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
(by multiplying top and bottom by 2)

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: 7/4 becomes 14/8 (by multiplying top and bottom by 2)

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

 

  Hard Question