Question

How do you write the expression for quotient of 4 and a number x increased by 6?

Answer 1

Hint: The following problem can be solved in 2 ways. In the first case, we find the quotient of number 4 and number x. The value of the quotient is then increased by 6. In the second case, we increase the value of number x by 6. Then the quotient of 4 with the value of x increased by 6 is found out.

Complete step by step solution:
The first case will be,
Let the number be x.
The Quotient is the value obtained by dividing the dividend with the divisor.
The dividend is the number that is getting divided.
The divisor is the number that divides the dividend.
The formula is hereby given as Quotient = Dividend/Divisor.
The quotient is the result of the division.
Now,
The Quotient of 4 and number x can be written in mathematical form as $\dfrac{4}{x}$
The Question says the quotient of 4 and a number x that is $\left( \dfrac{4}{x} \right)$ is increased by 6.
Writing the same in the form of expression, we get,
 $\Rightarrow \left( \dfrac{4}{x} \right)+6$
Hence, the expression for the quotient of 4 and a number x, increased by 6 is written as $\left( \dfrac{4}{x} \right)+6$

The second case will then be,
Let the number be x.
The phrase x increased by 6 can be written in mathematical form as, $x+6$
Now, we must find an expression for the quotient of 4 and x increased by 6.
Quotient = dividend / divisor
Substituting in the above formula we get,
$\Rightarrow \dfrac{4}{x+6}$
The expression for the quotient of 4 and a number x increased by 6 is written as $\dfrac{4}{x+6}$

Note: It is very important to change the phrases in English to expressions in maths with the meaning being precisely equivalent. The conversion of phrases to expressions must be done sequentially to avoid confusion.