# Types of Fractions

The various types of fractions are:

1. Like Fractions:

The fractions having the same denominators are known as like fractions.

We know that fractions such as 2/5, 3/5, 5/5, 7/5, 9/5, ….etc., are like fractions.

2. Unlike Fractions:

Fractions having different denominators are called unlike fractions.

$$\frac{3}{5}$$, $$\frac{2}{7}$$, $$\frac{5}{9}$$, $$\frac{4}{11}$$,  ......... are unlike fractions.

3. The same Numerator Fractions:

The factors having the same numerators are called the same numerator fractions.

Fractions such as 2/5, 2/7, 2/9, 2/11, …………, etc., are same numerator fractions.

4. Unit Fractions:

The fractions having one (1) as their numerator are called unit fractions.

1/3, 1/5, 1/7, 1/9, …………, etc., are unit fractions.

5. Proper Fractions:

A fraction in which the denominator is greater than the numerator is called a proper fraction. We can also say that a fraction with its numerator less than the denominator is known as a proper fraction.

1/2, 2/3, 4/5, 5/6, 7/10, 9/11, 11/21, 35/45, ……….., etc., are proper fractions.

A fraction in which numerator is less than its denominator.

[$$\frac{3}{4}$$, $$\frac{5}{7}$$, $$\frac{11}{17}$$ ...............]

Observe the following number line.

Consider the fraction $$\frac{5}{8}$$

It lies between 0 and 1 and its numerator is less than the denominator.

Fractions in which numerators are smaller than the denominators are called proper fractions.

6. Improper Fractions:

A fraction in which the denominator is smaller than or equal to its numerator is called an improper fraction. We can also say that a fraction with its numerator greater than or equal to the denominator is known as an improper fraction.

5/3, 9/5, 11/7, 17/8, 21/14, 19/15, …….., etc., are improper fractions.

A fraction in which numerator is equal to or greater than its denominator.

[$$\frac{15}{7}$$, $$\frac{24}{13}$$, $$\frac{5}{5}$$ ...............]

Consider the fraction $$\frac{10}{8}$$

It is greater than one and its numerator is greater than the denominator.

Fractions in which numerators are greater than the denominators are called improper fractions.

The fraction $$\frac{8}{8}$$ = 1, similarly $$\frac{3}{3}$$ = 1, $$\frac{7}{7}$$ = 1, $$\frac{11}{11}$$ = 1 .............

Fractions in which numerators are equal to the denominators are also called improper fractions.

7. Mixed Fractions:

When an improper fraction is written as a combination of a whole number and a proper number, it becomes a mixed fraction or mixed number.

As: 6/5 = 5 + 1/5 = 5/5 + 1/5 = 1 + 1/5 = 1$$\frac{1}{5}$$

1$$\frac{1}{2}$$, 1(\frac{1}{4}\), 2(\frac{3}{4}\), 3(\frac{5}{7}\), 5(\frac{1}{9}\), ……….., etc., are mixed fractions.

(All types of fraction may be categorized into three kinds, i.e., proper, improper and mixed fraction).

Mary ate 2 apples and Kerry ate $$\frac{1}{2}$$ of an apple. They are 2 and $$\frac{1}{2}$$ apples together.

 2 apples + $$\frac{1}{2}$$ apple = 2 + $$\frac{1}{2}$$ apples                             = 2$$\frac{1}{2}$$ apples 2 + $$\frac{1}{2}$$ = 2$$\frac{1}{2}$$

2$$\frac{1}{2}$$ is read as two and a half.

In 2$$\frac{1}{2}$$; 2 is the whole part and $$\frac{1}{2}$$ is the proper fraction.

Fractions like 3$$\frac{3}{4}$$, 5$$\frac{6}{13}$$, 1$$\frac{1}{4}$$ ................. are called mixed numbers.

A mixed number is the sum of a whole number and a proper fraction.

Questions and Answers on Types of Fractions:

I. Write whether the following are proper fractions, improper fractions or mixed numbers.

(i) $$\frac{5}{9}$$

(ii) $$\frac{13}{17}$$

(iii) $$\frac{121}{7}$$

(iv) $$\frac{1}{1}$$

(v) 16$$\frac{2}{3}$$

I. (i) Proper fraction

(ii) Proper fraction

(iii) Improper fraction

(iv) Improper fraction

(v) Mixed fraction

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