Use a unit rate to compare quantities.

Imagine you are at the grocery store. One brand sells 6 granola bars for $4.50, and another brand sells 8 granola bars for $5.60. Which is the better deal? You can't tell just by looking at the prices because the packages have different amounts. People have faced this exact problem for thousands of years, and the solution is something called a unit rate — a rate that tells you the amount per one unit.

The big question is: How do you compare two quantities that come in different-sized groups? The answer is to break each quantity down to a single unit. That's what this lesson is all about.

Before we dive in, let's make sure you know a few key terms. A rate is a ratio (a comparison) between two quantities that have different units, like dollars and pounds or miles and hours. A unit rate is a special rate where the second quantity is exactly 1. For example, '$3 per pound' is a unit rate because it tells you the price for one pound.

The diagram below shows two runners. Runner A covers 400 meters in 5 minutes, and Runner B covers 360 meters in 4 minutes. The bars on the left show their total distances, and the bars on the right show their unit rates (meters per 1 minute). Notice how the unit rate bars let you compare the runners fairly.

This is the power of unit rates. Runner A ran a longer distance overall, which might trick you into thinking Runner A is faster. But the unit rate strips away the unfair differences and shows you the true comparison per one minute.

Finding a unit rate always comes down to one operation: division. You divide the quantity you want to measure by the number of units it covers. Here is the formula you'll use again and again.

Let's look at a quick example. A store sells 5 notebooks for $8.75. What is the price per one notebook?

When you're comparing two options, find the unit rate for each one, then see which is higher or lower depending on what you need. A lower price per unit means a better deal. A higher speed per hour means faster travel.

Unit rates pop up everywhere. The diagram below organizes the most common types you'll see on the SSAT and in daily life. Each example shows what you divide and what 'per one' unit you end up with.

No matter the category, the process is the same. Identify the two quantities, decide which one should be 'per one,' and divide. On the SSAT, price-per-item and speed problems are the most common, so practice those extra.

Brand X sells a 48-ounce bottle of orange juice for $3.84. Brand Y sells a 64-ounce bottle for $4.80. Which brand has the lower price per ounce?

Unit rates are incredibly useful, but there are a few mistakes students commonly make. The table below highlights what makes unit rates so powerful and where to watch out for errors.

Once you master unit rates, you're ready for the next step: proportional reasoning. A proportion is an equation that says two ratios (or rates) are equal. Unit rates are the building blocks of proportions.

Here's the cool part: if you know the unit rate, solving a proportion is just multiplication. For example, if one pen costs $1.50 (the unit rate), then 10 pens cost $1.50 × 10 = $15.00. So learning unit rates well makes proportions much easier later on.