Question

Write in algebraic form:
Quotient of $x$ by 8 multiplied by $y$.

Answer 1

Hint: Quotient of A by B means the value we get when we divide A by B. If we multiply A by B then we write it as AB. Try thinking how we can algebraically write Quotient of x by 8. And the treat Quotient of x by 8 as another variable and write as AB.

Complete step-by-step solution -

When we write a statement in algebraic form, we write the algebraic expression which evaluates to the same result for every variable substitution as the substitution of a variable in that expression.
The letters a, b, c, etc in algebraic expressions are called variables and the numbers 1, 3, 1.5, etc are called the constants.
Quotient of x by 8 is given by $\dfrac{x}{8}$
Hence the given expression evaluates to $\dfrac{x}{8}\times y$ = $\dfrac{xy}{8}$.

Note: Writing algebraic expressions from statements is very important in mathematics. In solving mathematical problems, we are given statements which we must convert in algebraic form to be able to solve them. They play an important role in solving day to day problems.
e.g. Ram is half his brother's age. Three years from now he will be one third of his age. What is the age of Ram and his brother?
In this statement if we say Ram has age $x$ and his brother has age $y$ then the above statement converts to the following algebraic expressions
[i] $\dfrac{x}{y}=\dfrac{1}{2}$
[ii] $\dfrac{x+3}{y+3}=\dfrac{1}{3}$ which can later be solved by the methods used for solving two variable linear equations. It is important to note that the conversion of the statement to algebraic form was the primary step towards solving the problem.