Division of Monomials
Division of monomials means product of their quotient of numerical coefficients and quotient of their literal coefficients.
Since, the product of 3m and 5n = 3m × 5n = 15mn; it follows that
(i) \(\frac{15mn}{3m} = \frac{3 \times 5 \times m \times n}{3 \times m}\) = 5n
or, 15mn ÷ 3m = 5n
i.e. when 15mn is divided by 3m, the quotient is 5n.
(ii) \(\frac{15mn}{5n} = \frac{3 \times 5 \times m \times n}{5 \times n}\) = 3m
or, 15mn ÷ 5n = 3m
i.e. when 15mn is divided by 5n, the quotient is 3m.
1. Divide 35mxy
by 5my
35mxy ÷ 5my
= \(\frac{35mxy}{5my}\)
Now, we need to write each term in the expanded form and then cancel the terms which are common to both numerator and denominator.
= \(\frac{\not{5} \times 7 \times \not{m} \times x \times \not{y}}{\not{5} \times \not{m} \times \not{y}}\)
= 7x
14a7 ÷ 2a5
= \(\frac{14a^{7}}{2a^{5}}\)
Now, we need to write each term in the expanded form and then cancel the terms which are common to both numerator and denominator.
= \(\frac{\not{2} \times 7 \times \not{a} \times \not{a} \times \not{a} \times \not{a} \times \not{a} \times a \times a}{\not{2} \times \not{a} \times \not{a} \times \not{a} \times \not{a} \times \not{a}}\)
= 7 × a × a= 7a2
Or, we can solve this in the other way.
14a7 ÷ 2a5
= \(\frac{14a^{7}}{2a^{5}}\)
= \(\frac{14}{2} \times \frac{a^{7}}{a^{5}}\)
Now we will write the each numerical part \((\frac{14}{2})\) in the expanded form and then cancel the terms which are common to both numerator and denominator and in case of literal part subtract the smaller power of a literal from bigger power of the same literal.
= \(\frac{\not{2} \times 7}{\not{2}} \times a^{7 - 5}\)
= 7 × 2= 7a2
3. Divide the monomial: 81p3q6 by 27p6q3
81p3q6 ÷ 27p6q3
= \(\frac{81p^{3}q^{6}}{27p^{6}q^{3}}\)
= \(\frac{81}{27} \times \frac{p^{3}q^{6}}{p^{6}q^{3}}\)
Now we will write the each numerical part (\frac{81}{27}) in the expanded form and then cancel the terms which are common to both numerator and denominator and in case of literal part subtract the smaller power of a literal from bigger power of the same literal.
= \(\frac{\not{3} \times \not{3} \times \not{3} \times 3}{\not{3} \times \not{3} \times \not{3}} \times \frac{q^{6 - 3}}{p^{6 - 3}}\)
= \(3 \times \frac{q^{3}}{p^{3}}\)
= \(\frac{3q^{3}}{p^{3}}\)
● Terms of an Algebraic Expression
Types of Algebraic Expressions
Multiplication of Two Monomials
Multiplication of Polynomial by Monomial
Multiplication of two Binomials
Algebra Page
6th Grade Page
From Division of Monomials to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
2nd Grade Geometry Worksheet | Plane and Solid Shapes | Point | Line
Dec 10, 24 02:35 PM
2nd grade geometry worksheet -
Types of Lines |Straight Lines|Curved Lines|Horizontal Lines| Vertical
Dec 09, 24 10:39 PM
What are the different types of lines? There are two different kinds of lines. (i) Straight line and (ii) Curved line. There are three different types of straight lines. (i) Horizontal lines, (ii) Ver… -
Points and Line Segment | Two Points in a Curved Surface | Curve Line
Dec 09, 24 01:08 AM
We will discuss here about points and line segment. We know when two lines meet we get a point. When two points on a plane surface are joined, a straight line segment is obtained. -
Solid Shapes | Basic Geometric Shapes | Common Solid Figures | Plane
Dec 08, 24 11:19 PM
We will discuss about basic solid shapes. We see a variety of solid objects in our surroundings. Solid objects have one or more shapes like the following. Match the objects with similar shape. -
2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic
Dec 07, 24 03:38 PM
2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.
● Terms of an Algebraic Expression - Worksheet
Worksheet on Types of Algebraic Expressions
Worksheet on Degree of a Polynomial
Worksheet on Addition of Polynomials
Worksheet on Subtraction of Polynomials
Worksheet on Addition and Subtraction of Polynomials
Worksheet on Adding and Subtracting Polynomials
Worksheet on Multiplying Monomials
Worksheet on Multiplying Monomial and Binomial
Worksheet on Multiplying Monomial and Polynomial
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.