Multiplicative Inverse
 Lesson 3
 Topic Index  | Grade 6 Math | Intermediate Test Prep | StudyZone

Using the multiplicative inverse, you KNOW the answer to 
2/3 ÷  1/12  is 8, but the following shows you WHY !

What about division problems with two proper fractions?  What do those pictures look like?

 

2/3 ÷  1/12 = ?   

Let's use fraction bars to illustrate!

 

 

Step one: Line up fraction bars for  the 2/3.
 

 

 

1/3

 

1/3

 
Step two:  Using the 1/12 fraction bars, line them up under the two 1/3 bars.  
 

1/3

 

1/3
 

1/12

 

 1/12 1/12 1/12 1/12 1/12 1/12 1/12

 

Step three:  Count the 1/12 bars.

There are 8 of them.

Does that mean that:

2/3 ÷  1/12 = 8 ?

 Let's solve the problem, using the multiplicative inverse (reciprocal)!

2/3 ÷  1/12 =
2/3 x  12/1 = (multiply by the reciprocal)
24/3=    (multiply numerators and denominators)
8  (simplest form)

  So the picture "worked"!   It showed the answer!

 

Let's try one more!
   
 

Step one: Line up fraction bars for  the 3/6.

 

 
 

1/6

 

1/6

1/6
Step two:  Using the 1/12 fraction bars, line them up under the  three 1/6 bars.

 

    

 

1/6

 

1/6

1/6
 1/12 1/12 1/12 1/12 1/12 1/12

 

Step three:  Count the 1/12 bars.

 

There are 6 of them.

Does that mean that:

3/6 ÷  1/12 = 6 ?

 Let's solve the problem, using the multiplicative inverse (reciprocal)!

3/6 ÷  1/12 =
3/6 x  12/1 = (multiply by the reciprocal)
36/6=    (multiply numerators and denominators)
6 (simplest form)

  So again, the picture "worked"!   It showed the answer!

 

 

  
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