Math classes are important but why? What is math, what do they teach and why do you need them? Math classes are important because they teach you. Division is a fundamental part of our lives and we use it daily in the real world. The division helps us solve problems with numbers and we can be more successful in life if we have good math skills. Math is not just about counting money or adding up numbers; it’s also about solving problems and learning how to think critically.
What is Division?
The division process is essentially a series of subtraction operations. It is the multiplication operation’s inverse. The act of forming equal groupings is defined as it. When dividing numbers, we break down a larger number into smaller ones so that the multiplication of the smaller ones equals the larger number.
For instance, 4 2 = 2. This can be expressed as 2 2 = 4 as a multiplication fact.
How to do Division?
The division is one of the four basic operations of arithmetic, which gives a fair result for sharing or grouping objects. Division can be done in two ways, namely by grouping and by measurement. You can use division to reduce fractions, solve for x in algebraic equations, find roots of numbers, and even determine the slope of a line.
- To divide polynomials, first look for common factors and then divide each term in the numerator by each factor found. Use long division if there are no common factors between polynomials.
- To divide fractions multiply the numerator with the denominator and then increase the result with the denominator. Divide both sides then multiply the numerator by the reciprocal of the denominator on both sides to get your answer (a/b) ÷ c = (a × b) ÷ c = a / bc^2 + 1
Properties of Division
The properties of division are the same as the properties of multiplication. If you pay attention to how your teacher explains each one, you’ll find that it’s a lot easier to work with division problems.
- First, we have the associative property of division. This says that when 3 numbers are divided and then added together, it doesn’t matter what order they’re in:
a ÷ (b ÷ c) = (a ÷ b) ÷ c = a ÷ b ÷ c - Next up is the commutative property of division. This says that when two numbers are swapped over, it doesn’t matter which is first:
a ÷ b = b ÷ a - And finally, we have the distributive property of division. This says that when 2 numbers are multiplied together inside parentheses and then divided by another number outside those parentheses, it doesn’t matter whether one or both is divided by first:
(a × b) ÷ c = a × (b / c) = (a / c) × b
Remainder and Factor Theorems
Remainder theorem:
The remainder theorem states the following: Let P(x) be a polynomial function. Then for any real number a, if we divide P(x) by x − a, then the remainder is given by P(a). That is, if we divide the polynomial P(x) by x − a, then the remainder will be of the form R = c where c is equal to the value of P when x = a.
Factor Theorem,
we will see how to factorize polynomial expressions
A monic polynomial p with integer coefficients has degree n and leading coefficient 1. If p (m ) = 0 for some integer m , show that (x−m )|p.
In other words, show that there exists an integer r such that pr (x) = x−m.
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