Question

How do you simplify \[n + 5n\]?

Answer 1

Hint: In the question, we are given a mathematical equation that is a combination of both numerical values and alphabets, such types of mathematical equations are called algebraic expressions. The representation of numbers by alphabets in a formula or equation involving mathematical operations is known as algebra. “n” and “5n” represent the multiplication of 1 and ‘n’, and multiplication of 5 and ‘n’ respectively and they both are in addition.

Complete step-by-step solution:
Given, \[n + 5n\].
Here ‘n’ is an unknown variable. As the “n” term is present in both the multiplications, we take it as common and apply the mathematical operation on the terms left in the parenthesis as follows:
\[n + 5n = n(1 + 5)\]
We can add 1 and 5 we have,
\[n + 5n = 6n\]
Hence the simplified form of \[n + 5n\] is \[6n\]

Note: We can find the value of a given expression if we know the value of ‘n’. Algebra helps in converting a mathematical statement into an equation. To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too. For example in an arithmetic progression, each term is the sum of the previous term and the common difference that is it follows a pattern, so we use algebra to find out a generalized expression for the nth term of the sequence, there are many more examples of algebra being used in various branches of mathematics.