LESSON: Mixed Numbers and Improper Fractions

READ: Compare and Order Mixed Numbers and Improper Fractions

Compare and Order Mixed Numbers and Improper Fractions

How do we compare a mixed number and an improper fraction?

We compare them by first making sure that they are in the same form. They both need to be mixed numbers otherwise it is difficult to determine which one is greater and which one is less than.

Example

$6 \frac{1}{2} \ {\underline{\;\;\;\;\;\;\;}} \ \frac{15}{4}$

The easiest thing to do here is to convert fifteen-fourths into a mixed number.

$\frac{15}{4} = 3 \frac{3}{4}$

Now we know that six and one-half is greater than fifteen-fourths.

Our answer is $6 \frac{1}{2} > \frac{15}{4}$ .

How do we write mixed numbers and improper fractions in order from least to greatest or from greatest to least? We can work on this task in the same way as with the comparing. First, make sure that all of the terms you are working with are all mixed numbers.

Example

Write in order from least to greatest, $\frac{33}{2}, 4 \frac{2}{3}, \frac{88}{11}$ .

We need to convert thirty-three halves and eighty-eight elevenths to mixed numbers.

$\frac{33}{2} &= 16 \frac{1}{2}\\ \frac{88}{11} &= 8$

Our answer is $4 \frac{2}{3}, \frac{88}{11}, \frac{33}{2}$ .