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# Fraction

A fraction can be written as p/q where q: such as 3/4, 4/5, are called fractions.

If the numerator and denominator of a fraction are multiplied / divided by the same number then the value of the fraction does not change.

For any positive proper fraction p/q (p<q), the value of the fraction increases when both the denominator and numerator are added by the same positive number.

e.g 3/4=0.75, (3+1)/(4+1)= 4/5 =0.8.

For any positive proper fraction p/q (p<q), the value of the fraction decreases when both the numerator and denominator are subtracted by the same positive number.

e.g 3/4=0.75, (3−1)/(4-1) = 2=0.67

For any positive improper fraction p/q (p>q), the value of the fraction decreases when both the numerator and the denominator are added to the same positive. E.g. 5/4 = 1.25, adding 1 to the numerator and the denominator, we get

which is less than 1.25.

For any positive improper fraction p/q (p>q), the value of the fraction increases when both the numerator and denominator are subtracted by the same positive number. E.g. 5/4 = 1.25, by subtracting 1 from both the numerator and denominator we get,

# Types of fractions

Common or Vulgar Fractions: Fractions such 3/4, 32/43 etc are called common or vulgar fractions.
Decimal Fractions:
Fractions whose denominators are 10, 100, 1000, ... are called decimal fractions.
Proper Fraction:
A fraction whose numerator is less than its denominator is known as a proper fraction e.g. 3⁄4
Improper Fraction:
A fraction whose numerator is greater than its denominator is known as an improper fraction. e.g. 4/3
Mixed Fractions:
Fractions which consists of an integral part and a fractional part are called mixed fractions. All improper fractions can be

expressed as mixed fractions and vice versa. e.g. 1(3/4).

# Addition of Fractions

To find the sum of two or more fractions, we find the LCM of denominators and then add the product of numerator and the quotient of LCM divided by the denominator. In other words, if the fractions have different denominators, they must first be converted to equivalent fractions having the same denominator - which can be done taking the LCM of denominators.

Illustration 1:
4/5 + 6/7 + 9/10. The LCM of the denominators i.e. 5, 7 and 10 is 70. Thus 4/5 + 6/7 + 9/10 = 56/70 + 60/70 + 63/70 = 179/70 Mixed fractions can be added by adding the integral and fractional part separately or by converting them into improper fractions.

Illustration 2:

To find the product of two fractions, multiply their numerators and then divide this by the product of their denominators. e.g. (3/4)*(8/9)=24/36. In general

Division of Fractions

To divide a fraction a/b by another fraction c/d, multiply a/b by d/c.