# Working with Fractions, Step-by-Step

1.   WRITE THE NUMBERS VERTICALLY

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2.   DO YOU HAVE A COMMON DENOMINATOR?
(same bottom number = same size pieces)
NO:   Continue below...

Change to equivalent fractions with a common denominator:
• Find a number divisible by BOTH denominators (such as the LCM: Least Common Multiple).
• Multiply both the numerator AND denominator of one fraction by the SAME NUMBER to get an equivalent fraction with the common denominator.
• Repeat with the other fraction.

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3.   DO the Addition:
• Add the numerators   (to find the total number of pieces).
Keep the same denominator.

• Add the whole numbers (if any).

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4.   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 of a fraction using the same denominator.

Reduce 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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SAMPLE PROBLEM #1:
 2/7 + 4/7 = Look at the set-up. Check answer6/7 See the solution.

SAMPLE PROBLEM #2:
 2/3 + 1/4 = Look at the set-up:   Step 1   Step 2 Check answer11/12 See the solution.

SAMPLE PROBLEM #3:
 5/6 + 3/4 = Look at the set-up:   Step 1   Step 2 Check answer19/12 = 1 7/12 See the solution.

SAMPLE PROBLEM #4:
 5 1/2 + 6 3/8 = Look at the set-up:   Step 1   Step 2 Check answer11 7/8 See the solution.

SAMPLE PROBLEM #5:
 1 2/3 + 7 5/6 + 9 3/4 = Look at the set-up:   Step 1   Step 2 Check answer 17 and 27/12 17 + 2 and 3/12 19 and 1/4 19 1/4 See the solution.