Question

How do you write the algebraic expression given: 8 minus the quotient of 15 and y?

Answer 1

We will first write the quotient of 15 and y to get the term which we require to subtract from 8. Now, taking the negative sign on it and adding 8 to it, we will get the required situation.

Complete step-by-step answer:
We are required to find the algebraic expression of: 8 minus the quotient of 15 and y.
We know that if we divide 15 by y, we get: $\dfrac{{15}}{y}$. So, the quotient of 15 and y is $\dfrac{{15}}{y}$.
Now taking the negative of it, we get:- $- \dfrac{{15}}{y}$ Now, adding 8, we will then get:- $8 - \dfrac{{15}}{y}$

Hence, 8 minus the quotient of 15 and y is $8 - \dfrac{{15}}{y}$.

Note:
The students must note that whenever we divide a by b, we always get the quotient of them as the answer. So, the quotient of a and b will be always given by a / b or can be written as $\dfrac{a}{b}$. But, if we require to represent the remainder we obtain, we need to express it as a % b or the modulus symbol. So, always use the correct representation.
Now, we needed 8 minus something, so first of all we wrote 8 then introduced a negative sign and then the quotient. Here, 15 was given first and then y, therefore, we took 15 as the dividend and y as the divisor. If we would have given the quotient of y and 15, then the dividend would have been y and then we have divisor as 15.
Definition of Algebraic expression: In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).
In the given question, we have y as the variable and the operation is minus sign and the constants are 8 and 15.