How To Add Mixed Fractions

Mixed fractions are a combination of a whole number and a fraction. An example of a mixed fraction would be 1½ as in overtime pay is paid at the rate of 1½ times regular pay. Another example would be a recipe in which you are instructed to add 2 ¼ teaspoons of salt to the mixture.

Before going any further let's define the terms numerator and denominator. All fractions consist of two parts, a top part, which is called the numerator and the bottom part, which is called the denominator. Thus we have:

Numerator

Denominator

Next we have a couple of rules:

The First is: When adding any fractions we must first make sure that both fractions have the same denominator. If the fractions to be added do not have the same denominator then we must find a number into which the denominators of all the fractions to be added can be evenly divided into. While any number that can be evenly divided by each of the denominators will do, it is best if we find the smallest number that each can be evenly divided into – this is known as the least common denominator.

The Second is: we can either add fractions or whole numbers but not both together. To get around this, we convert the mixed number into a fraction by multiplying the whole number by the denominator and adding the result to the numerator. For example 1 ½ can be converted to a fraction by multiplying the whole number (1) by the denominator (2) to get the result of 2 which, when added to the numerator of 1 gives us 3. Our mixed number is now the fraction 3/2

Now that we know what is needed to add mixed numbers it is time for an example. Lets add:

1 ½ + 4 ¼ + 3 2/3

Since the denominators are all different, we will need to find the least common denominator which in this case is 12. Twelve is the smallest number that each denominator will divide into without leaving a fractional amount remaining. To give all of the fractions a 12 as the denominator we have to divide each denominator into 12 and multiply the result times the numerator to get our new numerator. Thus, to convert ½ to twelfths we change the denominator from 2 to 12 and divide two into twelve to get six. Multiplying the result which is six times the numerator which is 1 we get 6/12

Doing the same for the other fractions and leaving, for the moment, the numbers as mixed numbers we get:

1 6/12 + 4 3/ 12 +3 8/ 12

Next we convert the mixed numbers to fractions by multiplying the whole number by the denominator and adding it to the numerator to get:

18/ 12 + 51/ 12 + 44/ 12

Adding our numerators we get: 113/12

Finally, since the numerator is larger than the denominator, we convert this back to a mixed number by dividing the numerator 113 by the denominator 12 to get our answer which is: 9 5/12

This is how you add mixed fractions.