculator to verify your GCF calculations.

Real-world examples

Cooking: A recipe calls for 0.75 cups of milk and 1.25 cups of cream. The ratio is 0.75:1.25 = 75:125 = 3:5.

Scale models: A model is built at a scale of 1/48 : 1. Multiply by 48: the scale is 1:48.

Chemistry: A solution requires reagents in the ratio 2/3 : 5/6. LCM = 6. Multiply: 4:5.

FAQ

What if one part of the ratio is a whole number and the other is a fraction? Write the whole number as a fraction (e.g. 3 = 3/1) and use the LCM method.

Can ratios have negative numbers? Technically, but they rarely do in practical contexts. If they arise, treat the sign separately and simplify the magnitudes.

Is there a limit to how many parts a ratio can have? No. The method works for any number of parts. Just find the LCM of all denominators and multiply through.

Why do ratios need to be in whole numbers? Convention. Whole-number ratios are clearer and easier to work with. A recipe saying "use water and flour in a 2:3 ratio" is more practical than "in a 0.4:0.6 ratio".