Working with Fractions

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Dividing Fractions
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Follow the following steps to divide fractions:
   
1.   Write the numbers horizontally:

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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.

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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...)

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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.

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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.

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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.

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7.   Check your answer.
 

 

   
 

SAMPLE PROBLEM #1:  

4/5 ÷ 1/6 =

Step 1:

Solution:

 

SAMPLE PROBLEM #2:  

5 5/6 ÷ 2 1/10 =  

Setup:

Step 1:

Step 2:

Solution:

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