Mixed Fractions

(Also called "Mixed Numbers")

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
	=

dog looking

Converting Improper Fractions to Mixed Fractions

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

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).

Answer:

2 34

That example can be written like this:

Fraction 11/4 = 2 3/4

Example: Convert 103 to a mixed fraction.

Fraction 11/4 = 2 3/4

Answer:

3 13

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Converting Mixed Fractions to Improper Fractions

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

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

Example: Convert 325 to an improper fraction.

Multiply the whole number part by the denominator:

3 × 5 = 15

Add that to the numerator:

15 + 2 = 17

Then write that result above the denominator:

175

We can do the numerator in one go:

Fraction 2 2/5 = 17/5

Example: Convert 219 to an improper fraction.

Fraction 2 1/9 = 19/9

Are Improper Fractions Bad ?

NO, they aren't bad!

For mathematics they 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 ?
	it may be:	1 + 2 + 14	= 314
	Or it may be:	1 + 2 × 14	= 112

Improper Fraction:	What is:	1 + 94 ?
	It is:	44 + 94 = 134

But, for everyday use, people understand mixed fractions better.

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

We Recommend:

For Mathematics: Improper Fractions

For Everyday Use: Mixed Fractions

4955, 4956, 916, 917, 1374, 1375, 3538, 3536, 3537, 3539