Rational Numbers, Properties, Operations
Multiplication of rational numbers
Product of two rational numbers is equal to the product of numerators divided by the product of denominators.
i.e., \(
\frac{a}
{b} \times \frac{c}
{d} = \frac{{ac}}
{{bd}}
\)
Multiplication and division have an identitiy element; when we multiply or divide a number by one, the number doesn't change.
Multiplicative inverse of a number is nothing but reciprocal of a number :
Note:i) Reciprocal of a number x is \(
\frac{1}
{x}
\)
ii) Multiplicative inverse of \(
\frac{a}
{b}
\) is \(
\frac{b}
{a}
\)
Ex : Multiply \(
\frac{7}
{3}and\frac{5}
{2}
\)
Solution : \(
\frac{7}
{3} \times \frac{5}
{2} = \frac{{7 \times 5}}
{{3 \times 2}} = \frac{{35}}
{6}
\)
Division of rational nummbers:
To divide a rational number by a rational number, just multiply by the reciprocal of denominator
\(
\therefore \frac{a}
{b} \div \frac{c}
{d} = \frac{a}
{b} \times \frac{d}
{c}
\)
Ex : 1.\(
\frac{1}
{2} \div \frac{1}
{4} = \frac{1}
{2} \times \frac{4}
{1} = 2
\) 2. \(
\frac{7}
{3} \div \frac{2}
{3} = \frac{7}
{3} \times \frac{3}
{2} = \frac{7}
{2}
\)