Question

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

Answer 1

Hint: We use the meaning of each word given in the expression and write the expression step-by-step according to the sequence of words given in the expression. Assume the number as the variable ‘x’ and form the expression.
* Quotient is that value that is obtained when we divide the dividend by the divisor.
* Increased means increasing the value or adding the value.

Complete step-by-step answer:
We have to form an expression for the statement: quotient of 4 and a number x increased by 6.
We use the definitions of quotient and increased to form the expression.
Let us assume the number stated in the word phrase in the question as a variable.
Let the number be ‘x’ … (1)
Then the quotient of 4 and a number x can be written as 4 divided by x i.e. \[\dfrac{4}{x}\] … (2)
Now increase the quotient obtained in equation (2) by 6
i.e. Add value 6 to the quotient obtained in equation (2) , i.e. \[\left( {\dfrac{4}{x} + 6} \right)\] … (3)

\[\therefore \]The expression: The expression for quotient of 4 and a number x increased by 6 can be written as \[\left( {\dfrac{4}{x} + 6} \right)\].

Note:
Alternate Method:
Let the number be ‘x’ … (1)
Then the number increase by 6 will be written by adding 6 to the number i.e. \[x + 6\]
Then the quotient of 4 and a number increased by 6 can be written as 4 divided by \[x + 6\] i.e. \[\dfrac{4}{{x + 6}}\] … (2)
\[\therefore \]The expression: The expression for quotients of 4 and a number x increased by 6 can be written as \[\dfrac{4}{{x + 6}}\].