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Lesson 4: 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:
start fraction, 9, divided by, 4, end fraction, comma, start fraction, 5, divided by, 5, end fraction, comma, start fraction, 7, divided by, 3, end fraction

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, start fraction, 1, divided by, 2, end fraction, comma, 1, start fraction, 3, divided by, 8, end fraction, comma, 12, start fraction, 5, divided by, 6, end fraction

Rewriting a mixed number as an improper fraction

Rewrite 3, start fraction, 4, divided by, 5, end fraction as an improper fraction.
3, start fraction, 4, divided by, 5, end fraction, equals, start color #11accd, 3, end color #11accd, plus, start color #1fab54, start fraction, 4, divided by, 5, end fraction, end color #1fab54
empty space, equals, start color #11accd, 1, end color #11accd, plus, start color #11accd, 1, end color #11accd, plus, start color #11accd, 1, end color #11accd, plus, start color #1fab54, start fraction, 4, divided by, 5, end fraction, end color #1fab54
empty space, equals, start color #11accd, start fraction, 5, divided by, 5, end fraction, end color #11accd, plus, start color #11accd, start fraction, 5, divided by, 5, end fraction, end color #11accd, plus, start color #11accd, start fraction, 5, divided by, 5, end fraction, end color #11accd, plus, start color #1fab54, start fraction, 4, divided by, 5, end fraction, end color #1fab54
empty space, equals, start fraction, start color #11accd, 5, end color #11accd, plus, start color #11accd, 5, end color #11accd, plus, start color #11accd, 5, end color #11accd, plus, start color #1fab54, 4, end color #1fab54, divided by, 5, end fraction
3, start fraction, 4, divided by, 5, end fraction, equals, start fraction, 19, divided by, 5, end fraction
Problem 1A
• Current
Rewrite as an improper fraction.
5, start fraction, 1, divided by, 2, end fraction, equals

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

Rewriting an improper fraction as a mixed number

Rewrite start fraction, 10, divided by, 3, end fraction as a mixed number.
start fraction, 3, divided by, 3, end fraction, equals, 1, start text, space, w, h, o, l, e, end text
So, let's see how many wholes we can get out of start fraction, 10, divided by, 3, end fraction.
start fraction, 10, divided by, 3, end fraction, equals, start fraction, start color #11accd, 3, end color #11accd, plus, start color #11accd, 3, end color #11accd, plus, start color #11accd, 3, end color #11accd, plus, start color #1fab54, 1, end color #1fab54, divided by, 3, end fraction
empty space, equals, start color #11accd, start fraction, 3, divided by, 3, end fraction, end color #11accd, plus, start color #11accd, start fraction, 3, divided by, 3, end fraction, end color #11accd, plus, start color #11accd, start fraction, 3, divided by, 3, end fraction, end color #11accd, plus, start color #1fab54, start fraction, 1, divided by, 3, end fraction, end color #1fab54
empty space, equals, start color #11accd, 1, end color #11accd, plus, start color #11accd, 1, end color #11accd, plus, start color #11accd, 1, end color #11accd, plus, start color #1fab54, start fraction, 1, divided by, 3, end fraction, end color #1fab54
start fraction, 10, divided by, 3, end fraction, equals, start color #11accd, 3, end color #11accd, start color #1fab54, start fraction, 1, divided by, 3, end fraction, end color #1fab54
Problem 2A
• Current
Rewrite as a mixed number.
start fraction, 13, divided by, 8, end fraction, equals

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
• extreme laughing
(1 vote)
• 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
• Kahn academy is such a help in my math. Thank you guys!
• 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.
• Hey isn't the sun the smallest star?
• No, it is not and this is math, not science.
• 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!!
• 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!