# Fractions and Decimal Fractions Tricks and Formulas

## Fractions and Decimal Fractions Tricks and Formulas

**Fractions: **

Any unit can be divided into any numbers of equal parts, one or more of this
parts is called ** fraction** of that unit. e.g. one-forth
(1/4), one-third (1/3), three-seventh (3/7) etc.

The lower part indicates the number of equal parts into which the unit is divided, is called

**. The upper part, which indicates the number of parts taken from the fraction is called the**

*denominator***The numerator and the denominator of a fraction are called its**

*numerator.**terms*.

- A fraction is unity, when its numerator and denominator are equal.
- A fraction is equal to zero if its numerator is zero.
- The denominator of a fraction can never be zero.
- The value of a fraction is not altered by multiplying or dividing the numerator and the denominator by the same number.e.g. 2/3 = 2/6 = 8/12 = (2/4)/(3/4)
- When there is no common factor between numerator and denominator it is called in its lowest terms.e.g. 15/25 = 3/5
- When a fraction is reduced to its lowest term, its numerator and denominator are prime to each other.
- When the numerator and denominator are divided by its HCF, fraction reduces to its lowest term.

**
Proper fraction:** A fraction in which numerator is
less than the denominator. e.g. 1/4, 3/4, 11/12 etc.

**Improper Fraction:** A
fraction in which numerator is equal to or more than the denominator. e.g. 5/4,
7/4, 13/12 etc.

**Like fraction:** Fractions
in which denominators are same is called like fractions.

e.g. 1/12, 5/12, 7/12, 13/12 etc.

**Unlike fraction:** Fractions
in which denominators are not same is called, unlike fractions.

e.g. 1/12, 5/7, 7/9 13/11 etc.

**Compound Fraction:** Fraction
of a fraction is called a compound fraction.

e.g. 1/2 of 3/4 is a compound fraction.

**Complex Fractions:** Fractions
in which numerator or denominator or both are fractions, are called complex
fractions.

**Continued fraction:** Fraction
that contain additional fraction is called continued fraction.

e.g.

** Rule:** To
simplify a continued fraction, begin from the bottom and move upwards.

**Decimal Fractions:** Fractions
in which denominators are 10 or multiples of 10 is called, decimal
fractions. e.g. 1/10, 3/100, 2221/10000 etc.

**Recurring Decimal:** If
in a decimal fraction a digit or a set of digits is repeated continuously, then
such a number is called a recurring decimal. It is expressed by putting a
dot or bar over the digits. e.g.

** Pure recurring decimal:** A
decimal fraction in which all the figures after the decimal point is repeated
is called a pure recurring decimal.

** Mixed recurring decimal:** A
decimal fraction in which only some of the figures after the decimal point
is repeated is called a mixed recurring decimal.

**Conversion of
recurring decimal into proper fraction: **

*CASE I: Pure recurring decimal*

Write the repeated digit only once in
the numerator and put as many nines as in the denominator as the
number of repeating figures. e.g.

*CASE II: Mixed recurring decimal*

In the numerator, take the difference
between the number formed by all the digits after the decimal point and that
formed by the digits which are not repeated. In the denominator, take the
number formed as many nines as there are repeating digits followed by
as many zeros as is the number of non-repeating digits. e.g.

**Maths:**

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