Question

The quotient when \[\left( { - 56mn{p^2}} \right)\] is divided by \[\left( {7mnp} \right)\] is ……………………………..
A) \[ - 8p\]
B) \[8mnp\]
C) \[8p\]
D) \[8m\]

Answer 1

Hint:
Here, we will first write the given dividend and divisor in terms of a fraction such that the number which is to be divided will be in the numerator. We will break the numerator in terms of its factor and then simplify the expression to find the required value of the quotient.

Complete step by step solution:
We are given two variables \[\left( { - 56mn{p^2}} \right)\]and \[\left( {7mnp} \right)\].
The given statement can be represented in the form as \[\dfrac{{ - 56mn{p^2}}}{{7mnp}}\]
Let \[x\] be the quotient when \[\left( { - 56mn{p^2}} \right)\] is divided by \[\left( {7mnp} \right)\].
\[x = \dfrac{{ - 56mn{p^2}}}{{7mnp}}\]
Now breaking the numerator in terms of factor, we get
\[ \Rightarrow x = \dfrac{{\left( {7mnp} \right)\left( { - 8p} \right)}}{{7mnp}}\]
By cancelling the common terms, we get
\[ \Rightarrow x = \left( { - 8p} \right)\]
Thus, \[\dfrac{{ - 56mn{p^2}}}{{7mnp}} = \left( { - 8p} \right)\]
Therefore, the quotient when \[\left( { - 56mn{p^2}} \right)\] is divided by \[\left( {7mnp} \right)\] is \[ - 8p\].

Thus option (A) is the correct answer.

Additional Information:
Algebraic Expression is of three types based on the number of terms which are monomial, binomial and polynomial Expressions. A monomial expression is defined as an algebraic expression having only one term. A binomial expression is defined as an algebraic expression having two terms and these terms must be unlike. A polynomial expression is defined as an algebraic expression more than two terms and must have non-negative integral powers of a variable. Algebraic expression is of two types based on the term. A numeric expression is defined as an algebraic expression with only numbers and arithmetic operation. A variable expression is defined as an algebraic expression with both numbers and variables and arithmetic operation.

Note:
We should note that the given algebraic expression is a binomial expression. An algebraic expression is defined as a combination of variables, constants and coefficients along with an arithmetic operation. A variable is represented by the letters of an alphabet and can take any values. A constant is a number and a coefficient is a constant value always multiplied with a variable.