Adding And Subtracting Fractions

	Quick Definition: A Mixed Fraction is awhole number and a fraction combined, such as 1 3/4.
1 3/4
(one and three-quarters)

To make it easy to add and subtract them, just convert to Improper Fractions first:

	Quick Definition: An Improper fraction has a top number larger than or equal to the bottom number, such as 7/4 or 4/3 (It is "top-heavy")
7/4
(seven-fourths or seven-quarters)

Adding Mixed Fractions

I find this is the best way to add mixed fractions:

• convert them to Improper Fractions
• then add them (using Addition of Fractions)
• then convert back to Mixed Fractions:

Example: What is 2 ³/₄ + 3 ¹/₂ ?

Convert to Improper Fractions:

2 ³/₄ = ¹¹/₄

3 ¹/₂ = ⁷/₂

Common denominator of 4:

¹¹/₄ stays as ¹¹/₄

⁷/₂ becomes ¹⁴/₄

Now Add:

¹¹/₄ + ¹⁴/₄ = ²⁵/₄

Convert back to Mixed Fractions:

²⁵/₄ = 6 ¹/₄

When you get more experience you can do it faster like this:

Example: What is 3 ⁵/₈ + 1 ³/₄

Convert them to improper fractions:

3 ⁵/₈ = ²⁹/₈
1 ³/₄ = ⁷/₄

Make same denominator and add:

²⁹/₈ + ¹⁴/₈ = ⁴³/₈ = 5 ³/₈

Subtracting Mixed Fractions

Just follow the same method, but subtract instead of add:

Example: What is 15 ³/₄ - 8 ⁵/₆ ?

Convert to Improper Fractions:

15 ³/₄ = ⁶³/₄

8 ⁵/₆ = ⁵³/₆

Common denominator of 12:

⁶³/₄ becomes ¹⁸⁹/₁₂

⁵³/₆ becomes ¹⁰⁶/₁₂

Now Subtract:

¹⁸⁹/₁₂ - ¹⁰⁶/₁₂ = ⁸³/₁₂

Convert back to Mixed Fractions:

⁸³/₁₂ = 6 ¹¹/₁₂