In these worksheets, students will solve problems involving direct and indirect variation.

In a Direct Variation relationship between two variables, one is a constant multiple of the other (x = 3y) so that as one variable changes the other changes in proportion to it. In an Inverse Variation relationship, the product is a constant, so that as one variable increases the other decreases in proportion so that the product remains the same. Direct and inverse variation helps us to find a way of changing one number variation into another number. Equations with these two have a little attractive sound. Direct variation let one number increases the other one. It is a change that makes one value directly proportional to another. You can take the example of the relationship between height and age. The size of anything increases with the increase in the age of anything. In mathematics solutions, use the equation y = kx to show the direct variation. For example, there are two quantities x and y that is age and the height. Also, you can use equation y = kx to show direct variation. Here, k is the constant value of proportionality. You will consider the size increase in y to get a boost in x. For example, the amount will double; you have an increase in values that is y = 2x. In inverse variations, the situation will be different or opposite as one value increase when another one will decrease. We will call all this process an inverse proportion. The ratio between spending time in your class and the grade on the midterm. When your leisure time increase, your test or exam score will decrease.

In these worksheets, students will work with direct and inverse variation. Problems are presented as word problems, and students will be required to write the problem as an equation and then solve. Extra paper may be required in order for students to do their calculations. This set of worksheets contains lessons, step-by-step solutions to sample problems, both simple and more complex problems, reviews, and quizzes. It also includes ample worksheets for students to practice independently. Most worksheets contain between eight and ten problems. When finished with this set of worksheets, students will be able to solve word problems involving direct and indirect variation. These worksheets explain how to solve problems involving direct and indirect variation. Sample problems are solved and practice problems are provided.

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Direct and Inverse Variation Worksheets

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Direct and Inverse Variations Lesson

This worksheet explains how to solve problems involving direct variation. A sample problem is solved, and two practice problems are provided.

Practice Worksheet

You will solve word based problems like: The speed of the car travelling from A to B varies inversely with the time taken for the travel. If its speed is 60km/hr, it would take 3 hours for the journey. Find the time it would take for the journey if its speed is 90 km/hr.

More Student Practice

If y varies inversely as x, and y = 7 when x = 6, what is y when x = 3? What is x when y = 3? Ten problems are provided.

Full Skill Review and Practice

You will work on problems like: If d varies directly as f and d is 12 when f is 24, find the constant of variation.

Direct and Inverse Variations Quiz

Students will demonstrate their ability with these types of problems.

Topic Check

You will learn how to solve for constants here.

Direct Variations Lesson

If n varies directly as j and n is 6 when j is 18, find the constant of variation.


There are about 15 calories in 60 grams of chicken. Mike ate 20 grams of this chicken. About how many calories were in the chicken he ate.


If G varies directly as H and G is 3 when H is 48, find the constant of variation.

Review and Practice

The concept of how to solve problems involving direct variation is reviewed. A sample problem is solved. Six practice problems are provided.


Students will demonstrate their proficiency with this topic and series of concepts. Ten problems are provided.


Students will work on a wide variety of problems to test their skills out.