Mixed numbers and improper fractions review

CCSS Math: 4.NF.B.3
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:
94,55,73\dfrac94, \dfrac55, \dfrac73

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:
412,138,12564\dfrac12, 1\dfrac38, 12\dfrac56

Rewriting a mixed number as an improper fraction

Rewrite 3453\dfrac45 as an improper fraction.
345=3+453\dfrac45=\blueD3+\greenD{\dfrac45}
345=1+1+1+45\phantom{3\dfrac45}=\blueD1+\blueD1+\blueD1+\greenD{\dfrac45}
345=55+55+55+45\phantom{3\dfrac45}=\blueD{\dfrac55}+\blueD{\dfrac55}+\blueD{\dfrac55}+\greenD{\dfrac45}
345=5+5+5+45\phantom{3\dfrac45}=\dfrac{\blueD5+\blueD5+\blueD5+\greenD4}5
345=195{3\dfrac45}=\dfrac{19}5
Want to learn more about rewriting mixed numbers as improper fractions? Check out this video.
Want to try more problems like this? Check out this exercise.

Rewriting an improper fraction as a mixed number

Rewrite 103\dfrac{10}3 as a mixed number.
33=1 whole\dfrac33=1\text{ whole}
So, let's see how many wholes we can get out of 103\dfrac{10}3.
103=3+3+3+13\dfrac{10}3=\dfrac{\blueD3+\blueD3+\blueD3+\greenD1}3
103=33+33+33+13\phantom{\dfrac{10}3}=\blueD{\dfrac33}+\blueD{\dfrac33}+\blueD{\dfrac33}+\greenD{\dfrac13}
103=1+1+1+13\phantom{\dfrac{10}3}=\blueD1+\blueD1+\blueD1+\greenD{\dfrac13}
103=313\dfrac{10}3=\blueD3\greenD{\dfrac13}
Want to learn more about rewriting improper fractions as mixed numbers? Check out this video.
Want to try more problems like this? Check out this exercise.