Question

How do you express the phrase “the second power of the quotient of 80 divided by twice a number” as an algebraic expression?

Answer 1

Hint: We know that mathematical expression and algebraic expression are both the same. An algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations. An expression is a group of terms. Here algebraic operations are addition, subtraction, division and multiplication etc. We know quotient means division.

Complete step by step solution:
We have “the second power of the quotient of 80 divided by twice a number”
Here we don't have that number so we take ‘x’ as some number.
Twice a number means \[ \Rightarrow 2x\]
80 divided by twice a number \[ \Rightarrow \dfrac{{80}}{{2x}}\]
Now “the second power of the quotient of 80 divided by twice a number” means
 \[ \Rightarrow {\left( {\dfrac{{80}}{{2x}}} \right)^2}\] is the required algebraic expression. Because we have a constant ’80, 2’ and a variable ‘x’ and \[2\] is a coefficient of ‘x’, as it is a constant value used with the variable term and it is well defined. Also we have algebraic operation division and multiplication.
(A variable is a symbol for a number that we don’t know yet. Generally it is represented by alphabetic letters. A number on its own is called a constant)
So, the correct answer is “ \[ {\left( {\dfrac{{80}}{{2x}}} \right)^2}\] ”.

Note: Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation \[( + )\] . Similarly If we have ‘less’ or ‘difference’ we use subtraction \[( - )\] . If we have a ‘quotient’ we use division operation \[( \div )\] . 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.