Question

How do you translate “the quotient of twice a number t and 12” into a mathematical expression?

Answer 1

Hint: First understand the definition of an algebraic expression using examples. Now, consider the required algebraic expression as a linear expression in t. Take the product of this variable t with 2 and divide the obtained result with the given numerical value 12 to get the required expression and answer. Take the exponent of t equal to 1.

Complete step by step answer:
Here, we have been provided with the sentence ‘the quotient of twice a number t and 12’. We have been asked to convert it into the mathematical expression. But first we need to understand the term ‘algebraic expression’.
In mathematics, an algebraic expression is an expression that contains constants, variables and algebraic operations like: - addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number. For example: - \[5{{x}^{3}}-3{{x}^{2}}y+xy+10\] is an algebraic expression.
Now, there are certain types of algebraic expression based on integral exponents of the variables. For example: - an algebraic expression with exponent of the variable as 1 is called linear algebraic expression, like: - \[x+y+3\]. If the exponent of the variable becomes 2 then it is called a quadratic algebraic expression, like: - \[{{x}^{2}}+3x+10\]. Similarly, we name cubic expressions for the exponent 3 and biquadratic expression for the exponent 4.
Let us come to the question. We have to write the algebraic expression for the sentence: - the quotient of twice a number t and 12. Clearly, we can see that the variable is t and its exponent is 1. So, the expression we are going to form will be a linear algebraic expression. Let us assume the required expression as E.
Now, considering the product of 2 and t, we get,
\[\Rightarrow 2t\]
Now, the term ‘quotient’ is used when we divide any number by another number, here we have to take the quotient of 2t and 12, so dividing 2t by 12, we get,
\[\Rightarrow E=\dfrac{2t}{12}\]
We can simplify this relation further by cancelling the common factor, so we get,
\[\Rightarrow E=\dfrac{t}{6}\]
Hence, the expression \[\dfrac{t}{6}\] is our required mathematical expression and answer.

Note:
One may note that we must not substitute the obtained algebraic expression equal to 0. This is because if we do so then the algebraic expression will become an algebraic equation. Here, we just have to find the expression and not the equation. You may note this difference between the terms ‘expression’ and ‘equation’. In general, if we just write a combination of constants and variables then it is called an expression and when we substitute this expression equal to 0 then it becomes an equation.