Sipnayan GOAT

Prime and Composite Numbers

noreply@blogger.com (Sipnayan GOAT) — Wed, 01 Jun 2022 10:09:00 +0000

Before we discuss Prime and Composite Numbers, we should take note that in this topic our desired quotients would be focused on Natural Numbers.

Now, let us begin to know what are Prime Numbers and Composite Numbers.

Prime Numbers

These are numbers whose divisors are only 1 and itself.

Example:

1. The number 2 is a prime number.

\[\frac{2}{2}=1\]

\[\frac{2}{1}=2\]

Since there are no more divisors that can divide 2, we can say that 2 is a prime number.

2. The number 5 is a prime number.

\[\frac{5}{1}=5\]

\[\frac{5}{5}=1\]

If we try to divide 5 by 4, 3 and 2, we will not obtain a Natural Number answer. Since the only divisors for 5 is 1 and itself, we can say that 5 is a prime number.

Composite Numbers

These are numbers that has other divisors other than 1 and itself.

Example:

1. The number 6 is a composite number.

\[\frac{6}{1}=6\]

\[\frac{6}{2}=3\]

\[\frac{6}{3}=2\]

\[\frac{6}{6}=1\]

Since 6 appears to have other divisors other than 1 and itself , namely 2 and 3, we can say that 6 is a composite number

2. The number 4 is a composite number

\[\frac{8}{1}=8\]

\[\frac{8}{2}=4\]

\[\frac{8}{4}=2\]

\[\frac{8}{8}=1\]

Since 8 appears to have other divisors other than 1 and itself , which are 2 and 4, we can say that 8 is a composite number

Prime and Composite Numbers From 1-100

Multiplying Binomials: FOIL Method

noreply@blogger.com (Sipnayan GOAT) — Mon, 30 May 2022 05:31:00 +0000

FOIL Method is a method used to multiply two binomials. FOIL is an abbreviation used to identify the terms to be multiplied in the binomials. The meaning of the letters of the FOIL are as follows:

F - First Terms

O - Outer Terms

I - Inner Terms

L - Last Terms

Here are some examples on how to multiply binomials using FOIL Method:

Example 1

Since the given are binomials, (x-3) and (x+2), we can use the FOIL Method here. Following the order of FOIL we have:

F - (x)(x)

O - (x)(2)

I - (-3)(x)

L - (-3)(2)

Getting the products on each term, we will have \[\large x^{2}+2x-3x-6\]

Combining similar terms, 2x and -3x, we will have

\[\large x^{2}-x-6\]

Example 2

Since the given are binomials, (x+5) and (x+9), we can use the FOIL Method here. Following the order of FOIL we have:

F - (x)(x)

O - (x)(4)

I - (5)(x)

L - (5)(9)

Getting the products on each term, we will have \[\large x^{2}+9x+5x+45\]

Combining similar terms, 2x and -3x, we will have

\[\large x^{2}+14x+45\]

Example 3

Since the given are binomials, (4x-5) and (x-3), we can use the FOIL Method here. Following the order of FOIL we have:

F - (4x)(x)

O - (4x)(-3)

I - (-5)(x)

L - (-5)(-3)

Getting the products on each term, we will have \[\large 4x^{2}-12x-5x-15\]

Combining similar terms, 2x and -3x, we will have

\[\large 4x^{2}-17x-15\]

Example 4

Since the given are binomials, (2a+b) and (3x+2y), we can use the FOIL Method here. Following the order of FOIL we have:

F - (2a)(3x)

O - (2a)(2y)

I - (b)(3x)

L - (b)(2y)

Getting the products on each term, we will have \[\large 6ax+4ay+3bx+2by\]

Since there are no similar terms, the expression \[\large 6ax+4ay+3bx+2by\] is the final answer.

Parts of A Right Triangle

noreply@blogger.com (Sipnayan GOAT) — Sat, 07 Aug 2021 07:59:00 +0000

Parts of a Right Triangle

The hypotenuse is the longest side in a right triangle. It is also the side opposite the right angle.

The legs are the sides that make the right angle. These sides are also perpendicular to each other.

Right Triangle

noreply@blogger.com (Sipnayan GOAT) — Fri, 06 Aug 2021 06:53:00 +0000

Right Triangles

A right triangle is a triangle that contains a right angle.

The acute angles in a right triangle are complementary.

Similar Terms

noreply@blogger.com (Sipnayan GOAT) — Tue, 03 Aug 2021 14:25:00 +0000

Similar terms in algebra are two or more terms having the same variable/s whose exponents are also the same.

Similar terms and like terms are just the same thing. Do not be confused when these terminologies are mentioned in algebra, they just mean the same idea.

In addition and subtraction of algebraic expressions, we consider that the terms should be similar terms or like terms.

The Real Number System

noreply@blogger.com (Sipnayan GOAT) — Wed, 09 Jun 2021 03:37:00 +0000

Most of the time in a Mathematics class, Real numbers are always mentioned and we tend to think or rethink what are Real Numbers. In this blog, we will discuss what are real numbers.

The Set of Real Numbers

The Set of Real Numbers is divided into different sets. It is designed for the use of each number set. All of the numbers/sets of numbers that will be discussed are under the Set of Real Numbers.

Irrational Numbers

Irrational Numbers are numbers that are neither terminating nor repeating decimals. Some of the examples of Irrational numbers are trigonometric values, logarithmic values, square roots of positive non-perfect square numbers, the value of pi (

π

),

and many more.

Rational Numbers

Rational numbers are numbers that can be represented as a relation between two numbers such that the relation is in the form \[\frac{a}{b}\] where a and b are any integer but b is not 0.

Integers

Since Integers are mentioned in the above paragraph, let us know what are integers. Integers are numbers that we use to count or to represent the number of objects discretely. Integers are divided into three sets, naming the following:

Positive Integers

The Positive Integers are part of the Real Number System. These numbers are the ones that we commonly use, such as 1, 2, 3, and so on. We also call these numbers counting numbers.

Zero

The number zero represents nothing. It is also part of the Real Number System. It is also neither positive nor negative. It is a neutral number.

Negative Integers

The Negative Integers are related to the Positive Integers. The numbers that we use for counting but differ in signs. Negative integers (numbers) tend to have a negative sign (-) before the number. We can also say that negative numbers are the opposites of the Positive Integers.

Non-Integers

The Non-integers are numbers that represent a comparison of quantities or showing a part of a whole. The numbers under the Non-Integers are fractions, terminating decimals, repeating decimals, percent, and ratio.

What are the Real Numbers?

From the line of Irrational Numbers up to the Non-integers, these are the numbers that belong to the Real number. Whenever the word "Real Number" is mentioned it can be a counting number, a negative number, a fraction, a decimal, a trigonometric value, a percent, and anything as long as it is a number under the above-mentioned subsets.