Question

How do you solve, $\dfrac{5}{6}=\dfrac{x}{15}?$

Answer 1

Hint: As, $\dfrac{a}{b}=\dfrac{c}{d}$ then $(ad)$ will equal to $(bc)$
$\Rightarrow ad=bc$
And $d=\dfrac{bc}{a}$
Use this concept to determine the value of $\left( 2 \right)$
Like,
$\Rightarrow$$\dfrac{1}{4}=\dfrac{2}{x}$
So, $d=x=\dfrac{4\times 2}{1}=8$
Apply this concept to determine the value of $(x)$.

Complete step-by-step answer:
As per data given the question,
As we have,
$\Rightarrow$$\dfrac{5}{6}=\dfrac{2}{15}$
Here, we have to determine the value of $x.$ in the question, both the given fractions are equal,
So,
Cross multiplying the fractions,
We will get,
$\Rightarrow$$\dfrac{5}{6}=\dfrac{x}{15}$
$\Rightarrow 5\times 15=6\times x$
$\Rightarrow x=\dfrac{75}{6}$
$\Rightarrow x=\dfrac{25}{2}$
Hence, value of $x$ will be $\dfrac{25}{2}=12.5$
So, after putting the value of $'x'$
Above expression becomes,
$\Rightarrow$$\dfrac{5}{6}=\dfrac{12.5}{15}$
Additional Information:
As, here we have determine the value of $x=12.5$
So,
Fraction are,
$\Rightarrow$$\dfrac{5}{6}=\dfrac{12.5}{15}$
Here, after putting the value of $'x'$ when both the fractions are converted into simplest/smallest form then the value of numerator and denominator will be equal.
As,
$\dfrac{5}{6}$ is already in simplest form.
Now,
$\Rightarrow$$\dfrac{12.5}{15}=\dfrac{125}{150}=\dfrac{5}{6}$
So, here we can conclude that,
When fractions of L.H.S. and R.H.S, are written in their simplest form, then the value of numerator and denominator of both fractions becomes equal. We can also solve such expressions, by another method.
Let us consider an example,
If, $\dfrac{4}{9}=\dfrac{2}{x}$
We can also solve the above given fraction using cross multiplication techniques.
As here, both the fractions are equals,
So,
$\Rightarrow$$\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,
$\Rightarrow$$\dfrac{4}{9}=\dfrac{2}{x}$
Here, we can say that,
As, $4=2\times 2$
So, we can conclude 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 able to be the denominator of the second fraction.

Note:
As,
$\Rightarrow$$\dfrac{a}{b}=\dfrac{c}{d}$
$\Rightarrow b=\dfrac{bc}{a}$, Here use only cross multiplication to solve the fraction.
After putting the value of $'x'$
$\Rightarrow$$\dfrac{5}{6}=\dfrac{12.5}{15}$ are called as equivalent fraction both the fractions represent the same fraction proportion.