Mixed numbers and improper fractions
In a nutshell
A mixed number is a number which consists of a whole number and a proper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Example 1
Below are some examples of mixed numbers:
221,541,8103
Below are some examples of improper fractions:
213,77,527
Writing a mixed number as an improper fraction
procedure
1. | Multiply the whole number by the denominator of the fraction part. |
2. | Add the answer to Step 1 to the numerator of the fraction part. |
3. | Write the answer to Step 2 over the denominator of the fraction part. |
Example 2
Convert the following mixed number into an improper fraction:
297
Multiply the denominator and the whole number:
2×9=18
Add the answer to the previous step to the numerator:
18+7=25
Write the answer to the previous step above the denominator.
925(=297)
Writing an improper fraction as a mixed number
procedure
1. | Divide the numerator by the denominator using long division with remainders. |
2. | Write down the whole number result. |
3. | Write the remainder over the denominator of the original improper fraction. This will be the fraction part of the mixed number. Note: If there is no remainder, the answer is a whole number with no fraction part. |
4. | Simplify the fraction part if required. |
Example 3
Convert the following improper fraction into a mixed number:
723
Divide the numerator by the denominator:
23÷7=3R2
The whole number part is 3. The remainder is written over the original denominator.
372(=723)
Note: The fraction part in this example cannot be simplified.