Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Invert and Multiply

Date: 11/08/97 at 14:24:45
From: Anonymous
Subject: Fractions!

Hi Doc,

I am a student teacher, currently taking a methods course in 
elementary mathematics. I am struggling with how to explain to a class 
"why" we invert and multiply when dividing fractions. I read your FAQ 
on this, but still don't understand how I would explain it using 
concrete materials in a classroom.  Please help.

Thanks ever so much!

Date: 11/09/97 at 09:56:11
From: Doctor Chita
Subject: Re: Fractions!

Hi there:

Explaining "why" using concrete materials may be difficult. However, 
this is an opportunity, perhaps, to show students how mathematics 
relies on proof, rather than pictures or models.

Take an "easy" problem such as, 1/2 divided by 3/4.

Write this as a compound fraction: (1/2)/(3/4). (Use horizontal 
fraction bars, not diagonal bars as here. The computer has its 

Everyone knows that 1 is the multiplicative identity element. 

   1 * (1/2)/(3/4) = (1/2)/(3/4)

Substitute 4/4 for 1. Write:

   4/4 * (1/2)/(3/4)

Think of 4/4 as the compound fraction: (4/1)/(4/1). Then multiply the 
numerator and deminator of the compound fraction by 4/1:

   [4/1 * (1/2)]/4/1* (3/4)]

The new numerator is 2: the new denominator is 3. The answer is 2/3.

Therefore, the rule "invert and multiply" works because what you are 
really doing is multiplying the numerator and denominator of a 
compound fraction by the LCD of the fractions in the compound 

Try 3/8 divided by 9/5. Write as (3/8)/(9/5) using horizontal bars.

Multiply the fraction by 1 = 40/40, in the form of (40/1)/(40/1) where 
40 is the LCD of 8 and 5:

   (40/1)/(40/1) * (3/8)/(9/5)

   [40/1 * 3/8]/ [40/1 * 9/5]

   15/72 = 5/24

After a while, you can drop the 1s in the fraction that represents the 

Got it? Put this information together with what's in the archives and 
write back if you still need more help. Good luck.

-Doctor Chita,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
Associated Topics:
Elementary Fractions
Middle School Fractions

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.