Question

How do you write the mathematical expression for “the quotient of twice a number \[t\] and \[12\] ”?

Answer 1

Hint: A quotient is obtained when we divide two numbers. The result of the division is called the quotient. The quotient of \[6 \div 3\] is \[2\] . Twice a number refers to the sum of the number with itself or it can be understood as the product obtained after the multiplication of the number with \[2\]. Divide the resultant with \[12\] and you will get your answer.

Complete step by step answer:
A mathematical expression contains variables, numbers and operators. Using the given statement, we will have to write a mathematical expression.
The two numbers involved in the division are \[12\] and twice of \[t\]. Twice of \[t\] will be $2 \times t$ or $2t$ .
Therefore, the mathematical expression will be \[2t \div 12\] or \[\dfrac{{2t}}{{12}}\] .
We can further simplify it as $\dfrac{t}{6}$ .

Therefore, the mathematical expression will be $\dfrac{t}{6}$ .

Note: Students often make a mistake in determining the numerator and denominator of the division. Remember it would be \[\dfrac{{2t}}{{12}}\] and not \[\dfrac{{12}}{{2t}}\] .
Also, a mathematical expression does not involve any equal sign as it as an expression. It involves variables, constants, operators like addition, subtraction, division, multiplication, exponents of fractions. These all should be combined in a valid manner. Mathematical expressions are finite and are defined in accordance to the well-defined rules of mathematics. No arbitrary combination of constants, variables or operators is considered. Equal to signs are used in mathematical equations and not expressions.
Here, \[t\] is a variable. A variable is an alphabet whose value is unknown. Usually, variables are used temporarily in a question for the values that are unknown or are to be found after solving. Digits are considered to be constants as their values can never be changed in the entire question. A variable can have different values as per the given conditions.