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### Course: Arithmetic (all content)>Unit 5

Lesson 12: Mixed numbers

# Mixed numbers and improper fractions review

Review how to rewrite mixed numbers as improper fractions and improper fractions as mixed numbers.  Then, try some practice problems.

## What is an improper fraction?

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Below are examples of improper fractions:
$\frac{9}{4},\frac{5}{5},\frac{7}{3}$

## What is a mixed number?

A mixed number is a number consisting of a whole number and a proper fraction.
Below are examples of mixed numbers:
$4\frac{1}{2},1\frac{3}{8},12\frac{5}{6}$

## Rewriting a mixed number as an improper fraction

Rewrite $3\frac{4}{5}$ as an improper fraction.
$3\frac{4}{5}=3+\frac{4}{5}$
$\phantom{3\frac{4}{5}}=1+1+1+\frac{4}{5}$
$\phantom{3\frac{4}{5}}=\frac{5}{5}+\frac{5}{5}+\frac{5}{5}+\frac{4}{5}$
$\phantom{3\frac{4}{5}}=\frac{5+5+5+4}{5}$
$3\frac{4}{5}=\frac{19}{5}$
Problem 1A
Rewrite as an improper fraction.
$5\frac{1}{2}=$

Want to try more problems like this? Check out this exercise.

## Rewriting an improper fraction as a mixed number

Rewrite $\frac{10}{3}$ as a mixed number.
So, let's see how many wholes we can get out of $\frac{10}{3}$.
$\frac{10}{3}=\frac{3+3+3+1}{3}$
$\phantom{\frac{10}{3}}=\frac{3}{3}+\frac{3}{3}+\frac{3}{3}+\frac{1}{3}$
$\phantom{\frac{10}{3}}=1+1+1+\frac{1}{3}$
$\frac{10}{3}=3\frac{1}{3}$
Problem 2A
Rewrite as a mixed number.
$\frac{13}{8}=$

Want to try more problems like this? Check out this exercise.

## Want to join the conversation?

• some of them were hard maybe make it the same but easy.
thanks so much
• i got only the first one in correct. other then that i got all of them
• I figured out how to do the problems after 30 secends of silence
• Only improper fraction will create a whole number or mixed number. An improper fraction will always have a numerator that is equal to or larger than the denominator.

8/2 is an improper fraction. 8/2 becomes just a whole number = 4. There is no fraction as 0/2=0.

2/8 is a proper fraction (the numerator is less than the denomintor). It can't be changed into a mixed number. All you can do is reduce it down to 1/4.

Hope this helps.
• Dose it matter if you don't use paper to work it out because I do not need to?
• I sometimes use paper but good job. You're helping the enviorement!
• do we have to be smart to pass our test about improper fractions and mixed numbers because i don't understand how to do improper fractions and mixed numbers :(
• you don't have to be smart,you just have to take the time to understand it
• this is really easy! Just work hard and it will be. 😁
• maybe 4 u and me it is, but others may have some trouble, and that is OKAY!!
• Kahn academy is such a help in my math. Thank you guys!
• I also like Khan Academy
(1 vote)
• would 8/2 as a mixed number be 4 0/2 ?
and what is the difference of the mixed number of 2/8? I dont get it.
• Only improper fraction will create a whole number or mixed number. An improper fraction will always have a numerator that is equal to or larger than the denominator.

8/2 is an improper fraction. 8/2 becomes just a whole number = 4. There is no fraction as 0/2=0.

2/8 is a proper fraction (the numerator is less than the denomintor). It can't be changed into a mixed number. All you can do is reduce it down to 1/4.

Hope this helps.
• How do you subtract fractions?
• There's a nice trick for subtracting fractions.

To find the numerator: cross-multiply numerators with denominators and subtract the products. Specifically, find (1st numerator * 2nd denominator) - (2nd numerator * first denominator).
To find the denominator: multiply the denominators.
Then reduce the answer as needed.

Example: Let's do 5/6 - 2/9.
The numerator is (5*9) - (2*6) = 45-12 = 33.
The denominator is 6*9 = 54.
So we get 33/54, which reduces to a final answer of 11/18 (from dividing top and bottom each by 3).

This trick is an example of Vedic math. Try looking up Vedic math online and you might find other arithmetic tricks that you like!