Improper Fractions

An Improper Fraction has a tiptop number larger than (or equal to) the bottom number.
Information technology is commonly "top-heavy"

More Examples

iii ii seven 3 16 15 15 15 100 5

Run into how the summit number is bigger than (or equal to) the bottom number?
That makes it an Improper Fraction, (but at that place is zero incorrect nigh Improper Fractions).

Three Types of Fractions

There are three types of fraction:

Fraction Types: Proper, Improper, Mixed

Fractions

A Fraction (such as 7/four ) has two numbers:

Numerator Denominator

The top number (the Numerator) is the number of parts nosotros take.
The bottom number (the Denominator) is the number of parts the whole is divided into.

Example: 7/4 means:

  • We have vii parts
  • Each part is a quarter ( one/4 ) of a whole

And then nosotros tin can define the three types of fractions like this:

Proper Fractions: The numerator is less than the denominator
Examples: 1/3 , iii/4 , 2/seven
Improper Fractions: The numerator is greater than (or equal to) the denominator
Examples: iv/3 , xi/4 , seven/seven
Mixed Fractions: A whole number and proper fraction together
Examples: ane 1/3 , 2 1/iv , 16 2/5

Improper Fraction

So an improper fraction is a fraction where the pinnacle number (numerator) is greater than or equal to the bottom number (denominator): it is top-heavy.

4/4
iv 4

Can be Equal

What about when the numerator is equal to the denominator? For case 4/4 ?

Well it is the same as a whole, just it is written equally a fraction, and then most people agree information technology is a type of improper fraction.

Improper Fractions or Mixed Fractions

We can utilize either an improper fraction or a mixed fraction to testify the same amount.

For example 1 3 4 = 7 4 , equally shown hither:

Converting Improper Fractions to Mixed Fractions

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

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  • Separate the numerator by the denominator.
  • Write down the whole number answer
  • Then write downwards any remainder in a higher place the denominator.

Example: Convert 11 4 to a mixed fraction.

Divide:

eleven ÷ 4 = 2 with a residual of 3

Write down the 2 and so write downward the remainder (3) above the denominator (4).

Respond:

two three 4

That example can be written like this:

Fraction 11/4 = 2 3/4

Example: Catechumen 10 three to a mixed fraction.

Fraction 11/4 = 2 3/4

Reply:

3 i 3

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 past the fraction's denominator.
  • Add together that to the numerator
  • Then write the result on height of the denominator.

Example: Convert 3 ii five to an improper fraction.

Multiply the whole number part by the denominator:

3 × 5 = 15

Add together that to the numerator:

15 + 2 = 17

So write that result above the denominator:

17 5

Nosotros can practise the numerator in one go:

Fraction 2 2/5 = 17/5

Instance: Catechumen 2 ane nine 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 exist disruptive when nosotros write them in a formula: should the two parts be added or multiplied?

Mixed Fraction: What is: ane + 2 1 4 ?
Is it: 1 + 2 + 1 4 = 3 one 4 ?
Or is it: i + two × one 4 = 1 1 two ?
Improper Fraction: What is: 1 + ix four ?
It is: 4 four + 9 4 = 13 4 yes

Just, for everyday use, people understand mixed fractions amend.

Instance: Information technology is easier to say "I ate ii 1 four sausages", than "I ate 9 4 sausages"


We Recommend:

  • For Mathematics: Improper Fractions
  • For Everyday Employ: Mixed Fractions