Ratio Calculator

A ratio compares two (or more) quantities, showing how much of one thing there is relative to another — 2:1 might describe two parts sand to one part cement in a concrete mix, or a 16:9 aspect ratio for a widescreen photo. Unlike a fraction, which represents part of a single whole, a ratio compares two separate quantities to each other, though the arithmetic used to simplify or scale ratios borrows heavily from fraction math. Simplifying a ratio means dividing both sides by their greatest common factor (GCF) so the numbers are as small as possible while keeping the same proportion. For example, a mixing instruction of "8 parts water to 12 parts concentrate" simplifies to "2:3" once both sides are divided by their GCF of 4 — the same real-world proportion, expressed with the smallest possible whole numbers, which is far easier to scale up or down mentally. The second common ratio problem is solving a proportion: given A:B = C:?, find the missing fourth value. This comes up constantly in recipe scaling ("if 2 cups of flour needs 3 eggs, how many eggs for 10 cups of flour?"), map scales, and unit price comparisons. The rule is cross-multiplication: since A/B equals C/x, multiplying both sides by B and x gives A×x = B×C, so x = (B×C)/A. Worked example for simplifying: a ratio of 45:60. Both numbers share a GCF of 15, so dividing each by 15 gives 3:4 — the simplest equivalent ratio, confirmed by checking that 3 and 4 have no common factor left besides 1. Worked example for the missing value: if 2:5 = 8:?, then using x = (B×C)/A = (5×8)/2 = 20. So the full, scaled proportion is 2:5 = 8:20, and you can double-check it by dividing both sides of the second ratio by 4: 8/4 = 2 and 20/4 = 5, confirming the two ratios are indeed equivalent. A common misconception is treating a ratio as if it were an ordinary subtraction or addition problem — assuming that going from a 2:5 ratio to an 8:? ratio means simply adding 6 to get "8:11" since 2+6=8. Ratios scale multiplicatively, not additively: because 2 was multiplied by 4 to reach 8, the other side must also be multiplied by 4, giving 20, not increased by a fixed amount. This is one of the most common proportional-reasoning errors in early algebra, and it's exactly what cross-multiplication protects against, since it forces the same multiplicative relationship on both sides of the equation rather than an arbitrary additive one.