Question

Let the unknown number be m. Write expression for: -
(a) The sum of the unknown number and 13.
(b) A number that will exceed the unknown number by 5.
(c) The difference between 25 and the unknown number.
(d) The unknown number cubed.
(e) A third of the unknown number plus 3.
(f) Four times the unknown number less than twice the number.

Answer 1

Hint: Assume the required expression as E for each of the cases. Now, find the value of E in terms of m one by one for each case by using appropriate mathematical operators like addition, subtraction, multiplication and division. Use the exponentiation for the expression in the subpart (d).

Complete step-by-step solution:
Here we have been provided with an unknown number m and we are asked to form an expression for each of the cases mentioned as the subparts of the question. Let us check each of the subparts one by one. We will assume the required expression as E in all the cases.
(a) Here we have the statement ‘the sum of the unknown number and 13’. So we need to take the sum of m and 13, so we get,
$\Rightarrow E=m+13$
(b) Here we have the statement ‘a number that will exceed the unknown number by 5’. That means the required number will be equal to the sum of m and 5, so we get,
$\Rightarrow E=m+5$
(c) Here we have the statement ‘the difference between 25 and the unknown number’. So we need to subtract m from 25, so we get,
$\Rightarrow E=25-m$
(d) Here we have the statement ‘the unknown number cubed’. So we need to raised the exponent of m by 3, so we get,
$\Rightarrow E={{m}^{3}}$
(e) Here we have the statement ‘a third of the unknown number plus 3’. Now, a third of the unknown number means m divided by 3 and further we need to take its sum with 3, so we get,
$\Rightarrow E=\dfrac{m}{3}+3$
(f) Here we have the statement ‘four times the unknown number less twice the number’. So four times the unknown number will be 4m and we have not been provided with the number whose twice the value we need to consider, so assuming it as x we will get 2x. Now, we have 4m less 2x that means 4m must be subtracted from 2x, so we get,
$\Rightarrow E=2x-4m$

Note: One may note that we must not substitute the obtained algebraic expression equal to any numerical value. This is because if we do so then the algebraic expression will become an algebraic equation. Here the sixth subpart can create some confusion because there we had to find the twice of a number but the number was not provided so we need to assume it ourselves as x or any other variable.