Question

How do you write the expression for the verbal phrase, “The quotient of fifteen and the product of two times $x$”?

Answer 1

Hint: We recall numerical and how to write a numerical expression. We recall that the word ‘quotient’ is used to represent the result of division and the word ‘times’ is used to represent the result of the multiplication. We use this information to write the given phrase in a numerical expression.

Complete step-by-step answer:
We know that a numerical expression is a mathematical expression with numbers and symbols of arithmetic operations like addition $\left( + \right)$, subtraction $\left( - \right)$, multiplication $\left( \times \right)$ , and division $\left( \div \right)$. The numbers are called operands. We use brackets to prioritize operations for example small brackets $\left( {} \right)$, curly brackets \[\left\{ {} \right\}\] , and square brackets $\left[ {} \right]$.
We know that the symbol for addition $\left( + \right)$ is read using the word plus and the result of the addition is called sum. So when we write $2 + 3 = 5$, it means 2 plus 3 equals 5 or the sum of 2 and 3 is 5. We similarly know that the symbols for multiplication are read using the words into or times. So when we say 3 times 4 we can write it as $3 \times 4$.
We are asked in the question to write the numerical expression for the phrase “The quotient of fifteen and the product of two times $x$”.
So, we first write for the phrase the product of two times $x$ as $2 \times x$. Now we understand the phrase “The quotient of fifteen and the product of two times $x$” as 15 divided by $2x$ which means we can write the numerical expression as
\[ \Rightarrow \dfrac{{15}}{{2x}}\]

Hence, the expression is $\dfrac{{15}}{{2x}}$.

Note:
We note the BODMAS rule that when we are given a numerical expression with multiple arithmetic operations and then we have first to simplify the terms with brackets and then order( or power or exponent), division, multiplication, addition, subtraction in sequence. We note that the result of subtraction is called difference, the result of the multiplication is called product and the result of the division is called the quotient.