The expression x/y is also written as x ÷ y. x is known as the numerator and y is known as denominator.
A fraction written as a combination of a whole number and a proper fraction is called a mixed fraction or mixed number.
To generate equivalent fractions of any given fraction, we proceed as follows:
Multiply the numerator and denominator by the same number (other than 0) or
Divide the numerator and denominator by their common factor (other than 1), if any.
The two fractions are equivalent if the product of numerator of the first and denominator of the second is equal to the product of the denominator of the first and numerator of the second.
Reducing fractions:
To reduce a fraction, divide both the numerator and denominator by the largest factor of both.
A fraction is in its lowest term, if the numerator and denominator have no
common factor other than 1.
Comparing fractions:
Of the two fractions having the same denominator, the one with greater
numerator is greater.
Of the two fractions having the same numerator, the one with greater
denominator is smaller.
Operations with Fractions:
To add or subtract unlike fractions, first we convert them into like fractions and then perform the required operation on like fractions so obtained.
The product of two or more fractions is a fraction whose numerator is the product of their numerators and whose denominator is the product of their denominators.
When the product of two fractions or a fraction and a whole number is 1, then either of them is called the reciprocal of the other.
The number zero (0) has no reciprocal.
Dividing a fraction or a whole number by a fraction or a whole number (other than zero) is the same as multiplying the first by the reciprocal of the second.