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.
Problem 1A
Rewrite as an improper fraction.
512=5\dfrac12=
  • Your answer should be
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4

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.
Problem 2A
Rewrite as a mixed number.
138=\dfrac{13}8=
  • Your answer should be
  • a mixed number, like 1 3/41\ 3/4

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