A ratio compares like quantities, a rate compares quantities with different units, and a proportion states that two ratios are equal. A paint mix of 2 parts blue to 3 parts white is a ratio; 60 miles per hour is a rate; 2/3 = x/12 is a proportion. Units reveal which calculation is being asked for.
What is the difference between a ratio and a rate?
A car travels 180 miles in 3 hours, so its average rate is 60 miles per hour. At that unchanged rate, x miles in 5 hours satisfies 180/3 = x/5, giving x = 300 miles. A 2:3 colour mix has no unit until a batch size is chosen: 20 total parts would contain 8 blue parts and 12 white parts.
When do I use a proportion?
Write every quantity with its unit. For a rate, divide the output quantity by the input quantity, such as kilometres per litre. For an equivalent scaling problem, set the two ratios equal and cross-multiply only after confirming the matching positions. The ratio calculator can scale an equal-part comparison; it does not decide whether the inputs form a meaningful rate.
How do units identify a rate?
A ratio of 2 red tiles to 3 blue tiles compares counts, so it can simplify to 2:3. A rate of 2 metres per second carries different units and describes change or exchange. A proportion is the equality 2/3 = 8/12, not merely a colon. Cancelling units is a useful check: 60 miles/hour times 5 hours leaves miles.
How do I solve a direct proportion?
Do not call a speed of 60 miles/hour a ratio of 60 miles to one hour and then add miles to hours. Do not cross-multiply values whose units occupy different positions. Do not average rates without weighting by the relevant distance or time. Do not assume a proportion is valid when a fixed fee, changing speed, or non-linear rule is present.
When does a ratio not describe the real relationship?
These tools describe direct proportional relationships. They do not handle a changing rate, a percentage applied to a changing base, compound growth, or a physical process with a threshold. When a real system changes conditions, calculate separate intervals or use the governing formula instead of extending one ratio.
Source for the external fact
OpenStax distinguishes rates as ratios with unlike units and uses unit cancellation in its proportions lesson; that distinction determines whether a unit belongs in the result.
Related calculators
Scale equal quantities in the ratio tool, calculate fuel-per-distance with the MPG calculator, and convert a portion with the fraction calculator.