Duck staring into space and smiling. Mathematical operations fly out from background.

Do you ever look at a mixed number and wonder, "What does that even mean?" or, "How do I change that into an improper fraction?"

Look no further! Learn how to convert mixed numbers into improper fractions in 4 easy steps!

Review: Proper Fractions & Mixed Numbers

Proper Fraction

A proper fraction. The numerator is 2 and the denominator is 5.

Denominator (5)

  • tells you how many equal parts make up one whole

Numerator (2)

  • tells you how many parts you have, out of the whole total

Mixed Number

A mixed number. 3 wholes and two-fifths.  The

Mixed numbers are fractions that consist of 2 parts: the whole number and a fraction.

Whole Number (3)

  • tells you how many whole pieces there are in total

Fraction (2/5)

  • tells you how many parts of a whole there are

Improper Fraction

A mixed number = improper fraction. 3 wholes and five-sevenths is equal to 26 over 7.

An improper fraction is another way to represent mixed numbers, where the numerator is greater than the denominator.

Imagine Pizzas

Let's imagine pizzas to help us understand mixed numbers.

2 wholes and two-fifths, represented using pizza slices.

The whole number, 3, tells us that there are 3 whole pizzas, with 5 equal pieces.

The denominator, 5, tells us that the whole pizza is divided equally into 5 pieces.

The numerator, 2, tells us that there is one pizza that isn't quite whole. There are 2 slices of the 5 that remain.

How Do I Convert a Mixed Number into an Improper Fraction?

Add all slices of the wholes and the fraction to create the Improper fraction, 17 over 5.


  • there are 5 slices in a whole and,

  • there are 3 wholes...

That means the 3 wholes are made of 15 equal slices!

The fraction tells us...

  • we have 2 remaining slices

So, if we have 15 slices from the wholes, and 2 slices from the fraction...

  • we have 17 slices in total!

Write 17 as the numerator. The numerator tells us how many equal parts we have.

Keep the denominator as 5, because the denominator tells us how many equal parts there are in a whole. It doesn't change.


If the mixed number is 5 wholes and one-fourths (5 1/4), what is the numerator in a mixed number?

Is There an Easier Way?

Why of course!

How to convert mixed number into improper fraction. Multiply whole number and denominator. Add numerator. Keep denominator,

  1. Multiply the whole number (3) by the denominator (7). This will tell us how many pieces make up the whole. 3 x 7 = 21

  1. Add the numerator (5). This will tell us how many pieces there are altogether. 21 + 5 = 26

  1. Write the sum as the new numerator of the improper fraction.

  2. Keep the same denominator. 26/7


Convert this mixed number into an improper fraction. 6 wholes and two-fifths (6 2/5).

Take Action

Rhett saying,

Was converting from a mixed number to an improper fraction easier than you thought? Sometimes, unfamiliar concepts can make you panic (I know I do), but with a little practice, you'll be a pro at converting fractions in no time!


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