How do I simplify a ratio?
Divide both terms by their greatest common divisor. 16:12 has a GCD of 4, so it simplifies to 4:3. If the terms are decimals, first multiply both by a power of ten to make them whole — 2.5:7.5 becomes 25:75, then 1:3. A simplified ratio describes the same proportion in the smallest whole numbers, which is why 4:3 and 16:12 describe identical shapes.
What is the difference between a ratio, a fraction and a percentage?
A ratio compares parts to each other: 3:1 means three of one for every one of the other. A fraction compares a part to the whole: those same quantities are 3/4 and 1/4. A percentage is a fraction scaled to 100: 75% and 25%. Reading a ratio as a fraction is a frequent error — 3:1 is not three-quarters of anything, it is three times as much.
How do I solve a proportion for a missing term?
Cross-multiply. For a:b = c:d, the products of the diagonals are equal, so a times d equals b times c. To find a missing d, calculate b times c divided by a. This is the arithmetic behind scaling recipes, converting map distances, mixing solutions and adjusting drawings — any situation where you know three of four related quantities.
How do I divide 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 450 in the ratio 4:5 means nine shares of 50, giving 200 and 250. The common mistake is dividing by one of the terms instead of by their sum, which produces answers that do not add back to the original amount — always check that they do.
What is an aspect ratio?
A ratio of width to height, used for screens, images and paper. 16:9 is standard widescreen, 4:3 the older television shape, 3:2 common in photography. Because it is a ratio, it says nothing about size — a 16:9 phone screen and a 16:9 cinema screen have identical proportions. Scaling to a different aspect ratio is what causes letterboxing or cropping.
Can a ratio have more than two terms?
Yes, and they work the same way. Concrete mixed 1:2:4 means one part cement, two parts sand, four parts aggregate — seven shares in total. Simplify by dividing all terms by their common divisor, and split amounts by dividing by the sum of all parts. Three-term ratios are common in construction mixes, chemistry and dividing profits between more than two partners.