Division of two like terms, Mathematics

Case 1: Suppose we have two terms 8ab and 4ab. On dividing the first by the second we have 8ab/4ab = 2 or 4ab/8ab = (1/2) depending on whether we consider either 8ab or 4ab as the first term. Irrespective of the order of division, the quotient of two positive terms will be a positive term.

Case 2: What will be the quotient if you divide -9ac by -3ac. We will get -9ac/-3ac = 3. In case of -3ac/-9ac, we will get 1/3. As in case 1, irrespective of the order of division, the quotient will be a positive term.

(Note: Observe that -9ac/-3ac is same as -9ac x 1/-3ac; 1/-3ac being the reciprocal of -3ac.)

We took monomials only for the sake of understanding the underlying principles in a better manner. However, these principles can be applied equally well to binomials, trinomials and polynomials also. The next part deals with them.

Now, do you find any difference between -7abc - 3bc and -7abc + (-3bc) and -7abc - (-3bc). The terms -7abc - 3bc and -7abc + (-3bc) are one and the same, the third expression is certainly different. The idea of introducing the bracket is to convey that the quantity within the brackets ought to be treated as a single quantity. Therefore, whenever one removes the brackets the necessary changes ought to be made specially with respect to the signs of the terms. Otherwise, you may end up with a wrong solution. And since we are mainly concerned with the multiplication aspect whenever brackets come into picture we apply the same four rules we have seen while going through multiplication of like and unlike terms. The expression -7abc + (-3bc) on removal of the brackets will be -7abc + x -3bc, where ‘x' is the multiplicative sign. Since + x - gives us -, the expression will get simplified to -7abc - 3bc. The third expression -7abc - (-3bc) would be simplified to -7abc + 3bc on removal of the brackets. Regarding the change of signs whenever brackets are present, we make the following two important observations:

Whenever a ‘+' sign precedes a bracket, the brackets can be removed without changing the signs of the elements within the brackets.

Whenever a ‘-' sign precedes a bracket, they can be removed only by changing the signs of the elements within the brackets.

From these observations we also conclude that if you want to introduce a ‘+' sign and include some of the terms of an expression in brackets, you can do so without changing the sign of the terms irrespective of them being ‘+' or ‘-'. That is, -7abc - 3ab can be written as -7abc + (-3ab) or 8a + bc can be written as 8a + (+bc). But if you want to introduce a ‘-' sign, more attention has to be paid. Every time you want to introduce a ‘-' sign, the signs of the terms to be included in the bracket has to be changed. In other words, a term which has a ‘-' sign should be changed to ‘+' sign and the term which has a ‘+' sign should be changed to ‘-' sign. Now we look at few examples as to how the basic operations are conducted in case of binomials, trinomials and polynomials.

Posted Date: 9/13/2012 2:51:55 AM | Location : United States







Related Discussions:- Division of two like terms, Assignment Help, Ask Question on Division of two like terms, Get Answer, Expert's Help, Division of two like terms Discussions

Write discussion on Division of two like terms
Your posts are moderated
Related Questions
HOW TO FIND THE HEIGHT OF A CYLINDER I NEED IT FOR ASSIGNMENT TO BE SUBMITTED BY 8;00 AM

Graph for the Sequence First we wish to think about the term graphing a sequence. To graph the sequence {a n } we plot the points {n, a n } as n ranges over every possible valu

Q. What is Addition Rule of probability? Ans. Suppose there are 17 girls and 15 boys in your stats class. There are 17 + 15 = 32 ways for your teacher to pick one student

At rest, the human heart beats once every second. At the strongest part of the beat, a person's blood pressure peaks at 120mmHg. At the most relaxed part of the beat, a person's bl

railway tunnel of radius 3.5 m and angle aob =90 find height of the tunnel

there are 5 small cubes and it reads the 5 small cubes is 1/100, then what is the ONE?

A firm is manufacturing 45,000 units of nuts. The probability of having a defective nut is 0.15 Compute the given i. The expected no. of defective nuts ii. The standard an


Evaluate the subsequent integral. ∫ (tan x/sec 4 x / sec 4 x)  dx Solution This kind of integral approximately falls into the form given in 3c.  It is a quotient of ta

Linear Approximation Method This is a rough and ready method of interpolation and is best used when the series moves in predicted interval