You are here:

Advanced Math/Cancellation & Multiplication

Advertisement


Question
Hello:

What is the mathematical reason that letters and units cancel from multiplication?

For example, 1/2x * 4x = 2 and 1/(2 ounces) * 4 ounces = 2

The x's and the ounces cancel. What is the reason for the cancellation or why or how does this occur?

I thank you for your reply.

Answer
To reduce a fraction to lowest terms, you cancel out any numbers that are factors in both numerator and denominator. Any units and variables that are common factors are treated the same way as the numbers.

When reducing the fraction 6/2, you are answering the question "how many times does 2 go into 6?"—3 times. That is why 6/2 = 3.

How many times does 1 foot go into 1 foot?—it goes in once. Thus, (1 ft)/(1 ft) reduces to 1.
How many times does x go into 2x? If x≠0, it goes in twice. (2x)/x reduces to 2.

I hope this representation helps.

Advanced Math

All Answers


Answers by Expert:


Ask Experts

Volunteer


Janet Yang

Expertise

I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

Experience

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Publications
Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

Education/Credentials
I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

©2016 About.com. All rights reserved.