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How do you define a variable and write an expression for each phrase: the quotient of 6 times a number and 16?

Last updated date: 20th Jun 2024
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Hint: We recall what quotient means when we divide the dividend by the divisor and recall Euclid’s division lemma $n=dq+r$. We assume the remainder is zero and we assume the variable as any number $x$, we multiply 6 to it to get the dividend as $6x$ and the divisor as 16 to express $q$ in terms of $n$ and $d$.

Complete step-by-step solution:
We know that in arithmetic operation of division the number we are going to divide is called dividend, the number by which divides the dividend is called divisor. We get a quotient which is the number of times the divisor is of dividend and also remainder obtained at the end of division. If the number is $n$, the divisor is $d$, the quotient is $q$ and the remainder is $r$, they are related by the following equation,
Here the divisor can never be zero. The above relation is called Euclid’s division Lemma. If remainder is zero which means the divisor exactly divides the number , then we shall have
  & n=dq \\
 & \Rightarrow q=\dfrac{n}{d} \\
 We are given the question that we have to define a variable and write an expression for the phrase “the quotient of 6 times a number and 16” . So we need an algebraic expression for the quotient. So let us assume the number as $x$ and 6 times the number is $6\times x=6x$. The word ‘and’ tells us that there is a division operation between $6x$ and 16. So we can express the quotient as

Note: We note that an algebraic expression is a finite mathematical expression involving constants and variables. The variables are unknown to us and constants are known numbers. Here in this problem in $\dfrac{3x}{8}$ the variable is $x$ and constants are $3,8$. The algebraic expression most of the time represents quantity.