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Tuesday, May 1, 2012

Adding and Subtracting Mixed Fractions

13/4 Quick Definition: A Mixed Fraction is a
whole 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:
4/43/4 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:

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

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