What next?
Ratios scale recipes, mixes and odds.
How to use this calculator
- Enter the numbers of your ratio.
- The tool simplifies as you type.
- Read the simplified ratio, fraction and decimal.
What your result means
The simplified ratio expresses the same proportion with the smallest whole numbers — 4:8 becomes 1:2. Use it to scale recipes, mixes or plans up and down while keeping the balance identical.
Why this one is different
The simplified ratio, the same relationship as a fraction and as a decimal, and the missing fourth term of A : B = C : ? all appear at once. The working names the divisor the ratio was reduced by and the multiplication that solved the proportion, so marked homework can show its method.
Simplify ratios and solve proportions
A ratio compares two quantities, like 16:9 for a screen or 2:1 for a recipe. To simplify it, divide both sides by their greatest common divisor — the same idea as reducing a fraction. So 1920:1080 simplifies to 16:9.
A proportion says two ratios are equal, A:B = C:D. If you know three of the four numbers you can find the fourth by cross-multiplying: D = B × C ÷ A. That is how you scale a recipe, a map or a mix while keeping the same proportions.
Formula
Simplify A:B by dividing both parts by their greatest common divisor (GCD).
Example calculation
Scaling 3 : 4 so the first part becomes 9:
D = (4 × 9) ÷ 3 = 12
so 3 : 4 = 9 : 12
Frequently asked questions
What does simplifying a ratio mean?＋
It means expressing the same relationship with the smallest whole numbers. 50:100 and 1:2 describe the same ratio; 1:2 is the simplified form.
How do I scale a recipe with this?＋
Enter the original ratio (say flour:water) as A:B, put the new amount of the first ingredient as C, and the answer shows how much of the second you need.
How do I split an amount in a given ratio?＋
Add the parts to get the total number of shares, divide the amount by that, then multiply by each part. Splitting 250 pounds in a 3:2 ratio means five shares of 50, giving 150 and 100.
What is the difference between a ratio and a fraction?＋
A ratio compares parts to each other, a fraction compares a part to the whole. In a 3:1 mix, the first ingredient is three quarters of the total, not three.
How do I use a ratio for a mix or dilution?＋
A 1:5 dilution usually means one part concentrate to five parts water, giving six parts in total. Some industries write the same mix as 1 in 6, so check the convention before mixing.
How do I scale a ratio to a required amount?＋
Work out the value of one share, then multiply. This is the same arithmetic as scaling a recipe, and the recipe scaler handles the fractions for you.
Related calculators
Assumptions & limitations
Ratios are exact where the numbers divide cleanly and approximate where they do not.
- Simplification divides both sides by their greatest common divisor, so 15:25 becomes 3:5 exactly.
- Ratios with decimal parts are scaled to whole numbers where possible; where no clean scaling exists, the result is rounded and marked as approximate.
- Solving a proportion assumes the relationship is genuinely linear. Many real-world relationships — mixing strengths, cooking times, drug doses — are not.
- A zero on either side of a ratio makes it undefined rather than simply small.
Sources & references
Ratio and proportion conventions follow standard curriculum definitions:
- NCETM — multiplicative relationships, covering ratio and proportional reasoning
- National Curriculum in England — ratio, proportion and rates of change
Further reading
Part-to-part and part-to-whole are different numbers
A ratio of 3:5 describes parts against each other, and the total is eight. So the first share is 3/8 (37.5%) of the whole, not 3/5 (60%). Reading a part-to-part ratio as though it were part-to-whole is the single most common mistake with ratios, and it produces answers that look plausible — which is why splitting money, mixing materials or dividing shares is worth doing by first converting to the total and then taking shares of it.
Scaling, simplifying and three-part ratios
A ratio is unchanged when every part is multiplied or divided by the same number, which is what makes 6:10, 3:5 and 0.6:1 the same relationship. Simplify by dividing all parts by their greatest common divisor; scale by multiplying all parts by the same factor. Three-part ratios such as 1:2:4 work identically — add the parts for the total, then take each share — and they are the form used for concrete mixes, portfolio splits and anything divided among three or more claims. Only ratios with the same number of parts can be compared directly.