Saturday, March 10, 2018

Basic Mathematics


Mathematics deal with numbers. Numbers are digits used in computations, analysis, and other forms of developing our world. There are many types of them too.

Prime Composite

One major type of numbers is called prime numbers. A prime number is any number that is a natural number greater than one that can't be formed by 2 natural numbers (these numbers can't be one). The number 5 is prime, because it can only be formed by 1 X 5 or 5 X 1. So, prime numbers are only divisible by itself and one. Natural numbers are positive integers. Therefore, prime numbers are: 2,3, 5, 7, 11, 13, 17, 19, 23, etc. The ancient world knew of prime numbers for years and years. A composite number is different. A composite number is a whole number that can be divided by itself, the number 1, and other numbers. They have much more factors than prime numbers. A factor is a number that you can multiply in order to get into a new number. For example, the simple math problem of 2 X 3=6 has the factors of 2 and 3. More examples of composite numbers include: 4, 6, 8, 9, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, etc. Prime and composite numbers are very diverse. The numbers of 0 and 1 are neither prime nor composite because of many reasons. 0 is not a product of 2 factors. The number 1 is not part of any factors and it has an infinite number of divisors. Any prime number must be greater than one, so one isn't a prime number. Number 1 is a unit. An unit is a special class of numbers. Natural numbers are counting numbers from 1, 2, 3, etc. Whole numbers include the pattern of 0, 1, 2, 3, etc.



Decimals are very unique in mathematics. A decimal is a fraction whose denominator is a power of ten. They exist to the right of the decimal point. One example is that the number 1984.56 has decimals. 0.56 is known as 56 hundredths. To the right of the decimal point is tenths, hundredths, thousandths, ten-thousandths, hundred-thousandths, millionths, etc. There is a link between decimals and fractions too. 0.1 is the same as 1/10. 0.25 is the same as 25/100 or 1/4. You can break down fractions in using the lowest common denominator. So, 3/6 can break down to 1/2. In using addition, subtraction, multiplication, and dividing any number, the decimal points must be in the right place, so mathematical accuracy can be complete.

A fraction is parts to one whole. It is not part of the complete whole. For example, 1/2 of 1 is not 1, but part of 1. The top number is the numerator and the bottom number is the denominator. If the numerator is greater than the denominator, then that fraction is more than one. If it is the opposite, then that number is less than one. Adding fractions with the same denominator is easy since you only need to add the numerators. For example, 2/3 + 1/3 equals to 3/3 or one. When the numerator and denominator is the same, then the answer is always one. To add, subtract, or multiply plus divide fractions with different denominators, then people must use alternative methods like finding the least common denominator or the common denominator. In dividing fractions, you can invert the second fraction as a recoprital, because division is the opposite of multiplication. For example,

1/2 ÷ 1/6 is the same as:

1/2 X 6/1=


3 is the answer as any fraction must be simplified.

In many mathematical problems, there is addition, subtraction, multiplication, and division. The numbers added in addition are called the addends like 6 and 6 in 6+6 are the addends. The solution to 2 addends being added is called the sum. In subtraction, the largest number in the problem is the minuend, the smaller number is the subtrahend, and the answer is the difference. So, in 4-1=3, the minuend is 4, the subtrahend is 1, and the difference is 3. In multiplication, the 2 numbers being used in multiplying are the factors. The answer is the product. So, in 2 X 15 =30, the 2 factors are 1 and 15 while the product is 30. THere are four basic terms to be known in division. THe dividend is the number divided. The divisor is the number that the dividend is divided by. The quotient is the number of times the divisor will go into the dividend. The remainder is a number that is less than the divisor and is too small to be divided by the divisor to form a whole number. So, in a problem with 49474 / 7 = 7067 R 5. In this example 7 is the divisor, 49474 is the dividend, 7067 is the quotient and 5 is the remainder of the division.

plus, minus, times, divide

Order of operations

The Order of operations is one of the most important parts of Elementary Mathematics. It is a simplistic method to solve long mathmetical problems. In order to use the order of operations, rules must be utilized. First, you have to look at the problem from left to right. Then, you solve the problem first with roots and exponents, then paraenthesis, then multiplication and division, and lastly with addition and substraction. For example, if a problem exists with the following:

√(1+3) + 5, then the answer is

√4  +5

2 +5

The answer is 7.

Another problem is :

3 + 6 x (5 + 4) ÷ 3 - 7

You solve first by handling the parenthesis, so the that would cause the problem to look like this:

3 + 6 X 9 ÷ 3 - 7

Then you go left and right to solve multiplication first:

3 + 54 ÷ 3 -7

Then, comes division

3 + 18 -7

21  -7

The answer is 14.

Involving numbers, there are tons of divisibility rules. One is that if a digit ends with the numbers of 0, 2, 4, 6, and 8, then it is an even number. If the sum of the digits of a number is divisible by 3, then it is an even number. There are other rules too. Math has many properties. Math properties include the associative, commutative, identity, and distributive properties.

*The commutative property is about how changing the order of addends or factors does not affect the sum or product.

Some examples include the following:

a x b = c

b x a = c

5 x 7 = 35

7 x 5 = 35

a + b =c

b + a = c

12 + 6 =18

6 + 12 = 18

*The associative property is that the order in which numbers are grounded does not affect the sum or product. Here are some examples of this:

(a + b) + c = d

a + (b+c) = d

(3+5) + 2 =10

3 + (5+2) =10

(a x b) x c = d

a + (b x c) = d

(4x7) x 3 -84

4 x (7x3) = 84

*The distributive property is when adding two or more numbers together, then multiplying the sum by a factor is equal to multiplying each number alone by the factor first, and then adding the products.

 One example is:

a (b + c) = (a x b) + (a x c)

4 (1+8) = (4 x 1) + (4X8)

4 X 9 = 4 + 32

36 = 36

*The Identity property is when the additive identity is zero, then you can add zero to the addend and the sum will equal to that addend. In Multiplication, the multiplicative identity is one. If you multiply a factor by one, the product is equal to that factor.

 Example are:

a + 0 =a


a x 1 = a

25 X 1 = 25

Problem solving deals with math too. It deals with everyday life, because we have to problem solve in terms of buying items, planning events, and learning new information as well.

By Timothy

Friday, January 26, 2018

Cold War History