Question

How do you simplify $\dfrac{1}{2}(x - 5)$ ?

Answer 1

On the division of a whole thing into equal parts, each part is called a fraction. A fraction is separated into two parts by a horizontal line, the upper part is called the numerator and the lower part is called the denominator, a fraction is expressed as - $\dfrac{{numerator}}{{denominator}}$ . By simplifying the fraction, we mean to convert it into the simplest form; it is done to make the calculations easier. For simplifying the fraction, we divide both the numerator and the denominator by their common
divisor. This way, we can find the correct answer.

Complete step by step answer:
We have to simplify $\dfrac{1}{2}(x - 5)$ but we see that it is already simplified and thus cannot be simplified further but it can be expanded. So, we can apply the distributive property.

According to the distributive property,
$a(b + c) = ab + bc \\\ \Rightarrow \dfrac{1}{2}(x - 5) = \dfrac{x}{2} - \dfrac{5}{2} \\\$

Hence, we can say that the simplified form of $\dfrac{1}{2}(x - 5)$ is $\dfrac{x}{2} - \dfrac{5}{2}$ .

Note: For simplifying a fraction, we first find out the common factor of the numerator and the denominator and divide both of them till the common factor is 1. But if the numerator and the denominator both are prime numbers, then the common factor of the numerator and the denominator will be one (as the prime numbers are the numbers that are only divisible by one and itself). In the given question, the terms in the numerator are x and 5, x is an unknown quantity that may be a prime number, 5 is a prime number and the denominator “2” is also a prime number, so the fraction is already in simplified form and cannot be simplified further.