Write an algebraic expression to represent each verbal expression.

72. quotient of a number and 3 increased by 1

The algebraic expression is obtained from verbal expression using mathematical operators like addition $+$, subtraction $-$, multiplication $\times$, division $÷$ and many such more and variable.

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

In the expression $4x+1$, the unknown quantity is x. So, the variable in this expression is x. 4 and 1 are constants values.

Consider the provided verbal expression.

The quotient of a number and 3 increased by 1.

Let the number be x.

The mathematical operators corresponding to quotient isdivision $÷$ and to increased is addition $+$.

Express the verbal expression for quotient of a number and 3 as $\frac{x}{3}$.

Now, this obtained expression is increased by 1. The algebraic expression obtained is $\frac{x}{3}+1$.

Hence, the algebraic expression is $\frac{x}{3}+1$