Dividing monomials is a method of dividing monomials by expressing the terms of the two given expressions in their expanded form and then canceling out the common ones. Dividing polynomials follow the same procedure as to how we multiply monomials.
In this article, let's learn about dividing monomials in detail with solved examples.
|1.||What is Dividing Monomials?|
|2.||How to Divide Monomials?|
|3.||Examples on Dividing Monomials|
|4.||Practice Questions on Dividing Monomials|
|5.||FAQs on Dividing Monomials|
What is Dividing Monomials?
When we multiply two monomials, we multiply the coefficients together and then you multiply the variables together. Similarly, while dividing monomials, divide the coefficients and then divide variables. When there are exponents with the same base, then as per exponent rules, divide by subtracting the exponents.
How to Divide Monomials?
Dividing monomials refers to the division of coefficients of the two given monomials and division of the variables separately and then combining them to get the result. Let's consider an example. 14x2y/7x
- Step 1: Consider the coefficients and variables separately.
- Step 2: Write each constant and variable in the expression in the expanded form grouping common bases. (14/7) (x2/x) (y)
- Step 3: For the coefficients, we can divide normally or cancel out the common factor, that is 2, from both, the numerator and the denominator. 14/7 = 2
- Step 4: For the variables, we can keep the common base and subtract the exponents or simply cancel out one 'x' from both, the numerator as well as the denominator. . (x2/x) = x2-1 = x
- Step 5: Multiply the coefficients and variables as obtained after division in step 3 and step 4. 2xy
Dividing Monomials with Exponents
While dividing monomials with exponents, we need to consider exponents' rules. Thus, in the case of the division of monomials, then their base is the same, just subtract the exponents. It's the opposite of the multiplication rule.
Let's consider an example. y4/y2
Now, in the above case, the monomials have only one term each consisting of the same variable or same base, that is y. Thus, applying the exponent rule, y4/y2 = y4-2 = y2.
Dividing Monomials with Negative Exponents
Dividing monomials with negative exponents is almost the same as multiplying them. In the case of multiplying monomials, we used to add the powers but in the case of dividing monomials, we need to subtract. If the bases are the same, subtract the exponents. Note that you need to flip the exponent and make it positive if needed.
Let's consider an example. 6xy3/3x2
Here, in order to divide x by x2, we will just subtract the powers as, x1-2 = x-1. Now, the overall result of 6xy3/3x2 will be (6/3)(x/x2)(y3) = 2x-1y3 or 2y3/x.
Dividing Monomials with Negative Coefficients
When dividing a monomial by another monomial, we divide the coefficients and apply the quotient law of exponents, x m ÷ x n = x m – n to the variables. If both the monomials have negative coefficients, the negative signs cancel out and the answer so obtained will be having a positive coefficient only. Consider the two monomials, -14x2 and 7x. On solving, we get -(14/7) (x2/x) = 2x. In case, there is a negative sign with even one of the monomials, the answer will have a negative sign too. Consider the two monomials, -14x and -7x. On solving, we get (-14/-7) (x/x) = 2.
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Examples on Dividing Monomials
Example 1: Divide 40x2 by 10x.
Let's divide 40x2 by 10x
- Step 1: Divide the coefficients. 40/10 = 4
- Step 2: Divide the variables using the quotient rule. x2 /x = x2 -1 = x
Example 2: Using the dividing monomials rule, divide 22m2n by 2n.
Given: Monomials, 22m2n by 2n.
- Step 1: Divide the coefficients. 22/2 = 11
- Step 2: Divide the variables. m2n /n = 11m2
FAQs on Dividing Monomials
What Is Dividing Monomials in Algebra?
Dividing monomials refers to the method of dividing monomials by expressing the terms of the two given expressions in their expanded form and then canceling out the common ones. Clearly, dividing polynomials follow the same procedure as multiplication of monomials following the different exponent rule.
How Do You Divide Monomials with Coefficients?
For dividing monomials follow the steps given below.
- Step 1: Write the terms in expanded form.
- Step 2: Divide the coefficients
- Step 3: Divide like variables using the exponent quotient rule.
How Do You Divide Negative Monomials?
As we already know that the variables of a monomial cannot have a negative or fractional exponent, whereas the dividing monomials with negative coefficients follow the rules as given below:
- In case both the monomials have negative coefficients, the negative signs cancel out and the answer so obtained will be having a positive coefficient only.
- In case, there is a negative sign with even one of the monomials, the answer will have a negative sign too.
How To Divide Polynomials by Monomials?
In order to divide a polynomial by a monomial, separately divide each term of the polynomial by the monomial and add each operation's result to get the overall result of the division of a polynomial by a monomial.
What Is the Property To Be Used When Dividing a Monomial by a Monomial?
When dividing a monomial with a monomial, we used to take up the division of coefficients and variables separately. In case there is more than one variable, use fraction multiplication, write one fraction for each variable. Then simplify the variables using the Quotient Property.