Improper Fractions

An Improper Fraction has a meridian number larger than (or equal to) the bottom number.
It is usually "top-heavy"

More Examples

three ii vii three xvi 15 15 15 100 five

See how the height number is bigger than (or equal to) the bottom number?
That makes it an Improper Fraction, (but at that place is nothing incorrect about Improper Fractions).

Three Types of Fractions

At that place are 3 types of fraction:

Fraction Types: Proper, Improper, Mixed

Fractions

A Fraction (such as 7/4 ) has 2 numbers:

Numerator Denominator

The summit number (the Numerator) is the number of parts we accept.
The bottom number (the Denominator) is the number of parts the whole is divided into.

Example: 7/4 means:

  • We have 7 parts
  • Each part is a quarter ( ane/4 ) of a whole

And so we can define the three types of fractions like this:

Proper Fractions: The numerator is less than the denominator
Examples: one/iii , three/4 , two/7
Improper Fractions: The numerator is greater than (or equal to) the denominator
Examples: 4/iii , 11/4 , 7/vii
Mixed Fractions: A whole number and proper fraction together
Examples: one 1/3 , ii ane/4 , 16 ii/five

Improper Fraction

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

4/4
4 4

Can be Equal

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

Well it is the same as a whole, but information technology is written as a fraction, then most people concord it is a type of improper fraction.

Improper Fractions or Mixed Fractions

Nosotros tin apply either an improper fraction or a mixed fraction to show the same amount.

For example i 3 four = 7 iv , as shown here:

Converting Improper Fractions to Mixed Fractions

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

dog looking
  • Divide the numerator by the denominator.
  • Write down the whole number respond
  • Then write down any remainder higher up the denominator.

Example: Convert 11 iv to a mixed fraction.

Split up:

eleven ÷ 4 = ii with a residuum of 3

Write downward the 2 and then write down the remainder (3) to a higher place the denominator (4).

Reply:

two iii four

That case tin be written similar this:

Fraction 11/4 = 2 3/4

Example: Convert x iii to a mixed fraction.

Fraction 11/4 = 2 3/4

Answer:

three 1 three

Converting Mixed Fractions to Improper Fractions

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

dog looking
  • Multiply the whole number part by the fraction's denominator.
  • Add that to the numerator
  • Then write the event on pinnacle of the denominator.

Example: Convert 3 2 5 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:

17 5

We can do the numerator in one become:

Fraction 2 2/5 = 17/5

Example: Catechumen 2 1 9 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. Considering mixed fractions tin exist confusing when we write them in a formula: should the two parts be added or multiplied?

Mixed Fraction: What is: i + 2 ane 4 ?
Is it: 1 + 2 + 1 4 = iii 1 4 ?
Or is it: 1 + two × 1 4 = ane 1 2 ?
Improper Fraction: What is: 1 + 9 4 ?
It is: iv 4 + 9 iv = xiii four yes

Simply, for everyday use, people empathize mixed fractions better.

Example: It is easier to say "I ate two 1 iv sausages", than "I ate nine four sausages"


We Recommend:

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