Question

How do you write the phrase as a variable expression: the quotient of 6 times a number and 16?

Answer 1

Hint: An algebraic expression is a mathematical phrase that contains a combination of numbers, variables, and operational symbols. A variable is a letter that can represent one or more numbers. In this question, we will assume the variable. And then from the phrase, construct the expression.

Complete step-by-step answer:
In this question, we want to write a variable expression of the given phrase.
The phrase is the quotient of 6 times a number and 16.
First, let us assume the number. The variable will be x for a number.
In the phrase, it is given that 6 times a number.
$ \Rightarrow 6 \times x$
That is equal to the answer
$ \Rightarrow 6x$
Now, it is given the quotient of 6 times a number and 16.
The quotient is the answer to a division.
Here, the word ‘and’ tell us the division between the above expression and 16.
That is equal to the answer

$ \Rightarrow \dfrac{{6x}}{{16}}$

Note:
To write an expression, we often have to interpret a written phrase.
Some examples of common phrases and corresponding expressions that involve addition are:
4 more than some number =$x + 4$ .
A number increased by 10 =$x + 10$.
8 plus some number =$x + 8$
The sum of the number and 13 =$x + 13$
Some examples of common phrases and corresponding expressions that involve subtraction are:
4 less than some number =$x - 4$ .
A number decreased by 10 =$x - 10$.
8 minus some number =$x - 8$
The difference between a number and 13 =$x - 13$
 Some examples of common phrases and corresponding expressions that involve division are:
The quotient of 4 some number =$\dfrac{4}{x}$ .
A number divided by 10 =$\dfrac{x}{{10}}$.
The ratio of 8 and some number =$\dfrac{8}{x}$
The quotient of a number and 13 =$\dfrac{x}{{13}}$
Some examples of common phrases and corresponding expressions that involve operations are:
6 more than 4 times a number=$4x + 6$ .
4 times the sum of the number and 7 =$4\left( {x + 7} \right)$.
3 less than the product 2 and a number=$2x - 3$