1. Fractions

1. What is a Fraction?

A fraction is part of a whole.

Half of anything is fraction ½.

Suppose an apple is cut into two equal halves between you and your brother, then each of you receive a fraction (one-half) of the apple, here half of it.

If the apple is divided between three friends, then each one gets a fraction (one-third) of the apple, here 1/3

Note:

1. A fraction is equal to 1 if both the numerator and the denominators are same.
2. A fraction is equal to 0 if only the numerator is 0
3. The denominator of a fraction is normally not 0.
4. The value of a fraction remains the same when both the numerator and denominators are multiplied or divided by a same value

2. Parts of Fraction:

Every fraction has two parts: a numerator and a denominator.

The number above the division bar is the numerator, while that below it is the denominator.

In the fraction ⅓:

Number 1 is called the numerator and number 3 is called the denominator of the fraction.

3. Types of Fractions:

a. Proper Fractions:

Fractions in which the numerator is less than the denominator are called proper fractions.

Examples: ½, 2/3, 4/7 and many others.

NOTE: The value of proper fractions is always less than 1.

b. Improper Fractions:

Fractions in which the numerator is greater than the denominator are called improper fractions.

Examples: 3/2, 7/5, 102/57 and so on.

NOTE: The value of improper fractions is always greater than 1.

c. Mixed Fractions:

Fractions that contain both a whole number and a fraction are called Mixed Fractions.

Examples: 2⅓, 4⅗, 9⅝ are all mixed fractions.

In the mixed fraction:
2⅓, the whole number is 2, while the fraction is ⅓, and
4⅗, the whole number is 4, while the fractions is ⅗, and
 9⅝, the whole number is 9, while the fraction is ⅝.

d. Decimal Fractions:

Fractions in which the denominators are either 10 or positive integral powers of 10 are called Decimal Fractions.

Examples: 3/10, 7/100, 10/1000

e. Vulgar Fractions:

Fractions in which the denominators are not 10 or powers of 10 are called Vulgar Fractions.

Examples: 3/8, 4/9, 5/31, 23/59 and so on.

f. Simple Fractions:

Fractions in which both the numerator and denominators are whole numbers are called Simple Fractions.

Examples: 7/11, 25/39, 62/131 and so on.

g. Complex Fractions.

Fractions in which either the numerator or the denominator or both are fractions are called Complex Fractions.

Examples: 7/⅝, 9/⅗ and so on.

In the complex fraction 7/⅝, the numerator is 7 and the denominator is ⅝, and

In the complex fraction 9/⅗, the numerator is 9 and the denominator is ⅗

h. Equivalent Fractions:

Fractions that have the same value on simplifying are called Equivalent Fractions.

Examples: 2/3, 4/6, 20/30 and so on.

Fraction 4/6 = 2/3 and 20/30 = 2/3

So, the three fractions 2/3, 4/6, 20/30 are same in value and the value is 2/3

Tip: To find equivalent fractions of a given fraction, multiply a same value to both numerator and denominator of the given fraction.

Example: A few equivalent fractions of the fraction 3/5 are:
(3 *4)/ (5*4) = 12/20, (3*7)/ (5*7) = 21/35 and so on.

i. Like Fractions:

Fractions in which the denominators are same are called Like Fractions.

Examples: 3/7, 5/7, 11/7 and so on.

J. Unlike Fractions:

Fractions in which the denominators are different are called Unlike Fractions.

Examples: ¾, 8/9, 11/15 and so on.