Fractions

Fractions:

Fraction:
A fraction is a number representing a part of a whole. The whole may be a single object or a group of objects.
In contrast, fraction is a number of the form \(\frac{a}{b} \), where a and b are whole numbers and b is not equal to zero.
Here, a is called the numerator and b is called the denominator.

Illustrative Examples:

1) To represent the fraction of the form \(\frac{2}{6} \) which is read as ‘two by six‘ in a rectangle, shade 2 parts out of 6 parts.
i.e., for \(\frac{2}{6} \) we divide a whole into 6 equal parts and take 2 parts of it.

2) For \(\frac{1}{8} \), we divide a whole into 8 equal parts and take 1 part of it.

3) Similarly, \(\frac{3}{7} \) is obtained when we divide a whole into 7 equal parts and take 3 parts.

Consider the fraction \(\frac{2}{11} \). This fraction is read as “two-eleventh” which means that 2 parts out of 11 equal parts in which the whole is divided. In the fraction \(\frac{2}{11} \), 2 is called the numerator and 11 is called the denominator.

Following are some more fractions:

Fraction	Meaning of the Fraction	Numerator	Denominator
\(\frac{1}{3} \) or one-thirds	One equal part out of three equal parts in which the whole is divided	1	3
\(\frac{4}{7} \) or four-sevenths	Four equal parts out of seven equal parts in which the whole is divided	4	7
\(\frac{5}{8} \) or five-eights	Five equal part out of eight equal parts in which the whole is divided	5	8

Fraction as a Part of a Collection:

Consider the following figure

Above figure contains collection of 15 balls, of which 6 balls are shaded.
Shaded balls represent the numerator part of the fraction which is 6 and denominator is represented by the whole i.e., total number of collection of balls which is 15.
Shaded balls represent \(\frac{6}{15} \) of the collection.

In simple terms, this fraction and whole number calculator allows you to solve fraction problems with whole numbers and fractions form.

Fraction as Division:

Division can be understood as equal sharing. For example, if 8 biscuits are distributed between 2 children equally, then each of them will get 4 biscuits.

If 4 biscuits are distributed between 2 children equally, then each of them will get \(\frac{4}{2} \) = 2 biscuits.

It follows from the above example that the division can be expressed as a fraction and vice-versa.

Types of Fractions:

Proper Fractions:
Fractions whose numerators are less than the denominators are called proper fractions.

Example:

These are proper fractions.

When we represent a proper fraction on a number line it always lies to the left of 1.

Improper Fractions:

Fractions with the numerator either equal to or greater than the denominator are called improper fractions.

Fractions like \(\frac{5}{4} \), \(\frac{7}{2} \), \(\frac{9}{4} \) etc., are not proper fractions.These are improper fractions.

Mixed Fraction:
A combination of a whole number and a proper fraction is called a mixed fraction.
Mixed Fractions are also called as Mixed Numbers.

Mixed Fractions are used when you need to count whole things and parts of things at the same time.

There are 1 whole circle and \(\frac{3}{4} \) of another circle.
We write as \(1\frac{3}{4}\) and read it as ‘one and three-fourth‘

We don’t put ‘+’ sign in between the numbers, this is why we say ‘and’.

There are 2 whole triangles and \(\frac{2}{3} \) of another triangle. This is 2 + \(\frac{2}{3} \) and is written as 2 \(\frac{2}{3} \).