Rates, Ratios and Proportions with Fractions


CCSS.MATH.CONTENT.7.RP.A.1 Compute unit rates, including those that involve complex fractions, with like or different units.

CCSS.MATH.CONTENT.7.RP.A.2.C. Represent proportional relationships by equations

Time Required

30-45 minutes

Technology Required

Projector and computer required to watch video in class. Alternatively, students can be assigned to watch on computer, phone or tablet at home. Google apps or PowerPoint required for slide presentation.

Lesson Summary

Students watch a 4-minute video giving examples of finding unit rates by simplifying fractions. They solve a problem together as a class and are given a short lecture on solving rate problems with complex fractions. Problems provided can be worked by students individually or done together in class.

Lesson Plan

This lesson plan assumes that your students understand simplifying complex fractions. They should know how to divide a fraction by an integer or by another fraction.

1. Watch video explaining unit rates

2. Solve a problem as a class

Using this Google slides presentation, students solve a problem together as a class. They are reminded the meaning of “reciprocal” and that in dividing one fraction by another, you multiply by the reciprocal of the fraction in the denominator. Additional slides give students instruction and tips on solving rates problems that include complex fractions.

3. Solve a variety of problems involving rates and complex fractions

The problem set is found here and the answer key with problems solved step–by-step is here. You know your class best. If you have already covered complex fractions and rate problems, these can be used as formative assessment or review. Alternatively, you may wish to either:

  • Assign the problems, have the students give these a try and then correct together as a class.
  • Select some of the problems to review together and assign the remainder as homework.
  • Assign the problems for students to complete individually, as either in-class work or homework and grade using the answer key provided.

4. Watch a video of a student applying ratio and proportion

At this point, many students will still need further clarification. In this video, Eva shows how she uses ratio and proportion to reduce a recipe for 4 dozen cookies to one for 2 dozen cookies.


Students will be assessed based on performance on the problems provided.

State Standards

Missouri Learning Standard 7.RP.A.1

Minnesota Math Standard – Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.