Question

What does $x$ equal in the sentence \[\dfrac{{27}}{{45}} = \dfrac{x}{{100}}\]?

Answer 1

Hint: In this question, we have to simplify the given expression and find out the value of $x$.
To simplify a given problem, we need to use a cross multiplication method.
Rule:
In a cross-multiplication method, we multiply the numerator of one fraction to the denominator of another and denominator of the first term to the numerator of another term.
First, we need to multiply the denominator of the first term to the numerator of another term and then the terms with $x$ in left hand side and the constant terms in right hand side. By simplifying this we will get the required solution.

Complete step-by-step solution:
It is given that, \[\dfrac{{27}}{{45}} = \dfrac{x}{{100}}\].
We need to simplify \[\dfrac{{27}}{{45}} = \dfrac{x}{{100}}\] and find out the value of $x$.
To simplify the given equation, we need to use the cross multiplication method and move the terms involved in $x$ in the left hand side and the constant term in the right hand side.
Following the above we get,
\[\dfrac{{27}}{{45}} = \dfrac{x}{{100}}\]
i.e.\[27 \times 100 = x \times 45\]
Simplifying we get,
\[45x = 2700\]
\[\Rightarrow x = \dfrac{{2700}}{{45}}\]
\[\Rightarrow x = 60\]
Therefore, we get, the value of $x$ is \[60\].

Note: Algebraic operation:
In mathematics, a basic algebraic operation is any one of the common operations of arithmetic, which include addition, subtraction, multiplication, division, raising to an integer power, and taking roots (fractional power).
To simplify algebraic expressions we will consider highest power first then less the powers accordingly and end it with the constant term.
“Operations” mean things like add, subtract, multiply, divide, squaring, etc. If it isn’t a number it is probably an operation.
You need to always follow the BODMAS rule. Calculate them in the wrong order, and you can get a wrong answer.