How do you simplify ratios step by step?
Find the GCF of all the parts and divide each part by it. You're done when the parts share no common factor except 1.
If you aren't sure of the GCF, divide by any common factor you can see and repeat. 18:24 becomes 9:12, then 3:4. The GCF calculator finds the factor in one step.
A simplified ratio describes the same relationship with smaller numbers. Eighteen red beads for every 24 blue beads is the same mix as 3 red for every 4 blue.
How do you simplify a ratio with decimals or fractions?
Multiply every part by the same number to clear the decimals or denominators, then simplify the whole numbers. Multiplying all parts by the same amount keeps the comparison the same.
Whole numbers are the standard way to present a ratio, so an answer like 1.5:2.25 usually isn't considered finished even though it is technically correct.
For decimals, multiply by 10, 100, or 1000 depending on the most decimal places. For fractions, multiply by the LCD of the denominators. The ratio simplifier does this for you, so you can type 1.5:2.25 or 1/2:3/4 as they are.
Can you simplify a ratio with three or more parts?
Yes. Use the GCF of all the parts, not just two of them. The calculator accepts up to six parts, which covers things like paint mixes, concrete recipes, and budget splits.
For 12:18:30, the GCF of 12, 18, and 30 is 6. Dividing gives 2:3:5. Some ratios are already in lowest terms, such as 2:3:4, because no number other than 1 divides all three parts, even though 2 and 4 share a factor.
What is the difference between a ratio and a fraction?
A fraction compares a part to a whole, while a ratio can compare a part to another part. That means the same numbers can describe different things.
Say a class has 12 girls and 18 boys. The part-to-part ratio of girls to boys is 12:18, or 2:3. The part-to-whole ratio of girls to all students is 12:30, or 2:5, and that one you can write as the fraction 2/5. Mixing these up is a frequent source of wrong answers.
| Comparison | Ratio | Simplified |
|---|---|---|
| Girls to boys (part to part) | 12:18 | 2:3 |
| Boys to girls (part to part) | 18:12 | 3:2 |
| Girls to all students (part to whole) | 12:30 | 2:5 |
Does the order of a ratio matter?
Yes. The first number always goes with the first thing named. Girls to boys is 2:3, but boys to girls is 3:2.
Read the question carefully and write the labels above the numbers before you simplify. It takes a few seconds and catches most order mistakes. The calculator keeps the order you type, so 15:5 becomes 3:1 and not 1:3. A ratio of 3:1 means the first quantity is three times the second.
How do you find equivalent ratios and scale a recipe?
Multiply or divide every part by the same number. 3:4, 6:8, and 9:12 are all equivalent ratios, and they all simplify to 3:4.
Recipes use this all the time. Suppose a pancake recipe uses 2 cups of flour to 3 cups of milk and you want to double it. Multiply both parts by 2 to get 4:6. For half a batch, divide both by 2 to get 1:1.5. To check that two ratios are equivalent, simplify both and compare, which is what an equivalent ratio calculator does.
To find a missing amount, use the ratio as a multiplier. The recipe uses 3 cups of milk for every 2 cups of flour, so milk is 3/2 of the flour. With 5 cups of flour, you need 5 × 3/2 = 15/2 = 7.5 cups of milk.
What are the ways to write a ratio?
You can write the same ratio with a colon, with the word to, or as a fraction. So 3:4, 3 to 4, and 3/4 all mean three of one thing for every four of another. The colon form is the usual one for ratios with three or more parts.
The fraction form is handy when you set up a proportion, but remember it doesn't always mean part of a whole. Type ratios into the calculator with colons, such as 3:4 or 2:3:5.
What are common mistakes with ratios?
Dividing only one part is the classic error, and it's easy to make when you're working fast. If you divide 18 by 6 but leave 24 alone, the comparison changes. Every part has to be divided by the same number.
Other slips: rounding decimals before scaling, swapping the order, and using a part-to-whole total when the question asked part to part. The calculator also only takes nonnegative quantities, so a ratio like −2:4 gets an error message.