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Division of Rational Numbers

Rational Numbers II - Concepts

Identity Property

Commutative Property

Multiplicative Inverse

Division of Rational Numbers

Multiplication of Rational Numbers

Rational Numbers between Two Rational Numbers

Properties of Rational Numbers

Simplification of Rational Numbers

Class - Navodaya Entrance 9th Subjects

Concept Explanation

Division of Rational Numbers

Division of Rational Numbers:

Recall that division of fractions is the inverse of multiplication. In case of rational number also, division is the inverse of multiplication as defined below:

Division: If x and y are two rational numbers such that $large yneq 0$ , then the result of dividing x and y is the rational number obtained on multiplying x by the reciprocal of y.

When x is divided by y, we write $large xdiv y$

Thus, we have $large x+y=xtimes frac{1}{y}$

If $large frac{a}{b}$ and $large frac{c}{d}$ are two rational numbers such that $large frac{c}{d}neq 0$ , then

$large frac{a}{b}div frac{c}{d}=frac{a}{b}times left ( frac{c}{d} right )^{-1}=frac{a}{b}times frac{d}{c}$

Dividend: The number to be divided is called the dividend.

Divisor: The number which divides the dividend is called the divisor.

Quotient: When dividend is divided by the divisor, the result of the division is called the quotient.

If $large frac{a}{b}$ is divided by $large frac{c}{d}$ , then $large frac{a}{b}$ is the dividend, $large frac{c}{d}$ is the divisor, and

$large frac{a}{b}div frac{c}{d}=frac{a}{b}times left ( frac{c}{d} right )^{-1}=frac{a}{b}times frac{d}{c}$ is the quotient.

Example: Divide:

$large (i);frac{3}{5}byfrac{4}{25}$ $large (ii);frac{-8}{9}byfrac{4}{3}$ $large (iii);frac{-16}{21}byfrac{-4}{3}$ $large (iv);frac{-8}{13}byfrac{3}{-26}$

Solution $large (i);;frac{3}{5}div frac{4}{25}=frac{3}{5}times frac{25}{4}=frac{3times 25}{5times 4}=frac{3times 5}{1times 4}=frac{15}{4}$

$large (ii);;frac{-8}{9}div frac{4}{3}=frac{-8}{9}times frac{3}{4}=frac{-8times 3}{9times 4}=frac{-2times 1}{3times 1}=frac{-2}{3}$

$large (iii);;frac{-16}{21}div frac{-4}{3}=frac{-16}{21}times frac{3}{-4}=frac{-16times 3}{21times (-4)}=frac{4times 1}{7times 1}=frac{4}{7}$

$large (iv);;frac{-8}{13}div frac{3}{-26}=frac{-8}{13}times frac{-26}{3}=frac{(-8)times (-26)}{13times 3}=frac{8times 26}{13times 3}=frac{8times 2}{1times 3}=frac{16}{3}$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

The cost of $large 3frac{1}{3}$ meters of cloth is Rs 75. Find the cost of cloth per metre.
A. Rs 25	B. Rs 45	C. Rs 22.5	D. Rs 45.5
Right Option : C
View Explanation

Question : 2

Divide the sum of $large frac{65}{12}$ and $large frac{12}{7}$ by their difference.
A. $large frac{599}{311}$	B. $large frac{680}{216}$	C. $large frac{642}{133}$	D. $large frac{501}{301}$
Right Option : A
View Explanation

Question : 3

Find (x+y)/(x-y),if $large x=frac{3}{2};;y=frac{2}{3}$
A. - 8	B. $large frac{13}{5}$	C. $large frac{12}{5}$	D. $large frac{15}{3}$
Right Option : B
View Explanation