LESSON: Mixed Numbers and Improper Fractions

READ: Rewrite Mixed Numbers as Improper Fractions

Rewrite Mixed Numbers as Improper Fractions

A mixed number is a number that has both wholes and parts in it.

Example

$5 \frac{1}{4}$

Here we have a mixed number. We have five whole items and one-fourth of a whole.

Now you know how to identify a mixed number. The opposite of a mixed number is an improper fraction.

What is an improper fraction? An improper fraction is a fraction that has a larger numerator and a smaller denominator.

Example

$\frac{12}{5}$

If the denominator tells us how many parts the whole has been divided into, then this whole has been divided into 5 parts. The numerator tells us how many parts of the whole we have in this case, we have twelve parts.

If we have twelve out of five parts, then we have MORE than one whole. One whole would be five out of five parts, but we have 12 out of 5 parts. This is where mixed numbers come in.

How do we write a mixed number as an improper fraction? To write a mixed number as an improper fraction, we want to write a fraction in terms of parts instead of in terms of wholes and parts.

Example

Change $2 \frac{1}{3}$ to an improper fraction.

To do this, we multiply the whole number times the denominator and add the numerator.Then we put this over the original denominator.

2 $\times$ 3 + 1 $=$ 7

Our original denominator is 3.

Our answer is $2 \frac{1}{3} = \frac{7}{3}$ .

Notice that the mixed number and the improper fraction are also equivalent.