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 blueD, 3, end color blueD, plus, start color greenD, start fraction, 4, divided by, 5, end fraction, end color greenD
empty space, equals, start color blueD, 1, end color blueD, plus, start color blueD, 1, end color blueD, plus, start color blueD, 1, end color blueD, plus, start color greenD, start fraction, 4, divided by, 5, end fraction, end color greenD
empty space, equals, start color blueD, start fraction, 5, divided by, 5, end fraction, end color blueD, plus, start color blueD, start fraction, 5, divided by, 5, end fraction, end color blueD, plus, start color blueD, start fraction, 5, divided by, 5, end fraction, end color blueD, plus, start color greenD, start fraction, 4, divided by, 5, end fraction, end color greenD
empty space, equals, start fraction, start color blueD, 5, end color blueD, plus, start color blueD, 5, end color blueD, plus, start color blueD, 5, end color blueD, plus, start color greenD, 4, end color greenD, divided by, 5, end fraction
3, start fraction, 4, divided by, 5, end fraction, equals, start fraction, 19, divided by, 5, end fraction
Want to learn more about rewriting mixed numbers as improper fractions? Check out this video.
Problem 1A
Rewrite as an improper fraction.
5, start fraction, 1, divided by, 2, end fraction, equals
  • Your answer should be
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4

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, space, w, h, o, l, e
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 blueD, 3, end color blueD, plus, start color blueD, 3, end color blueD, plus, start color blueD, 3, end color blueD, plus, start color greenD, 1, end color greenD, divided by, 3, end fraction
empty space, equals, start color blueD, start fraction, 3, divided by, 3, end fraction, end color blueD, plus, start color blueD, start fraction, 3, divided by, 3, end fraction, end color blueD, plus, start color blueD, start fraction, 3, divided by, 3, end fraction, end color blueD, plus, start color greenD, start fraction, 1, divided by, 3, end fraction, end color greenD
empty space, equals, start color blueD, 1, end color blueD, plus, start color blueD, 1, end color blueD, plus, start color blueD, 1, end color blueD, plus, start color greenD, start fraction, 1, divided by, 3, end fraction, end color greenD
start fraction, 10, divided by, 3, end fraction, equals, start color blueD, 3, end color blueD, start color greenD, start fraction, 1, divided by, 3, end fraction, end color greenD
Want to learn more about rewriting improper fractions as mixed numbers? Check out this video.
Problem 2A
Rewrite as a mixed number.
start fraction, 13, divided by, 8, end fraction, equals
  • Your answer should be
  • a mixed number, like 1, space, 3, slash, 4

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