## Fractions Formulae:

### Introduction:

Fractions are nothing but the part of whole numbers.

*Example:*

\dfrac {5}{2} – Here ‘5’ is the Numerator and ‘12’ is the denominator.

### Lowest forms of fractions:

To find the Lowest form of fraction, We divide the numerator and denominator with common

number in them.

*Example:*

\dfrac {6}{14} – Here ‘2’ is the common element for both ‘6’ and ‘14’ so we get upon dividing ‘ \dfrac {3}{7} ‘

### Equivalent Fraction:

To get the Equivalent fractions we multiply the numerator and denominator with same number,

Then the resulting fractions we get are called as **Equivalent fractions**.

*Example 1:*

\dfrac {1}{2} , \dfrac {2}{4} , \dfrac {3}{4} , \dfrac {8}{8}

These are Equivalent fraction but here ‘ \dfrac {1}{2} ‘ is the the lowest form.

*Example 2:*

Find the Equivalent fractions of \dfrac {2}{7} having numerator ‘6’?

**Sol:** We know that 2 x 3 = 6,

Hence we multiply both the numerator and denominator by ‘3’.

Therefore, the required fraction is \dfrac {2\times 3}{5\times 3}=\dfrac {6}{15}

### Addition and Subtraction of Fractions:

**(i)**If the denominators of two fractions are same.

*eg:*

1. \dfrac {3}{7}-\dfrac {1}{7}=\dfrac {2}{7} 2. \dfrac {2}{5}+\dfrac {4}{5}=\dfrac {6}{5}

**(ii)**When the denominators of two fractions are not same. We need to equate the denominators firstly by multiplying and finding a common denominator.

*eg:*

```
\dfrac {2}{5}+\dfrac {3}{7}=\dfrac {14+15}{35}=\dfrac {29}{35}
```

### Multiplication and Division of fractions:

*Example:*

` \dfrac {2}{3}\times \dfrac {4}{6}=\dfrac {2\times 4}{3\times 6}=\dfrac {8}{18}=\dfrac {4}{9} `

### Proper and Improper Fraction:

In a fraction , If the numerator is less than the denominator then it is called ‘**Proper Fraction**’.

*Eg:* \dfrac {2}{3} – Proper Fraction

If the numerator is greater than the denominator it is called ‘**Improper Fraction**’.

*Eg: * \dfrac {7}{3} – Proper Fraction

### Mixed Numbers:

It contains both ‘Whole Number’ and ‘Fraction’.

### Decimal Fractions:

The fractions in which the denominator has the power of 10 are called ‘**Decimal Fractions**’.

### Addition or Subtraction of Decimal Fraction:

In this we write the fractions in such a way that all the decimal points are in a same straight line, after that we add or subtract the numbers.

### Multiplication of Decimal Fractions:

In this firstly, We ignore the number of decimals and multiply and after the multiplication is done we place the decimals from the 10’s place.

### Division of Decimal Fractions:

In this firstly, We ignore the decimals and divide the number and once division is done we place the decimals from 10’s place.

### To find HCF and LCM of Decimal Fractions:

Firstly we equate the decimal digits of numbers same by putting zero’s if necessary.

Then we find the HCF and LCM and lastly we put the decimals accordingly.

### Terminating and Non –Terminating Recurring Decimals:

If the Decimal Expression of any Fraction be terminated then fraction is called terminating.

Example:

Write the following fractions in decimal form and test whether they are terminating or non-terminating recurring?

### Non – Terminating, Non- Recurring Decimals:

We can but every fraction in the form of terminating or non – terminating recurring decimals.

If the numbers are in the form ‘p/q’ these are called Rational Numbers.

But there are some numbers which cannot be in the form of ‘p/q’ these are called non-terminating and non-recurring. These are also called Irrational Numbers.

### Facts to Know:

1. The Smallest Factor for a given Number is ‘1’ and the greatest factor is number itself.

2. ‘1’ is the factor of Every Number.

3. If we divide any number with it’s factor, the Remainder is Always ‘0’.