Definition of Fractions
A fraction is a numerical value used to describe a part of a whole. Let us understand the concept of fractions with an example.
Suppose you divide a cake into 12 equal slices. Then each slice is a part of the whole cake. Alternatively, 1 whole of the cake is equivalent to 12 equal parts. So any selected slice or part of the cake can be expressed as 1 piece out of the whole (which is 12), hence the slice is numerically written as \(\frac{1}{2}\).
So the fraction, \(\frac{1}{12}\) is used to express each slice of the cake in numerical form.
Parts of Fraction
Any fraction will have two parts – numerator and denominator. The numerator is written on top and denominator on the bottom, with these two values separated by a horizontal bar-like symbol. In the example stated, \(\frac{1}{12}\)is a fraction where the numerator is 1, and the denominator is 12.
Types of Fractions
The table illustrates the different types of fractions.
Type | Description | Examples |
Like Fractions | Fractions with the same denominators. | \(\frac{1}{5}, \frac{12}{5}, \frac{3}{5}\) |
Unlike Fractions | Fractions with different denominators | \(\frac{1}{2}, \frac{9}{15}, \frac{100}{52}\) |
Proper Fractions | Fractions in which the numerator is less than the denominator. | \(\frac{1}{5}, \frac{11}{20}, \frac{112}{239}\) |
Improper Fractions | Fractions in which the numerator is greater than the denominator. | \(\frac{11}{2}, \frac{9}{5}, \frac{101}{55}\) |
Mixed Numbers | Fractions that consist of a whole number part and a fractional part. | \(1 \frac{1}{2},\text{ }3\frac{2}{5}\) |
Equivalent Fractions | Two or more fractions that are equal to the same value when simplified. | \(\frac{1}{2}, \frac{4}{8} = \frac{1}{2}, \frac{50}{100} = \frac{1}{2}\) |
Solved Examples
Example 1: Express the shaded parts as fractions in each figure.
a.
b.
c.
Solution:
a.
Here the whole (a circle) is divided into 2 equal parts. Out of 2 parts, 1 part is shaded. So,
\(Shaded parts \to \frac{Number\text{ }of\text{ }shaded\text{ }parts}{Total\text{ }number of \text{ }equal\text{ }parts} = \frac{1}{2}\)
So, \(\frac{1}{2}\) parts are shaded.
b.
Here the whole (a square) is divided into 4 equal parts. Out of 4 parts, 3 parts are shaded. So,
\(Shaded\text{ }parts \to \frac{Number\text{ }of\text{ }shaded\text{ }parts}{Total\text{ }number\text{ }of\text{ }equal\text{ }parts} = \frac{3}{4}\)
So, \(\frac{3}{4}\)parts are shaded.
c.
Here the whole (a rectangle) is divided into 4 equal parts. Out of 4 parts, 2 parts are shaded. So,
\(Shaded\text{ }parts \to \frac{Number\text{ }of\text{ }shaded\text{ }parts}{Total\text{ }number\text{ }of\text{ }equal\text{ }parts} = \frac{2}{4}\)
So, \( \frac{2}{4}\)parts are shaded.
[Note: The fraction \( \frac{2}{4}\) can be further simplified to \( \frac{1}{2}\), which shows that \( \frac{2}{4}\) is equivalent to \( \frac{1}{2}\)]
Example 2: Determine whether the given figures represent equivalent fractions or not.
Solution:
The first figure is a circle divided into 8 equal parts out of which 6 parts are shaded. So,
\( \frac{Number\text{ }of\text{ }shaded\text{ }parts}{Total\text{ }number\text{ }of\text{ }equal\text{ }parts} = \frac{6}{8}\)
\( = \frac{3}{4}\) [Divide numerator and denominator by 2]
The second figure is a square divided into 4 equal parts out of which 3 parts are shaded, So,
\( \frac{Number\text{ }of\text{ }shaded\text{ }parts}{Total\text{ }number\text{ }of\text{ }equal\text{ }parts} = \frac{3}{4}\)
\( \frac{6}{8}\) when simplified is equal to \( \frac{3}{4}\),that is, both fractions have the same value.
Hence, the two figures represent equivalent fractions.
A decimal is a numerical form used to represent whole and fractional parts. The whole number part on the left is separated from the fractional part on the right by a decimal dot symbol (‘.’). For example, 1.2, 2.33, 0.44 are examples of decimal numbers.
A mixed number is expressed as an improper fraction by multiplying the whole number part by the denominator and adding the product to the numerator. The sum obtained is the numerator and the original denominator is retained as the denominator of the improper fraction.
A fraction that has 1 as the numerator is called a unit fraction. For example 1/2 and 1/3.
To find the equivalent fractions of any given fraction, multiply or divide the numerator and denominator of the fraction by the same number.