Question

How do you solve $\dfrac{4}{9}=\dfrac{2}{x}?$

Answer 1

Hint: As we know that , $\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow \left( a\times d \right)=\left( c\times d \right)\Rightarrow ad=bc$
Applying this concept to solve the fractions given, and determine the value of $a.$
As, $bc=ad$
$\Rightarrow d=\dfrac{bc}{a},$ use this for getting the value of $x.$

Complete step-by-step solution:
As per question,
Here, we have to determine the value of $x.$
As here,
Both the fraction are equal,
So,
$\dfrac{4}{9}=\dfrac{2}{x}$
So, for solving it, we will use cross multiplication techniques, like
If $\dfrac{a}{b}=\dfrac{c}{d}$
Then $ad=bc$
Applying this technique in above fraction,
We will get,
$\dfrac{4}{9}=\dfrac{2}{x}$
$\Rightarrow 4\times 2=9\times 2$
$\Rightarrow 4\times 2=18$
$\Rightarrow x=\dfrac{18}{4}$
$\Rightarrow x=4.5$

Hence, value of $x$ will be $4.5$

Note: Equivalent fractions are those fractions which when converted in their simplest form then the value of numerator of first fraction is equal to the value of numerator of second fraction and value of denominator of first fraction is equal to value of denominator of second fraction.
As here $\dfrac{4}{9}=\dfrac{2}{x}$
We can also solve the above given fraction without using cross multiplication techniques.
As here, both the fractions are equals,
So, $\dfrac{4}{9}=\dfrac{2}{x}$
If we compare the numerator of first fraction with numerator of second fraction, and denominator of first fraction with denominator of second fraction,
We will get,
$\dfrac{4}{9}=\dfrac{2}{x}$
Here, we can say that,
As, $x=2\times 2$
So, we can calculate that,
First fraction is doubled as compared to the second fraction, as the numerator of the first fraction is twice as the numerator of the second fraction.
Hence, the denominator of the first fraction must be double to the denominator of the second fraction.
So,
$9$ will equal to twice of $x$
$\Rightarrow 9=2x$
$\Rightarrow x=\dfrac{9}{2}=4.5$
Hence, we can also determine the value of $'x'$ by comparing both the fractions.