Skill 30
Understand Mixed Numbers
Mixed numbers are combinations of whole numbers and fractions. For example, 
is a mixed number. It represents 1 whole 
like a whole pie 
more.
Converting a Mixed Number to a Fraction. The number 1 can also be expressed as 
so the number 
is the same as 
Let’s try another mixed number: 
If 1 is the same as 
then 3 must be 
Now add: 
Let’s try one final example. The mixed number 
is the same as 
That’s because 
Now add: 
There is an easier way to do this calculation. Let’s work again with 
Multiply the whole number 3 by the fraction denominator 2, then add the fraction numerator 1. Express the result as a fraction with the same denominator as the fraction in the original mixed number. So for 
you calculate:
Take 
as another example:
Converting a Fraction to a Mixed Number. You can work the same calculation backwards. If you are asked to express 
as a mixed number, simply divide the numerator 8 by the denominator 3 to get 
Similarly, 
can be expressed as 
or 
(Don’t forget to convert your answers to their lowest terms.)
Converting a Mixed Number to a Decimal. You can also convert mixed numbers to decimals. Take the mixed number, make it into a fraction, then divide the numerator by the denominator to get the decimal. Here are two examples:
Test Yourself!
Change the following mixed numbers into fractions.
Change the following fractions into mixed numbers.
Change the following mixed numbers into decimals.
