Working with Fractions, Step-by-Step

DIVIDING FRACTIONS

1.   Write the numbers HORIZONTALLY (across the page).

Go to the NEXT step...  



2.   ARE THERE ANY WHOLE OR MIXED NUMBERS?
YES:   Continue below...
 
NO:   Skip to the NEXT STEP.

Change whole or mixed numbers to improper fractions.
  • Write a WHOLE NUMBER OVER ONE in the denominator.
    (Any number divided by one is still itself.)
  • To change a MIXED NUMBER to an improper fraction:
    MULTIPLY THE DENOMINATOR
    (bottom number = the number of pieces in each whole thing) TIMES THE WHOLE NUMBER;
    THEN ADD THE NUMERATOR
    (top number = the number of extra pieces)
    Write this total OVER the original denominator
    (the total number of those-size pieces in all).
  • Repeat with the other fraction.

Go to the NEXT step...  



3.   MULTIPLY BY THE RECIPROCAL
  • Copy the FIRST FRACTION exactly;
  • Change the division sign to MULTIPLICATION;
  • Invert the SECOND FRACTION. (flip it upside-down: ORIGINAL numerator goes on the bottom...)

Go to the NEXT step...



4.   CAN YOU CANCEL?

YES:   Continue below...

 
NO:   Skip to the NEXT STEP.

SIMPLIFY: Eliminate common factors.
  • Divide ANY single numerator and ANY single denominator by the SAME NUMBER (a common factor);
  • Cross out the original and write the new numbers for each (remember to write the amount that's LEFT and not the common factor by which you'd divided).
  • Repeat as many times as possible; by sure to use one numerator and one denominator each time.

Go to the NEXT step...  



5.   DO the Multiplication:
MULTIPLY ACROSS:  
  • The PRODUCT of the NUMERATORS is the top number of the answer;
  • The PRODUCT of the DENOMINATORS is the bottom number of the answer.

Go to the NEXT step...  



6.   IS THE FRACTION IN LOWEST TERMS?
NO:   Continue below...
 
YES:   Skip to the NEXT STEP.

Improper fraction:   (Top number is greater than the bottom number.)
  • Divide the TOP BY the BOTTOM;
  • Write any remainder as the numerator and use the same denominator.

Simplify the fraction:
  • Divide both the numerator and the denominator by the same number.
  • Repeat until the only common factor is one.

Go to the NEXT step...  



7.   Check your answer.

 



SAMPLE PROBLEM #1:
  4/5 ÷ 1/6 =
Initial set-up.     Next step  
 
See the solution.





SAMPLE PROBLEM #2:
  3 3/4 ÷ 12 =
Set-up     First step     Second step

 
 
See the solution.





SAMPLE PROBLEM #3:
  5 5/6 ÷ 2 1/10 =  
Set-up     Step 1     Step 2
 
 
See the solution.





SAMPLE PROBLEM #1:
  4/5 ÷ 1/6 =
Set-up   Next step

 
 
See the solution.





SAMPLE PROBLEM #2:
  3 3/4 ÷ 12 =
Set-up   Step 1   Step 2
 
 
See the solution.





SAMPLE PROBLEM #3:
  5 5/6 ÷ 2 1/10 =  
Set-up   Step 1   Step 2
 
 
See the solution.





Amby's Math Instruction, Reinforcement, and Learning Activities
Math Education Resources
Math Puzzles & Learning Activities

Directory
Brain Games
Cat Site
Education
Internet
Mensa
Portfolios
Test Prep
Work Site

© 1999 Amby Duncan-Carr   All rights reserved.

The URL of this page is:
http://amby.com/educate/math/frac-div.html