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Dividing Monomials Calculator + Online Solver With Free Steps
A Dividing Monomial Calculator is a free online tool that performs division between two monomial expressions. Monomials are expressions that have only one term which can be either numbers, variables, or a product of both.
The calculator takes the two monomial expressions as input and returns the result of their division.
What Is the Dividing Monomials Calculator?
The Dividing Monomials Calculator is an online calculator that can be used to divide two monomials.
Monomials can also be considered the simplest form of any polynomial expression. They have various applications in areas like calculus, engineering, and finance. Many of the problems involve basic operations between monomials.
Simple operations like the division between monomials can be tough and time taking tasks when the monomials themselves are complex. You can quickly execute the operation of division by using the Dividing Monomials Calculator.
The calculator is a reliable and efficient tool as it provides users with accurate and precise results. Besides this, it is 24/7 accessible in browsers with an infinite number of uses.
How To Use the Dividing Monomials Calculator?
You can use the Dividing Monomials Calculator by putting various monomials into the mentioned boxes. You just need to enter expressions, press a button, and the solution of your problem will be presented.
The interface is so simple that anyone can easily comprehend and operate the calculator. It has two empty boxes for each expression and a button to process the solution.
To get the optimum performance from this calculator, you must follow the detailed instructions on how to use the calculator given below.
Step 1
Enter the first monomial that needs to be divided in the tab with the label “ Enter the Numerator.”
Step 2
Put the second monomial by which the first polynomial is going to be divided in the “Enter the Denominator” box.
Step 3
Make sure you have correctly entered the monomials. After this press the Submit button for the answer.
Output
The output of the calculator has two windows. The first window is an interpretation of the problem developed by the calculator. You can also confirm the input expression from this window.
Then the second window displays the desired outcome which is the division of expressions. It divides the two expressions by canceling out the similar terms in the numerator and denominator.
If there are no similar terms in the fraction then it simply returns the division of the coefficients of the fraction if any. It is because different terms like a variable x cannot be divided by a variable y.
For example, if you have a fraction like $\frac{12ab}{4bc}$, the result of the division will be obtained by canceling the term b from both the fraction and dividing the constant numbers. The final result will be 3ac.
How Does the Dividing Monomials Calculator Work?
This calculator works by dividing the given monomials and depicting the simplified quotient. This division is done by expanding the terms of both of the monomials and then nullifying the common terms.
The working of this calculator can be fully understood by knowing about the monomials and the rules for dividing monomials.
What Is a Monomial?
A Monomial is an algebraic expression that consists of one term. It includes constants, variables, or both that are multiplied together. Monomials are the building blocks of polynomials.
The sum of exponents of all the variables is equal to the degree of the monomial.
What Is Dividing Monomials?
Dividing monomials is the process of dividing the coefficients of monomials first and then dividing their variables. It is a similar procedure as followed while multiplying two monomials.
When it is required to divide the two monomials, first separate the coefficients and variables, then express each coefficient and variable in the expanded form and group the common bases.
Afterward, divide the coefficients or cancel out the common factor from the numerator and denominator, and for the division of variables, subtract the exponents of the common variables.
Multiply the resultant coefficients and variables that are obtained from the above-mentioned procedure to get the required solution.
Dividing Monomials With Exponents
The division of monomials with exponents takes place as per the quotient law of exponents.
When there is the division of monomials then for the same bases, subtract their exponents, such as the division of $x^a/x^b$ is equal to $x^{a-b}$ because the base x is the same for both of the terms.
Dividing Monomials With Negative Exponents
The division of the monomials with negative exponents is also the same as that for positive exponents by just subtracting the exponents for the common bases. However, the resultant negative exponent can be made positive by flipping it.
For instance, the division of $x^2/x^4$ results in $x^{-2}$. This negative exponent can be made positive by flipping it as $1/x^2$.
Dividing Monomials With Negative Coefficients
When there is a division of monomials, the positive coefficients are simply divided. However, the negative coefficients may affect the resulting solution.
The division of monomials having negative coefficients of both of the expressions results in a positive solution because the negative signs cancel out such as $-ax^2/-bx$ resulting in $ \frac{a}{b}x$.
The division with one negative coefficient monomial yields a negative result, for example, the division of $-ax^2/bx$ gives $ -\frac{a}{b}x$.
Solved Examples
To better understand the working principle of the calculator, please refer to the problem solved by the calculator below. Each of the examples is described in detail.
Example 1
A mathematician is solving a calculus problem and he came up with two monomial expressions. To further solve the problem, it is required to divide these expressions which are as follows:
\[ f_{1}(x) = 7x^{6} y^{4} z^{3} \]
\[ f_{2}(x) = 56x^{2} y^3 z \]
Divide the expression $f_{1}(x)$ by $f_{2}(x)$.
Solution
The answer to the problem by the calculator is given as:
\[ \frac{1}{8} x^{4} y z^{2} \]
Example 2
An engineer is required to design the curves for the roller coaster. While designing the curves he came up with two monomial expressions that are $14a^{7}6b^3$ and $-2a^{5}18b^{6}$. He is required to divide these monomials for designing curves.
Solution
This division can easily be performed by using a dividing monomials calculator. The required solution is given as:
\[- \frac{7a^2}{3b^3}\]