# Ratios, Rates, and Proportions on the SAT: Examples & Practice Source: https://1600.now/sat-skill/ratios-rates-proportions --- Math · Problem-Solving and Data Analysis ## Ratios, Rates, and Proportions Keep the compared quantities in a fixed order and write their units. Convert a rate by multiplying by conversion factors whose unwanted units cancel. Written by [Luke Finigan](https://1600.now/about) 2 min read Updated Oct 2, 2026 ### Turn a ratio into equal-sized parts A mixture has red and blue beads in the ratio $3:5$. There are 8 equal parts in all. If there are 40 beads, each part contains 5 beads, giving 15 red and 25 blue. The fraction of red beads is $\frac{3}{8}$, not $\frac{3}{5}$. The latter compares red to blue; the former compares red to the total. Decide which comparison the question requests. ### Find a unit rate before scaling If 6 kilograms cost 27 dollars, the unit price is $\frac{27}{6}=4.5$ dollars per kilogram. At the same rate, 10 kilograms cost 45 dollars. This assumes a constant unit price; a fixed fee would require a different model. A proportional relationship has the form $y=kx$ and passes through $(0,0)$. A model such as $y=4x+7$ is linear but not proportional because of the added constant. ### Cancel units through conversions To convert 72 kilometers per hour into meters per second, compute $72\cdot\frac{1000}{3600}=20$. The factor 1000 converts kilometers to meters, while 3600 converts hours to seconds in the denominator. Write the unit cancellation beside the arithmetic. If converting square units, square the conversion factor: one square meter equals 10,000 square centimeters, because each of its two dimensions contains 100 centimeters. ### Check whether the proportion keeps the same order If 4 notebooks cost 10 dollars, then $\frac{4}{10}=\frac{n}{25}$ compares notebooks to dollars on both sides. Solving gives $n=10$. Writing $\frac{4}{10}=\frac{25}{n}$ swaps the comparison and answers a different equation. For a miss, record whether the error was total parts, unit order, fixed fee, or conversion power. Repeat that setup before adding time pressure. ### Check your understanding Try it yourself A bag has green and yellow counters in the ratio 2:7. What fraction of all counters are green? A $\frac{2}{7}$ B $\frac{2}{9}$ C $\frac{7}{9}$ D $\frac{7}{2}$ ### Sample ratios, rates, and proportions questions Ratios, Rates, and Proportions · Easy A dog has a mass of 42 kilograms. What is the dog's mass, in *grams*? (1 kilogram = 1,000 grams) A 42,000 B 1,764 C 1,042 D 958 - [Open the question and explanation](https://1600.now/bank/math/660fabd6) Ratios, Rates, and Proportions · Easy The ratio $12$ to $2$ is equivalent to the ratio $60$ to $2k$, where $k$ is a constant. What is the value of $k$? A $0.4$ B $5$ C $10$ D $120$ - [Open the question and explanation](https://1600.now/bank/math/7fb4cdc4) Ratios, Rates, and Proportions · Easy An object moves at a speed of $\frac{6}{25}$ feet per second. What is this speed, in *yards* per second? (3 feet = 1 yard) A 25 B 9 C $\frac{18}{25}$ D $\frac{2}{25}$ - [Open the question and explanation](https://1600.now/bank/math/54493ca7) ### Practice this skill 1. Label the numerator and denominator of every ratio. 2. Solve one unit rate, one part-to-total problem, and one conversion. 3. Check whether doubling the input should double the output before using a proportion. [Practice ratios, rates, and proportions](https://1600.now/bank/math/skill/Ratios%2C%20rates%2C%20proportional%20relationships%2C%20and%20units) [Print the ratios, rates, and proportions worksheet and worked answers](https://1600.now/sat-ratios-rates-proportions-worksheet). Then use a [mixed practice module](https://1600.now/modules) to check whether you can choose this method among other question types. ### Source and question labels The bank label for this guide is "Ratios, rates, proportional relationships, and units" in Problem-Solving and Data Analysis. The worked examples above are written for this guide. - [College Board: Types of Math tested](https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types) ### Related skills - **[Percentages](https://1600.now/sat-skill/percentages)** Use the starting quantity as the denominator for percent change. - **[Linear Functions](https://1600.now/sat-skill/linear-functions)** A linear function changes by the same amount for each equal increase in its input. - **[Area and Volume](https://1600.now/sat-skill/area-and-volume)** Choose the formula for the requested quantity, then identify its perpendicular height and units.