A ratio written as “a to b” becomes a fraction by placing the first number in the numerator and the second number in the denominator. The ratio 3 to 4 becomes 3/4. That core move is simple, but ratios show up in different formats and contexts, so knowing how to handle decimals, mixed numbers, and simplification makes the skill genuinely useful.
The Basic Conversion
Ratios compare two quantities. They can be written three ways: with the word “to” (3 to 5), with a colon (3:5), or as a fraction (3/5). All three mean the same thing. To convert any ratio to a fraction, take the first value as the numerator (top number) and the second value as the denominator (bottom number).
For example, if a classroom has 12 boys and 18 girls, the ratio of boys to girls is 12:18. Written as a fraction, that’s 12/18. Order matters here. The ratio of girls to boys would be 18/12 instead, which is a completely different fraction. Always match the first term in the ratio to the numerator and the second term to the denominator.
Simplifying the Fraction
Most of the time, you’ll want to reduce the fraction to its simplest form. To do that, find the greatest common factor (GCF) of the numerator and denominator, then divide both by it.
Take the 12/18 example. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The greatest common factor is 6. Divide both the numerator and denominator by 6, and you get 2/3. That’s the ratio in its simplest fractional form.
You can divide by any common factor along the way if spotting the GCF isn’t obvious. Dividing 12/18 by 2 first gives you 6/9, then dividing by 3 gives you 2/3. You’ll reach the same answer. The fraction is only fully simplified when the numerator and denominator share no common factor other than 1.
Handling Ratios with Decimals
When a ratio includes decimals, like 0.8 to 0.05, you can still write it as a fraction: 0.8/0.05. The goal is to eliminate the decimals by multiplying both the numerator and denominator by the same power of 10.
Look at whichever number has more decimal places and use that to decide your multiplier. In 0.8/0.05, the denominator has two decimal places, so multiply both top and bottom by 100. That gives you 80/5, which simplifies to 16/1, or just 16. The key rule: as long as you multiply both parts by the same number, the ratio stays equivalent.
A simpler case like 0.5 to 2.5 would become 0.5/2.5. Multiply both by 10 to get 5/25, then simplify to 1/5.
Handling Ratios with Mixed Numbers
If your ratio involves mixed numbers like 2½ to 1¼, the process has one extra step. Write the ratio as a fraction (2½ over 1¼), then convert each mixed number to an improper fraction. 2½ becomes 5/2, and 1¼ becomes 5/4.
Now you have a fraction divided by a fraction: (5/2) ÷ (5/4). To divide fractions, flip the second one and multiply: (5/2) × (4/5) = 20/10, which simplifies to 2/1, or just 2. So the ratio 2½ to 1¼ expressed as a fraction in simplest form is 2.
Part-to-Whole vs. Part-to-Part
There’s an important distinction between what kind of ratio you’re converting. A part-to-part ratio compares two separate groups. A part-to-whole ratio compares one group to the total. Which one you need depends on the question you’re answering.
Say you’re mixing paint in a ratio of 2 parts blue to 3 parts yellow. The part-to-part ratio of blue to yellow is 2/3. But if someone asks what fraction of the mixture is blue, you need a part-to-whole fraction. Add the parts together (2 + 3 = 5 total parts), then put the blue portion over the total: 2/5. The fraction that is yellow would be 3/5. The part being described becomes the numerator, and the sum of all parts becomes the denominator.
This comes up constantly in real life. If two people split savings in a 5:3 ratio, there are 8 total parts. One person gets 5/8 of the money, the other gets 3/8. For a total of $96 split this way, each part is worth $12 ($96 ÷ 8), giving one person $60 and the other $36.
Ratios with Three or More Terms
Some ratios compare more than two quantities, like 2:4:3. You can’t write this as a single fraction, but you can convert each part into a fraction of the whole. Add up all the parts (2 + 4 + 3 = 9), then each term becomes a fraction with 9 as the denominator: 2/9, 4/9, and 3/9 (which simplifies to 1/3).
If three people split $72.90 in a 2:4:3 ratio, each of the 9 parts is worth $8.10. The first person gets 2 × $8.10 = $16.20, the second gets $32.40, and the third gets $24.30.
Quick Reference for Converting
- Whole numbers: Place the first number over the second (3:7 becomes 3/7), then simplify by dividing both by their greatest common factor.
- Decimals: Write as a fraction, then multiply top and bottom by 10, 100, or 1,000 until both numbers are whole. Simplify from there.
- Mixed numbers: Convert each to an improper fraction, then divide the first by the second (flip and multiply).
- Part-to-whole: Add all parts of the ratio to get the denominator, and use the relevant part as the numerator.