SAT Ratios, Rates and Percentages

By Muntasir Jul 30, 2026 7 min read

TL;DR

Ratio, rate and percentage questions sit inside the SAT Problem-Solving and Data Analysis domain, worth 5 to 7 questions per Math test. Set up a ratio as a matching fraction, then cross multiply to solve for the unknown. A unit rate compares one quantity to a single unit of another, and unit conversion multiplies by a conversion factor which cancels the old unit. Percent change equals the difference between the new and original values, divided by the original value, times 100. Markup and discount add or subtract a percent of the original price, and tax applies to the discounted price, not the original one. Practice every level with our free drills, no signup required.

Ratio, rate and percentage questions turn everyday situations, recipes, sale prices, mixing solutions, into equations you solve in a handful of steps. They show up across the SAT Math section, inside single-step items and multi-part word problems, and each one tests whether you track units and reference points correctly.

This guide walks through setting up ratio and rate word problems, converting units inside a rate, calculating percent increase and decrease, and solving markup, discount and tax problems. Original worked examples appear in every section, and the traps section near the end names the wrong-answer patterns the SAT builds into its distractors.

Where Ratios, Rates and Percentages Fit in Problem-Solving and Data Analysis

Ratios, rates and percentages are tested inside the SAT Math Problem-Solving and Data Analysis domain, one of four Math domains along with Algebra, Advanced Math, and Geometry and Trigonometry. Problem-Solving and Data Analysis carries 5 to 7 questions on every full Math test, alongside 13 to 15 Algebra questions, 13 to 15 Advanced Math questions, and 5 to 7 Geometry and Trigonometry questions.

For the full section breakdown, see our SAT Math section guide. College Board lists seven skills inside Problem-Solving and Data Analysis. This guide covers ratios, rates and percentages. One-variable data and two-variable data and scatterplots appear in our guide to SAT One- and Two-Variable Data. The table below maps each skill to its coverage here.

Problem-Solving and Data Analysis skill	Covered in this guide
Ratios and rates	Yes
Percentages	Yes
One-variable data	No, see SAT One- and Two-Variable Data
Two-variable data and scatterplots	No, see SAT One- and Two-Variable Data
Probability	Not covered in this guide
Statistical inference and margin of error	Not covered in this guide
Evaluating statistical claims: observational studies and experiments	Not covered in this guide

Setting Up Ratio and Rate Word Problems

A ratio compares two quantities, and getting its setup right decides the entire problem. Before writing a proportion, name exactly what each number in the ratio represents.

Reading a Ratio as Part-to-Part or Part-to-Whole

A part-to-part ratio compares two pieces of a group directly, red marbles to blue marbles, for example. A part-to-whole ratio compares one piece to the entire group, red marbles to all marbles combined. A bag holding red and blue marbles in a ratio of 3 to 5 has 3 red marbles for every 5 blue marbles, a part-to-part ratio, not 3 out of 8 total marbles unless the problem restates it as a fraction of the whole.

Writing a Proportion and Solving with Cross-Multiplication

Set the two ratios as equal fractions with matching quantities in matching positions. Cross multiplication then clears the fractions and leaves one equation to solve. These four steps handle any proportion.

Write both ratios as fractions with the same quantity type on top in each.
Set the fractions equal to each other.
Cross multiply to remove the fractions.
Solve the resulting equation for the unknown.

Here is an original example: a recipe uses flour and sugar in a ratio of 4 to 3, and a baker measures 18 cups of sugar. Find the cups of flour needed.

Write the proportion with flour on top in both fractions: 4/3 = x/18.
Cross multiply: 3x equals 4 times 18, so 3x = 72.
Divide both sides by 3: x = 24.
The baker needs 24 cups of flour.

Unit Rates and Unit Conversion Inside Rate Problems

A rate compares two different types of quantities, miles and hours or dollars and ounces. A unit rate reduces the comparison to a single unit of the second quantity. Unit rates put prices, speeds and densities on a common footing, which is why value-comparison questions ask for them.

Finding a Unit Rate

Divide the first quantity by the second to find how much of the first quantity matches one unit of the second. Here is an original example: a 15-ounce jar of honey costs $6.00. Find the price per ounce.

Name the target unit: dollars per one ounce.
Divide the price by the ounces: 6.00 divided by 15 equals 0.40.
State the unit rate: the honey costs $0.40 per ounce.

Converting Units Within a Rate

Some rate problems state the two quantities in units which do not match the units the question asks for. Multiply by a conversion factor written as a fraction which cancels the unwanted unit, leaving the target unit in its place.

Here is an original example: a drone flies at 45 miles per hour. Find its speed in feet per minute.

Convert miles to feet: 45 times 5,280 equals 237,600 feet per hour.
Convert hours to minutes: divide 237,600 by 60.
State the answer in the target units: 3,960 feet per minute.

Percentage Increase, Decrease, Markup, Discount and Tax

Percent problems on the SAT compare a change against a starting value, and the starting value decides which number belongs in the denominator. Pick the wrong base and every later step inherits the error. Markup, discount and tax questions all run on the same percent change relationship with a different base.

The Percent Change Formula

Percent change equals the difference between the new value and the original value, divided by the original value, times 100. A positive result is a percent increase, a negative result is a percent decrease.

Here is an original example: a jacket's price rises from $40 to $52. Find the percent increase.

Subtract to find the change: 52 minus 40 equals 12.
Divide the change by the original value: 12 divided by 40 equals 0.30.
Multiply by 100: the price rises by 30%.

Markup and Discount Problems

Markup adds a percent of the original price to set a higher selling price. Discount subtracts a percent of the original price to set a lower selling price. Both use the original price as the base for the percent.

Scenario	Formula
Markup	New price = original price plus (percent times original price)
Discount	New price = original price minus (percent times original price)

Here is an original example: a store buys a lamp for $24 and marks up the price by 45%. Find the retail price.

Calculate the markup: 0.45 times 24 equals 10.80.
Add the markup to the cost: 24 plus 10.80 equals 34.80.
State the retail price: $34.80.

Tax and Successive Percentage Changes

Tax adds a percent to a price, and it applies after a discount, not before. Two percent changes applied one after another do not combine into one simple sum, since the second change applies to a new base value, not the original one.

Here is an original example: an $80 jacket is discounted 25%, then 8% sales tax applies to the discounted price. Find the final price.

Apply the discount to the original price: 80 times 0.75 equals 60.
Apply tax to the discounted price: 60 times 1.08 equals 64.80.
State the final price: $64.80.
Note the trap: treating the pair as a single 17% net decrease gives 80 times 0.83 equals 66.40, a wrong result, since the discount and the tax use different base values.

Common Proportional-Reasoning Traps

The SAT builds wrong-answer options around common setup mistakes, not random numbers. Naming the trap while solving prevents picking it under time pressure.

Adding two percent changes when they apply to different base values, instead of applying them one after another.
Confusing a part-to-part ratio with a part-to-whole ratio, then setting up the wrong proportion.
Skipping a needed unit conversion inside a rate problem, so the two rates being compared use mismatched units.
Computing percent change against the new value instead of the original value, which flips the size of the result.
Applying tax to the original price instead of the discounted price in a discount-then-tax problem.
Cross-multiplying a proportion with the terms placed in the wrong position, which inverts the ratio instead of solving it.

Practice Ratios, Rates and Percentages With Us

We built free drill sets for ratios and rates, and for percentages, at three difficulty levels, easy, medium and hard. Work through every level on the SAT practice hub to build accuracy under time pressure. No signup required.