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# What is the quotient of $\dfrac{6}{5}$ divided by $\dfrac{2}{3}$ ?

Last updated date: 21st Jul 2024
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Hint: Componendo and Dividendo: Componendo and dividend is a theorem on proportions that allows for a quick to perform the calculations and reduces the number of steps or expansion needed. It is useful when we are dealing with equations and fractions.
To solve this we first write given terms in the numerator and denominator form. Then we solve the given fraction to find the quotient as per rule of componendo and dividendo.

Complete step by step solution:
Given equation,
First fraction is, $\dfrac{a}{b} = \dfrac{6}{5}$
Second fraction is, $\dfrac{c}{d} = \dfrac{2}{3}$
As we know that
$\dfrac{{\dfrac{a}{b}}}{{\dfrac{c}{d}}}$
Then
$= \dfrac{a}{b} \times \dfrac{d}{c}$
Put the number
$\dfrac{{\dfrac{6}{5}}}{{\dfrac{2}{3}}}$
The number will become
$= \dfrac{6}{5} \times \dfrac{3}{2}$
$= \dfrac{3}{5} \times 3$
$= \dfrac{9}{5}$
Hence the answer is $\dfrac{9}{5}$ .
So, the correct answer is “ $\dfrac{9}{5}$ ”.

Note: Fraction: Fractions are numerical quantities that are a fraction of a whole number.
When a number or an object is split into equal parts, each part becomes a fraction of the whole. Where an is the numerator and b is the denominator, a fraction is written as a/b.
Way to solve fraction:
When adding or subtracting fractions, we must first determine if the denominators are the same or different. For the same denominators, we can directly add or subtract the numerators, keeping the denominator common. But if the denominators are different, then we need to simplify them by finding the LCM.