Mixed Fractions

(Also called "Mixed Numbers")

pie full3/4
134
(one and three-quarters)


A Mixed Fraction is a whole number and a proper fraction combined.

Such as 134

Examples

238 714 11415 2145

See how each example is made up of a whole number and a proper fraction together? That is why it is called a "mixed" fraction (or mixed number).

Names

We can give names to every part of a mixed fraction:

mixed fraction 2 1/3

Three Types of Fractions

There are three types of fraction:

Fraction Types

Mixed Fractions or Improper Fractions

We can use either an improper fraction or a mixed fraction to show the same amount.

For example 134 = 74, as shown here:

134   74
pie fullpie 3/4 = pie 4/4pie 3/4

Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, follow these steps:

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  • Multiply the whole number part by the fraction's denominator.
  • Add that to the numerator
  • Write that result on top of the denominator.

 

Example: Convert 325 to an improper fraction.

Multiply the whole number (3) by the fraction's denominator (5):

3 × 5 = 15

Add the fraction's numerator (2) to that:

15 + 2 = 17

Then put that above the denominator, like this:

17 5

Converting Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, follow these steps:

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  • Divide the numerator by the denominator.
  • Write down the whole number answer
  • Then write down any remainder above the denominator.

Example: Convert 114 to a mixed fraction.

Divide:

11 ÷ 4 = 2 with a remainder of 3

Write down the 2 and then write down the remainder (3) above the denominator (4), like this:

2 3 4

When to Use Improper Fractions or Mixed Fractions

For everyday use, people understand mixed fractions better:

Example: It is easier to say "I ate 214 sausages", than "I ate 94 sausages"

But for mathematics improper fractions are actually better than mixed fractions.

Because mixed fractions can be confusing when we write them in a formula: should the two parts be added or multiplied?

Mixed Fraction: What is:   1 + 214   ?
  Is it:   1 + 2 + 14   = 314 ?
  Or is it:   1 + 2 × 14   = 112 ?
           
Improper Fraction: What is:   1 + 94   ?
  It is:   44 + 94 = 134   yes

 

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