Adding And Subtracting Mixed Fractions - Math Is Fun

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Adding and Subtracting Mixed Fractions

A Mixed Fraction is a whole number and a fraction combined:

1 whole pizza3/4
1 34
(one and three-quarters)

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

An Improper fraction has a top number larger than or equal to the bottom number:

4/43/4
74
(seven-fourths or seven-quarters)

Can you see that 134 is the same as 74 ?

In other words "one and three quarters" is the same as "seven quarters".

(You may like to read how to Convert from or to Mixed Fractions)

Adding Mixed Fractions

To add mixed fractions:

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

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:

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

935, 1414, 1415, 1416, 936, 1417, 3585, 3586, 3587 Introduction to Fractions Simplifying Fractions Equivalent Fractions Least Common Multiple Least Common Multiple Tool Least Common Denominator Subtracting Fractions Multiplying Fractions Dividing Fractions Fractions Index

Tag » How To Add Improper Fractions