Working with Fractions, Step-by-Step

MULTIPLYING 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-sized pieces in all).
  • Repeat with the other fraction.

Go to the NEXT step...  



3.   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...  



4.   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...  



5.   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...  



6.   Check your answer.

 



SAMPLE PROBLEM #1:
  2/7 * 4/5 =  
Look at the set-up.

 
 
See the solution.





SAMPLE PROBLEM #2:
  5/12 * 9/10 =
Set-up     Next step
 
 
See the solution.





SAMPLE PROBLEM #3:
  25/8 * 6 =  
Set-up     Next step
 
 
See the solution.





SAMPLE PROBLEM #4:
  5 1/3 * 6 3/8 =
Set-up   Step 1   Step 2
 
See the solution.





SAMPLE PROBLEM #5:
  4 1/6 * 2 * 7 4/5 * 7/10 =
Initial set-up
Step 1   Step 2   Step 3
 
Solution (Part 1)  
Solution (Part 2)  




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