Number Word Math

Introduction to Number Word Math:

The numbers are the basic source of math. The numbers can be written in many several forms such as word form, expanded form, and standard form and also in place value form. The word form can be written for the numerals or numbers in English words. For example: 1 can be written as one, etc in math. The numbers are the symbolic representation or abstract object of math. Let us see about the numbers in word form in this article.Please express your views of this topic Adding Rational Numbers by commenting on blog.


Representation of Numbers in Word Form


The numbers can be classified into 1 to infinity. Those numbers can be written in words such as:

Counting of Word Form from 1 - 10 for Numbers in Math:

1 – The number 1 can be written as one.

2 – The number 2 can be written as two.

3 – The number 3 can be written as three.

4 – The number 4 can be written as four.

5 – The number 5 can be written as five.

6 – The number 6 can be written as six.

7 – The number 7 can be written as seven.

8 – The number 8 can be written as eight.

9 – The number 9 can be written as nine.

10 – The number 10 can be written as ten.

Counting of Word Form from 11 - 20 for Numbers in Math:

11 – The number 11 can be written as eleven.

12 – The number 12 can be written as twelve.

13 – The number 13 can be written as thirteen.

14 – The number 14 can be written as fourteen.

15 – The number 15 can be written as fifteen.

16 – The number 16 can be written as sixteen.

17 – The number 17 can be written as seventeen.

18 – The number 18 can be written as eighteen.

19 – The number 19 can be written as nineteen.

20 – The number 20 can be written as twenty.


Other Word Forms for Numbers in Math


Counting of Word Form from 21 - 30 for Numbers in Math:

21 – The number 21 can be written as twenty-one.

22 – The number 22 can be written as twenty-two.

23 – The number 23 can be written as twenty-three.

24 – The number 24 can be written as twenty-four.

25 – The number 25 can be written as twenty-five.

26 – The number 26 can be written as twenty-six.

27 – The number 27 can be written as twenty-seven.

28 – The number 28 can be written as twenty-eight.

29 – The number 29 can be written as twenty-nine.

30 – The number 30 can be written as thirty.

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Problems to Practice in Number Word Math


Example 1:

Write the given number in words?

748

Solution:

Let us write the number 748 in words like,

748 = seven hundred and forty-eight.

Example 2:

Write the given number in words?

93572

Solution:

Let us write the number 93, 572 in words like,

93, 572 = ninety-three thousand five hundred and seventy-two.

Example 3:

Write the given number in words?

403507820

Solution:

Let us write the number 403507820 in words like,

403, 507, 820 = four hundred and three millions, five hundred and seven thousands, eight hundred and twenty.

6th Grade Math Terms

Introduction to 6th grade math terms:
Studying 6th grade math terms is an essential one because it provides the foundation for solving various mathematical problems and also for learning basic operations in math.
In this article of 6th grade math terms, the various 6th grade math terms related to Number system, Pre-algebra, Algebra and Geometry are given.

6th grade math terms on Number system, Pre-Algebra and Algebra :


Numbers:

Natural Numbers

To count a given number of objects, we use numbers which we call counting numbers or natural numbers. The numbers 1,2,3,4... are called natural numbers.

Even and odd numbers

The numbers which are divisible by two are called even numbers and the numbers which are not divisible by two are called odd numbers.

Pre - algebra:

Prime factorisation

Every natural number ( except 1) is either a prime number or a composite number. A composite number may be expressed as the product of two or more prime numbers, that is they can be expressed as product of  prime factors. The process of doing this is called as prime factorisation.

Fractions

A fraction whose numerator is less than its denominator is called a proper fraction. A fraction whose numerator is equal to or greater than the denominator is called improper fraction. The sum of a whole number and a proper fraction is called as mixed fraction. Fractions that show the same amount are called equivalent fractions.

Algebra:

Algebraic equation

It refers to any equation that contains only algebraic expressions and signs of operations.

Algebraic expression

It consists of various algebraic terms connecting with the help of signs of operations. When an algebraic expression consists of only one term, it is called a monomial.When an algebraic expression consists of two terms, it is called a binomial.When an algebraic expression consists of three terms, it is called a trinomial.

Like and Unlike terms

Terms that differ in their numerical coefficients but do not differ in symbol are called like terms.Terms may or may not differ in their numerical coefficient are called unlike terms.

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6th grade math terms on Geometry:


Ray

A ray starts from a fixed point and extends endlessly in one direction.

Planes

A plane is a set of points on a flat surface that extends without end in all directions.

Collinear points

If three or more points lie on a line,then the points are called collinear points.

Concurrent lines

If two or more straight lines pass through the same point, then they are called concurrent lines. The point through which the lines pass is known as point of concurrency.

Perpendicular lines

If two lines lie in the same plane and intersect at right angles, they are called perpendicular lines.

Parallel lines

The lines that lie in the same plane and never intersect are called as Parallel lines.

Angles

An angle is formed by two rays with a common end point called the vertex. An angle which is greater than 0o but less than 90o is called an acute angle. An angle which is greater than 90o but less than 180o is called an obtuse angle. An angle of measure 90o is called a right angle. An angle of measure 180o is called a straight angle.

Complementary and Supplementary angles

Two angles are said to be complementary if the sum is equal to 90o and the two angles are said to be Supplementary if the sum is equal to180o

Math 125 Solution

Introduction to Math 125 Solution:

The four basic operations in math are subtraction, addition, division and multiplication. The simplifications can be performed using the above operations. Simplifying can be expressed in the form of algebraic expression. The solution can be obtained with decomposing numbers or else written as one’s, ten’s, hundred’s, and thousands, etc. Let us see about how to solve a math 125 solution.

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Example Problems using Place Values in 125 Math


Example 1:

Decompose the numbers 125.

Solution:

Step 1:

Let us write the given number 125.

Step 2:

Split up into (1) (2) and (5).

Step 3:

1 hundred’s + 2 ten’s + 5 one’s

Step 4:

Place the digit as it is in the above step.

Put 1 in the hundred’s place, 2 in the ten’s place and 5 in the one’s place.

Example 2:

Add the given numbers.

1, 2, 5

Solution:

Let us write the numbers one by one.

1

2

5

8

The solution for adding the given numbers is 8.

Example 3:

Subtract the given numbers 125.

Solution:

Subtraction can be performed from the highest number to the least number.

Step 1:

The number 1 can be subtracted from 2.

2

1

1

Step 2:

The number 1 can be subtracted from the number 5.

5

1

4

The solution for subtracting 125 is 4.

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More Examples to Practice for 125 in Math


Example 4:

Multiplying

5 × 5 × 5

Solution:

Step 1:

Multiplying first 5 × 5

5 ×

5

25

Step 2:

Multiplying the third term with the above result you obtained from the step (1).

25 ×

5

125

The solution for multiplying 5 × 5 × 5 is 125.

Example 5:

What solution will you obtain by adding 50 + 75?

Solution:

50

75

125

The solution for adding 50 + 75 is 125.

Example 6:

What solution will you obtain by subtracting 982 – 857?

Solution:

982

857

125

The solution for adding 982 – 857 is 125.

Define Integers in Math

Introduction to define integers in math:

In mathematics, define integer is one interesting topics in number representation. Integer has a set of numbers in which includes positive integer, negative integer and zero. An integer contains complete entity or unit. In integer, there are no fractional parts. Integer performs different arithmetic operations such as addition, subtraction, multiplication and division. Let us solve some example problems for define integers in math.

Example for define integers: 789, - 246, 0, 54, etc.

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Different rules for define integers in math:


Different rules for define integers in math are,

Integer Addition Rules:

In addition, we use the same sign. If we add the same sign integer values then we get the same sign.

Positive integer + Positive integer = Positive integer

Negative integer + Negative integer = Negative integer

Otherwise, we use different signs. We subtract the different sign integer values then we get the largest absolute value.

Positive integer + Negative integer

Negative integer + Positive integer

Integer Subtraction Rules:

In subtraction, we keep the first integer as same, change the subtraction sign to addition and change the second integers sign into its opposite then we follow the rule for integer addition.

Integer multiplication Rules:

Like addition rule,

Positive integer × Positive integer = Positive integer

Negative integer × Negative integer = Positive integer

Positive integer × Negative integer = Negative integer

Negative integer × Positive integer = Negative integer

Integer Division Rules:

Like multiplication,

Positive integer ÷ Positive integer = Positive integer

Negative integer ÷ Negative integer = Positive integer

Positive integer ÷ Negative integer = Negative integer

Negative integer ÷ Positive integer = Negative integer

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Example problems for define integers in math:


Some example problems for define integers in math are,

Example 1:

Using integer addition, simplify the given integers

782 + 854

Solution:

Given two integer numbers are

782 + 854

Both are two positive integers so, the result is also a positive numbers

Here we add 782 into 854, and then we get the result

782 + 854

1636

Solution to the given two integers is 1636.

Example 2:

Using integer subtraction, simplify the given integers

758 – 500

Solution:

Given two integer numbers are

758 – 500

Both are two positive integers so, the result is also a positive numbers

Here we subtract 758 into 500, and then we get the result

758 – 500

258

Solution to the given two integers is 258.

Example 3:

Using integer multiplication, simplify the given integers

85 × 54

Solution:

Given two integer numbers are

85 × 54

Both are two positive integers so, the result is also a positive numbers

Here we multiply 85 into 54, and then we get the result

85 × 54

4590

Solution to the given two integers is 4590.

Example 4:

Using integer division, simplify the given integers

9875 ÷ 25

Solution:

Given two integer numbers are

9875 ÷ 25

Both are two positive integers so, the result is also a positive numbers

Here we divide 9875 by 25, and then we get the result

9875 ÷ 25

395

Solution to the given two integers is 395.

Example 5:

Using integer multiplication, simplify the given integers

- 456 × 25

Solution:

Given two integer numbers are

- 456 × 25

Given integer number has both positive integers and negative integers so; the result is a negative numbers

Here we multiply - 456 into 20, and then we get the result

- 456 × 20

- 9120

Solution to the given two integers is -9120.

Example 6:

Using integer addition, simplify the given integers

- 76 + (- 112)

Solution:

Given two integer numbers are

- 76 + (- 112)

Both are two negative integers so, the result is also a negative numbers

Here we add - 76 into - 112, and then we get the result

- 76 - 112

-188

Solution to the given two integers is -188.

Math Question To Do

Introduction to math question to do:
Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences.Please express your views of this topic practice problems for algebra 2 by commenting on blog.

Now, we are going to get some of the math questions with answers.


Math questions and answers:


Example problem 1:

Simplify the expression: 2x – 21 + 21x - 3x + 20

Solution:

Add the like terms in the given expression

2x – 21 + 21x - 3x + 20 = 2x + 21x - 3x – 21 + 20

= (2 + 21 -3) x + (-21 + 20)

= 20x - 1

So, the answer is 20 x - 1.

Example problem 2:

Factor the expression completely:  x2 + 37x + 36.

Solution:

Here, a = coefficient of x2 = 1,

b = coefficient of x = 37,

c = constant = 36.

Here we find a*c = 1 × 36 = 36 and a + c = 1 + 36 = 37 = b.

By splitting the middle term,

x2 + 37x + 36 = x2 +1x + 36x + 36

= x(x + 1) + 36(x + 1)

= (x + 1) (x + 36)

Example problem 3:

Solve for the variable y: y + 28 = 39

Solution:

y + 28 =39

Subtract 28 on both sides of the equation

y + 28 – 28 = 39 – 28

y = 11

So, the answer is y = 11.

Example problem 4:

Solve for the variable m: m – 13 = 17

Solution:

m – 13 = 17

Add 13 on both sides of the equation

m – 13 + 13 = 17 + 13

m = 30

So, the answer is m = 30.

Example problem 5:

Solve for the variable t: 7t = 35

Solution:

7t = 35

Divide by 7 on both sides of the equation

`(7t) / 7 = 35 / 7`

t = 5

So, the answer is t = 5.


Few more math questions and answers:


Example problem 6:

Solve for the variable x:` x / 11` = 11

Solution:

`x / 11` = 11

Multiply 11 on both sides of the equation

`(x / 11) ` * 11 = 11 * 11

x = 121

So, the answer is x = 121.

Example problem 7:

Evaluate the expression (-2 + y) × (-2) + 21 ÷ 7 - y when y = 1.

Solution: Here, we substitute the value of 1 in the place of y,

(-2 + y) × (-2) + 21 ÷ 7 - y becomes

(-2 + 1) × (-2) + 21 ÷ 7 - 1 = -1 × (-2) + 21 ÷ 7 – 1

= 2 + 3 - 1

= 4.

So, the answer is 4.

Example problem 8:

Evaluate the expression (3 + x) × 3 + 24 ÷ 4 - x when x = 1.

Solution: Here, we substitute the value of 1 in the place of x,

(3 + x) × 3 + 24 ÷ 4 - x becomes

(3 + 1) × 3 + 24 ÷ 4 - 1 = 4 × 3 + 24 ÷ 4 – 1

= 12 + 6 - 1

= 17.

So, the answer is 17.

Example problem 9:

Find the distance between the two points (20, 7), (16, 10)?

Solution: Let d be the distance between A and B.

Then d (A, B) = `sqrt((x2 - x1)^2 + (y2 - y1)^2)`

=  `sqrt((16 - 20)^2 + (10 - 7)^2)`

=  `sqrt((-4)^2 + (3)^2)`

= `sqrt(16+9)`

= `sqrt(25)`

= 5 units.

So, the distance between the given points is 5 units.

Example problem 10:

Find the midpoint of a line segment whose end points are (9, 19) and (11, 21).

Solution:

Let us take the point A (9, 19) and the point B (11, 21) and also take the midpoint is C (x, y).

(x1, y1) = (9, 19)

(x2, y2) = (11, 21)

Midpoint: (`(1/2)` ( x1+x2), `(1/2)` ( y1+y2))

First find the x-coordinate of C.

X=` (1/2)` (x1+x2) =` (1/2)` (9+11) =20=10

Next, find the y-coordinate of C.

y= `(1/2)` (y1+y2) =` (1/2)` (19+21) =40 =20

So, the midpoint is C(10, 20)

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Practice math questions and answers:


1) Simplify the expression: 2x – 1 + 1x + 20. (Answer: 3x + 19)

2) Simplify the expression: 2x + 3y + x + 4z +y (Answer: 3x + 4y + 4z)

3) Factor the expression completely:  x2 + 38x + 37. (Answer: (x+1) (x + 37)

4) Solve for the variable y: y + 31 = 39 (Answer: y = 8)

5) Solve for the variable m: m – 1 = 17 (Answer: m = 18)

6) Solve for the variable t: 8t = 32 (Answer: t = 4)

7) Solve for the variable t: (t/3) = -1 (Answer: -3)

8) Evaluate the expression (-1 + t) × (-3) + 27 ÷ 3 - t when t = 1. (Answer: 8)

9) Evaluate the expression (-3 + t) × 2 + 24 ÷ 6 - t when t = 3. (Answer: 1)

10) Find the distance between the two points (0, 7), (6, 2)? (Answer: 7.8)

Math Problems to Solve On

Introduction to math problems to solve on algebra

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.

Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries.(Source: From Wikipedia)

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Example math problems to solve on algebra


Solve the following math problem on algebra

Example 1

Solve x^2 - x - 30 by factoring method.

Solution

To solve this math problem on algebra, we follow the following steps

Step 1:

The given quadratic equation is of the form `x + bx + c = 0` , where  `b = -1` and `c = -30`

From the given problem, find two real numbers n1 and n2 such that, n1+n2 = -1 and n1n2 = -30.

The two numbers are -6 and 5.

Step 2:

Sum of the roots = (-6) + 5

= -6+5

= -1

Step 3:

Product of the roots = (-6) (5)

= -30

Step 4:

So, we can write x2 - x - 30 as (x - 6) and (x + 5).

(x- 6) (x+ 5) = 0

Now, we can use zero product property and simplify.

(x- 6) (x+ 5) = 0

x - 6= 0 or x +5 = 0

x = 6 or x = -5

Step 5:

Answer: {6, -5}

Practice math problems to solve on algebra

1. Solve the following equations,

x + y = 11
3x - y = 5
2. Solve for z: 6z+4= 58

Answers:

(4, 7)
9
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Example math problems to solve on geometry


Solve the following math problem on geometry

Example 1

Find the area of a circle with radius 4 cm.

Solution

The area of a circle = `pi r^2` square units

here, `pi` = 3.14

r = 4 cm

So the are of the circle = 3.14 * 42 square cm

= 3.14 * 4 * 4

= 50.24 square centimeter

The area of the circle with radius 4 cm is 50.24 square cm.

Practice math problems to solve on geometry

Problem 1

What is the area of a square of side lengths 3 m.

Answer: 9 square meter.

Problem 2

Find the area of a rectangle. Given the length and breadth of the rectangle are 15 ft and 10 ft.

Answer: 150 square ft

What is a GCF in Math

Introduction to what is a gcf in math:

In math, the expansion of gcf is greatest common factor. A number which is largest number in factors of any two numbers. In other words, the gcf is dividing the other numbers in factors. The prime factors also used for gcf determination.Now we are going to see what a gcf in math. Understanding How to Find Prime Factors is always challenging for me but thanks to all math help websites to help me out.


Explanation for what is gcf in math


What is a gcf?

A factor is defined the number in multiplication. For example, 3 x 2 is indicating the multiplication operation. In this, the number 3 and 2 are called as factors. Common factor is chosen from list of factors of given numbers.

What are all the types in gcf?

We can find the greatest common factor of given numbers by using two ways. They are list the factors and list the prime factors.

What is factor method?

In this method, the given number’s factors are listed for gcf determination.

What is prime number method?

In this method, the greatest common factor is chosen from prime number list. The common prime factor is multiplied. Having problem with Surface Area of Cone keep reading my upcoming posts, i will try to help you.


More about what is a gcf in math


Example problems for what is a gcf in math:

Problem 1: What is the greatest common factor for given numbers?

36 and 25

Answer:

Given whole numbers are 30 and 25.

The factors of number 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

The factors of number 25 are 1, 5, and 25.

In this list, we choose the common factor as 1, 5.

Therefore, the greatest common factor of given numbers are 5.

Problem 2: What is the greatest common factor for given numbers?

45 and 81

Answer:

Given numbers are 45 and 81.

The factors of number 45 are 1, 3, 5, 9, 15 and 45.

The factors of number 81 are 1, 3, 9, 27 and 81.

In this list, we choose the common factor as 1, 3 and 9.

Therefore, the greatest common factor of given numbers are 9.

Exercise problems for what is a gcf in math:

1. What is the gcf value of 56 and 68?

Answer: Greatest common factor for 56 and 68 is 4.

2. What is the gcf value of 64 and 80?

Answer: Greatest common factor for 64 and 80 is 8.

7th Grade Pre Algebra Math

Introduction for 7th grade pre algebra math:

Already we study simple algebraic expressions like x + 3, 10y – 5 and so on. In 7th grade, we see how these expressions are useful in formulating pre algebra problems. We also see some examples of several expressions in this chapter on simple equations. Expressions are a central concept in pre algebra. 7th grade pre algebra Chapter is committed to algebraic expressions. When you study this 7th grade Chapter, you will know how algebraic expressions are formed, how they combined, how to find their values and how they used.


7th grade pre algebra math:


When terms have the same algebraic factors, they are like terms. An expression with only one term is called a monomial; For example, 7xy, – 5m, 3z, 4 etc.,

An expression contain two unlike terms is called a Binomial. For example, x + y, m – 5, mn + 4m, a2 – b2 are binomials.

The expression 10pq is not a binomial; because it contain one term, so it is a monomial.

The expression (a + b + 5) is not a binomial.

Since it contain three terms.

An expression which contains three terms is called a Trinomial; For example,

The Algebraic Expressions x + y + 7, ab + a +b,

3x2 – 5x + 2, m + n + 10 are trinomials.

The expression ab + a + b + 5 is, however not a trinomial; it contains four terms and not three. The expression x + y + 5x is not a trinomial as the terms x and 5x are like terms. Generally, an Algebraic Expression with one or more terms is known as polynomial. Thus a monomial, binomial and trinomial are all polynomials.

Adding and subtracting like terms of 7th grade pre algebra:

The simplest expressions are monomials. In pre algebra monomial consist of only one term. To start 7th grade pre algebra we shall learn how to add or subtract like terms. Is this topic what are variables hard for you? Watch out for my coming posts.


7th grade pre algebra math problems:


Example 1:

solve: 4x + 5x

Solution:

4x + 5x = (4 × x) + (5 × x)

Let us add 4x and 5x. We know x is a number and so also are 4x and 5x.

4x + 5x = (4 × x) + (5 × x)

= (4 + 5) × x (using distributive law)

9x = 9 × x

Similarly 3x + 4x = 7x

2) Let us subtract 4x from 7x.

7x– 4x = (7 × x) – (4 × x)

(7 – 4) × x = 3 × x

= 3x

(or) 7x – 4x = 3x.

Similarly 6x - 2x = 4x

Example 2:

solve: 2x + 4x + 3

Solution:

Take f(x) = 2x + 4x + 3

Put f(x) = 0

2x + 4x + 3 = 0

6x + 3 = 0

Subtract 3 on both side

6x + 3 - 3 = 0 -3

6x = - 3

Divide by 6 on both side

`(6x)/(6)` = `- 3/6`

x = `-1/2`

Math Solution Sentence

Introduction Math Solution Sentence

The expression with equal sign is said to be as math sentence. Thus the expression means equation where the left side is equal to right side or vice versa. Example:  (5+5=10). LHS is the sum of 5 and 5 which is equal to RHS. Math solution for sentence is to find the unknown term by using known term from the expression. Example: 7+x=14. by using known term of 7 and 14 we can find the unknown term x. Please express your views of this topic Solve Radical Expressions by commenting on blog.


Example Problems - Math Solution Sentence:


Addition math solution sentence

Example 1: What is the solution for the math sentence 80 + x = 140?

Solution:

Given:  80 + x = 140

Step 1: Subtract both sides by 80

80 + x - 80 = 140 - 80

0 + x = 60

Step 2: x = 60

Check the answer:

Step 1: By substituting value of x in the expression 80 + x = 140

80 + 60 = 140

140 = 140,

Answer: Thus the value of x = 60 is the correct solution for the math sentence

Subtraction math solution sentence

Example 2:

What is the solution for the math sentence x - 25 = 50?

Solution:

Given: x - 25 = 50

Step 1: Add both sides by 25

x - 25 + 25 = 50 + 25

x - 0 = 75

Step 2: x = 75

Check the answer:

Step 1: By substituting the value of x in the expression x – 25 = 50

75 - 25 = 50

50 = 50

Answer: Thus the value of x = 75 is the correct solution for the math sentence.

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Practice Problems - Math Solution Sentence:


Problem 1: What is the solution for the math sentence 15 + x = 45?

Answer: 30

Problem 2: What is the solution for the math sentence 220 + x = 440?

Answer: 220

Problem 3: What is the solution for the math sentence x - 55 = 45?

Answer: 100

Problem 4: What is the solution for the math sentence x - 450 = 110?

Answer: 560

Math Equation for 3 of 520

Introduction to math equation for  3 of  520:

Percentage calculation is one of the most important calculation which, every student must be aware of. Finding percentage is a calculation performed to find out the amount of portion or amount of consumption is done. Percentage calculation is said as a very important aspect because, they are used in our day to day life, almost in every field. The percentage is expressed in two forms of equations in math which is explained in the following sections. Examples to solve percentage problems, is illustrated in the following sections. I like to share this Reciprocal Definition with you all through my article.


Math equation for 3 of 520


Finding percentage in math is a calculation performed to find out the amount of portion or amount of consumption is done by a parameter of the other. As said earlier percentage calculation equation is of two types. For example: The problem, solve 3 of 520 can be expressed in two forms of equations as shown below.

Equation to solve what percent is 3 in  520 == > `(x%)/100` * 520 = 3
Equation to find 3% of 520. ==> `3/100 ` *520 = ?
The calculation of the above two formats is explained in the next section.

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Basic equation for percentage calculation:


The basic math equation for the calculation of percentage is as follows,

===>        x * `y/100` = z

where,

'x' is the whole amount

'y' is the percentage

'z' is the percentage value

Example math problems:


Here are few examples explaining the calculation of percentage using the above mentioned math equations,

Example 1:

Solve 3 of 520

Solution:

Lets assume the question in this format,

Solve what percent is 3 of 520

So the percent value = 3

The whole amount is 520

So substituting in the equation,

x * `y/100 ` = z

520 * `y/100 ` = 3

therefore,

`y/100` = `3/520` ,

y = `(3*100)/(520)`

y = `300/520`

y = 0.57%

Example 2:

Solve 3 of 520

Solution:

Lets assume the question in this format,

Solve what is 3 percent  520

So the percentage is given = 3

The whole amount is 520

So substituting in the formula,

x * `y/100 ` = z

520 * `3/100 ` = z

Therefore,

`1560/100` = z

z = `(156)/(10)`

z =` 15.6`

Therefore, 3% 0f 520 is 15.6

Properties in Math

Introduction of properties in math:

Math is the learning of measure, structure, space and change. Math is progressed from counting, calculation, measurement, and systematic learning of the shapes and motions of physical entities by the use of abstraction and logical reasoning. Math is used in the world as an important tool in various fields, such as natural science, engineering, medicine and the social sciences. Today all are working is based on mathematics. I like to share this Statistical Probability with you all through my article.


Properties in math:


Let we see about properties of math. All these properties are already defined by the mathematical experts it could not be changed. It is useful for all kinds of math.

Let us take x, y, z are real numbers, + = addition, - =subtraction, * = multiplication, / = division.

Associative Property:

Associative property refers that grouping of element within the parenthesis. It is performed for addition and multiplication and more than three values involved in it.

Associative property is defined as,

Addition: x+(y+z) = (x+y)+z

Multiplication: x*(y*z) = (x*y)*z

Example:

Find the value of 3+(6+10) and 3(6*10) using associative property.

Solution:

Given 3+(6+10)
Associative property: (3+6)+10

=9+10

=19

Given 3(6*10)
Associative property: (3*6)10

= 18*10

= 180

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Commutative Property:

It refers the changing the order of the element but does not change the result.

It is defined as,

Addition: a+b =b+a

Multiplication: a*b = b*a

Example:

Find the value of 12+98 and prove the commutative property value is equal.

Solution:

Given 12+98

=12+98= 110

Commutative property: 98+12=110

Hence, two results are equal.

Distributive property:

It defines distributing some elements. It is defined as,

Addition: a*(b+c) = ab+ac

Subtraction: a*(b-c) = ab – ac

Example:

Find the value of 5*(2+3) using distributive property.

Solution:

Given 5*(2+3)

Distributive property: (5*2) + (5*3)

= 10 + 15

= 15

Additive Identity Property:

Zero is called identity. Any value that is added with 0 it gives the same result. It is defined as,

x + 0 = x and 0 +  x = x

Multiplicative Identity Property:

Any value that is multiplied with 0 it gives the result as zero. It is defined as

x * 0 = 0 and 0 *  x = 0

Additive Inverse Property:

Any value that is added with inverse of the same value the result is zero. It is defined as

x + (-x) = 0

Multiplicative Inverse Property:

Any value that is multiplied with inverse of the same value the result is one.

x * (1/x) = 1

Now all are clear about  properties of math. Now see some more properties.


Some more properties in math:


Reflexive Property of Equality:

It is defined as result is same as question, that is x=x.

Symmetrical Property of Equal:

It is defined as x=y then y=x

Transitive Property of Equal:

It is defined as If x = y and y = z, then z = a

Substitution Property:

If x = y, then y can replace x in any equation.

Definition of Subtraction:

x - y = x + (-y)

Definition of Division:

0 / x = 0, x / x = 1, x / 0 = infinity

Now all are understood the properties of math.

Introduction Matrices Math

Introduction to matrices math:

Let us see introduction of matrices math. Matrices are the plural expression of matrix. An item in matrix is specified as specified as element. In matrix the numbers are represented by either row or column. Matrices are one of the key apparatus in math linear algebra. It is also used to represents the linear transformations.

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Definition of matrices:


The matrix is a rectangular array of numbers. It is a prearranged set of numbers. The math matrices are represented within square braces.  This is the introduction of basis matrices.

Let consider the matrix,

A=`[[2,3],[6,8]]`

The matrix A contains 2 rows and 2 columns. So it is simply called as 2 x 2 matrixes. If it contains 3 rows and 3 columns it is called as 3 x 3 matrices. There are many types of matrices in math.

Types of matrices:

There are 11 types of matrices in the introduction of math.

Type 1: Square matrices.

Type 2: oblique matrices.

Type 3: Row matrices.

Type 4: Column matrices.

Type 5: Matrices of same kind.

Type 6: Transpose of matrices.

Type 7: Zero matrices.

Type 8: Identity matrices.

Type 9: Scalar matrices.

Type 10: symmetric matrices.

Type 11: Skew-symmetric matrices.

Operations in matrices:

There are four operations in matrices. The introduction of operations is following below:

Operation 1: Addition of matrices.

Operation 2: Subtraction of matrices.

Operation 3: Multiplication of matrices.

Operation 4: Division of matrices.

Properties of matrices:

There are five properties in matrices. The introduction of properties is following below.

Property 1: Transpose of matrices.

Property 2: Inverse of matrices.

Property 3: Commutative of matrices.

Property 4: Associative of matrices.

Property 5: Distributive of matrices.

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Matrices example problem:


Let us see some introduction examples of matrices.

Problem 1:

Multiply two matrices, where the matrices are

A= `[[3,7],[5,2]]`     B = `[[6,2],[3,8]]` .

Solution:

The matrix multiplication is following below:

N = `[[3,7],[5,2]]`  * `[[6,2],[3,8]]` .

=`[[18+21,6+56],[30+6,10+16]]`

= `[[39,62],[36,26]]` .

This is the solution for the given matrices.

Problem 2:

Find the inverse matrices of given matrix.

A= `[[7,9],[3,5]]`

`Solution:`

Inverse matrices is the process of alternating the rows as columns and columns as rows.

So, A = `[[7,3],[9,5]]` .

This is the inverse matrices of given problem.

Problem 3:

Add the matrices with unit matrices. The matrix is A=`[[3,5],[7,8]]`

Solution:

The unit matrix is = `[[1,0],[0,1]]`

The addition  is  = `[[3,5],[7,8]] + [[1,0],[0,1]]`

= `[[3+1,5+0],[7+0,8+1]]` .

= `[[4,5],[7,9]]`

This is the addition of matrices.

Math Terms Product

Introduction:

Math tern Product means nothing but a multiplication of two numbers is called Math term product.Product or multiplication is one of the arithmetic operations. Multiplication operation is used in all fields.Math term of product defined simply repeated addition of given terms.For example 10 X4 means nothing but a 4 times of 10 is the meaning for Math terms of product.From the given example 4 times of 10 mean 10+10+10+10=40.This math terms is also used to solve the word problems in arithmetic.I like to share this Arithmetic Mean Formula with you all through my article.


Notation for math terms product


Evaluation of product notation:

Product notations are dot(.),(*),()(),(x)

These all are symbols are using product of two numners.

dot  (•)

It is symbol of Dot used to find the product of two variables or numbers

Star(*)

It is a symbol of star used to find the products

Parentheses ( )( )

It is a symbol for Parentheses Used for finding the multiplication of sign numbers.It is a special Symbol for only signed numbers

cross (x)

This is the  cross symbol  product in between two numbers. Understanding Define Arithmetic Mean is always challenging for me but thanks to all math help websites to help me out.


Example problems Math term Product:


Example 1:

Multiply 81 by 12

Solution:

81 and 12(it is nothing but 12 times of 81

It can written as like

=two times of 81+1 times of 81

=972

Answer =972

Example 2:

(a) Solve: 14x10= 14 times 10=140

(b) Solve: 5x5=5  times 5 = 25

(c)Solve:5x8 =5 times 8 =40

(d) Solve: 1000*14 =1000times 14 = 14000

(e) Solve: (13).(13)=13 times 13 = 169

Example : 3

A  cost of  one bags are 2 dollars. Find the  the price of 20 bags?

Solution:

Price of 1 bag  = 2 dollars

Price of 20 bags = 20x 2

Price of 20 bags = $40

Example 4:

There are 10 boys and 16 girls in the class.All boys are having individualy 2 pencil’s find the total no of pencils boys having?

solution:

Total Number of boys = 10

Total Number of girls = 16

Each boy having 2 pencils

Total no of pencils=10* 2=20

What Does Range Mean in Math

Introduction:

In math, plenty of terms are available. One of the notable terms in math is the range. Range comprises of several meanings. The meaning of range is the set of all the output values, which are produced by a function. Another common meaning for range is the value that is obtained as a result of maximum and minimum value in a given set of numbers. This article mainly focuses on finding the range value in a given set of numbers. In this article, we are going to discuss the steps involved in finding the range of given set of numbers and few example problems are given based on finding the range value. In addition, few practice problems are given for the students, which helps to understand what does the math term 'range' really meant for.


Step-by-step explanation for finding range in math:


The following steps are essential for finding the range value for given set of numbers.

Step 1: Position the numbers from ascending to descending order.

Step 2: Find the maximum value

Step 3: Find the minimum value

Step 4: Find out the difference between the given maximum and minimum value


Worked examples for finding range in math:


Example 1:

Find the range value for the given set of numbers:

24, 36, 46, 59, 34, 43, 17, 20

Solution:

Maximum value is 59

Minimum value is 17

Range     =  Maximum value - Minimum value

=  59 - 17

=  42

Hence, the range value is 42.

Example 2:

Find the range value for the given data set:

{ 67, 56, 45, 10, 24 }

Solution:

Maximum value is 56

Minimum value is 10

Range     =  Maximum value - Minimum value

=  56 - 10

=  46

Hence, the range value is 46.

Practice problems for range:

Practice problem 1:

Find the range value for the given set of numbers:

90,160,260, 50, 320, 243, 217

Answer: Range value is 270.

Practice problem 2:

Find the range value for the given data set:

{ 4, 8, 16, 64 }

Answer: Range value is 60.

Range In Math

Introduction to range in math:

In math, Data set is a collection of data, which is usually presented, in tabular form. Each column represents a variable. In math, Range is generally defined as the value we obtained as a result of difference between a greater value and a smaller value.
In other words, range is defined as the difference between a maximum and minimum value. I like to share this Domain and Range Calculator with you all through my article.

Steps to learn the range in math:


In order to learn the range of data set the following steps are necessary.

Step 1: Arrange the numbers from ascending to descending order.

Step 2: Identify the greater value in the given set

Step 3: Identify the smaller value in the given set

Step 4: Find the difference between the greater value and the smaller value to identify the range of the given data set.


Worked Examples for range in math:


Example 1:

Find the range of the data set given below:

8 , 15 , 13 , 7 , 24 , 37 , 6.

Step 1: Arranging the numbers given in data set from least to greatest.

6 , 7 , 8 , 13 , 15 , 24 , 37.

Step 2: Identify the greater value in the given set

From the given set, we can identify 37 as the greater value.

Step 3: Identify the smaller value in the given set

From the given set, we can identify  6 as the smaller value.

Step 4: Find the Range.

Range     =   Greater value – Smaller value

=   37 - 6

=  31

Hence, the range of the given data set is 31.

Example 2:

Find the range of the data set shown below:

33 , 12 , 79 , 24 , 34 , 53 , 27 , 61

Step 1: Arranging the numbers given in data set from least to greatest.

12 , 24 , 27 , 33 , 34 , 53 , 61 , 79.

Step 2: Identify the greater value in the given set

From the given set, we can identify 79 as the greater value.

Step 3: Identify the smaller value in the given set

From the given set, we can identify  12 as the smaller value.

Step 4: Find the Range.

Range    =   Greater value – Smaller value

=   79 - 12

=   67

Hence, the range of the given data set is 67.

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Practice problems for range in math:


1) Find the range of the data set shown below:

7 , 9 , 19 , 31 , 37 , 43 , 6 , 37

Answer: 37

2) Find the range of the data set shown below:

14 , 11 , 32 , 10 , 32 , 77 , 27 , 43

Answer: 67