# Working with Fractions, Step-by-Step

MULTIPLYING FRACTIONS

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

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2.   ARE THERE ANY WHOLE OR MIXED NUMBERS?
YES:   Continue below...

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;
(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.

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3.   CAN YOU CANCEL?

YES:   Continue below...

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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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.

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5.   IS THE FRACTION IN LOWEST TERMS?
NO:   Continue below...

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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