The lesson

This lesson teaches Unit Rates with Fractions. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.

A unit rate is 'per one'

A unit rate tells you how much of one quantity goes with exactly one of another - like miles per hour or cost per pound.

When you study a unit rate is 'per one', slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

When the numbers are fractions

The denominator tells you how many equal parts the whole is split into. The numerator tells you how many of those parts you have.

Always ask: "What is the whole?" In 3/4 of a pizza, the whole is one pizza. In 3/4 of 20 students, the whole is 20 students.

When you study when the numbers are fractions, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

1Write the rate as a fraction (a complex fraction).
2Divide the top by the bottom - multiply by the reciprocal.
3Simplify to get the rate per one.

The denominator tells you how many equal parts the whole is split into. The numerator tells you how many of those parts you have.

Always ask: "What is the whole?" In 3/4 of a pizza, the whole is one pizza. In 3/4 of 20 students, the whole is 20 students.

A person walks 1/2 mile in 1/4 hour. What is the speed in miles per hour?

1Set up the rate: (1/2) ÷ (1/4).
2Multiply by the reciprocal: 1/2 × 4/1 = 4/2 = 2.
3The unit rate is 2 miles per hour.

Why this matters

Unit Rates with Fractions shows up constantly in find a per-one rate even when the quantities are fractions. It also connects to what you will see on homework, quizzes, and the next unit in this grade.

Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.

Common mistakes to avoid

Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.

Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.

Key ideas from this lesson

A unit rate is 'per one'
When the numbers are fractions
Write the rate as a fraction (a complex fraction).
Divide the top by the bottom - multiply by the reciprocal.
Simplify to get the rate per one.

Video walkthrough

Khan Academy

Determining Rates with Fractions

Turn a ratio of fractions into a clean unit rate.

Watch on YouTube

Other

Rates and Unit Rates

A refresher on cost-per-item and speed rates.

Watch on YouTube

Practice

For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.

Exercise 1

Try it yourself

A jogger runs 3/4 mile in 1/2 hour. Find the speed in miles per hour.