What is Distributive in Math

Introduction to what is distributive in math:

The distributive is basic law in the math for the binary operation. It is used in the algebra and also the ordinary binary number. Distributive is one of the law in the math for perform the basic operations. Distributive law is based on the order of operation. Distributive is used to do the basic operation to get the correct result for the equation. Looking out for more help on factoring polynomials online in algebra by visiting listed websites.


Distributive law in math:

Take a set S and the two binary operations + and also -.

If the operation is left distributive over + and -, then the given elements are x, y and z of S. The distributive law is,

x- (y +z) = (x-y) + (x-z)

If the operation is left distributive over + and -, then the given elements are x, y and z of S. The distributive law is,

(y +z) -x = (y-z) + (z-x)


Examples for distributive in math:


Example 1 for distributive in math:

Solve the equation 3 (x+7) using the distributive law.

Solution:

The given equation is 3 (x+7).

By the distributive law, x- (y +z) = (x-y) + (x-z).

Multiply the number for both x and also 7 to get the simplified value.

3 (x+7) = 3x + 3(7)

3 (x+7) = 3x + 21

The value for the equation 3 (x+7) is 3x+21.

Example 2 for distributive in math:

Find the value for the equation 3x (13+ 7) using the distributive law.

Solution:

The given equation is 3x (13+ 7).

3x (13+ 7) = (3 x 13) + (3 x 7)

3x (13+ 7) = 39 + 21

3x (13+ 7) = 60

The value for the equation 3x (13+ 7) is 60.

Example 3 for distributive in math:

Find the value for the equation 16 x (16- 10) using the distributive law.

Solution:

The given equation is 16 x (16- 10).

16 x (16- 10) = (16 x 16) - (16 x 10)

16 x (16- 10) = 256 - 160

16 x (16- 10) = 96

The value for the equation 16 x (16- 10) is 96.

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Practice problem for distributive in math:


Find the value for the equation 2- (33 +7).
Answer: 38.

Find the value for 5 x (23 -9) using the distributive law.
Answer: 70.

Easy Way to do Division

Introduction to Easy Way to do Division:

A division method can be done by the division symbol ÷.  The number present in the left of the division symbol is dividend and the number present in the right of the division symbol is divisor. The answer you get from the division process is called quotient. The number after dividing process over the remaining number left below the division line is called as remainder. Let us see about an easy way to do division.

Shortest and Easy Way to do Division Problems

Example Problems for Dividing by 9:

Example 1:

Solve the problem using easy way to do division method.

20016 ÷ 9

Solution:

Let us write 20016/9

First find the sum of each digit adding with the next digit and the  total sum got by adding each and every number.

2 (2 + 0) (2 + 0 + 0) (2 + 0 + 0 + 1) last term is (2 + 0 + 0 + 1 + 6)

Write the terms as it is and if the total sum has any carry, it can be add it to the before term.

2 (2) (2) (3) last term is (9)

Divide the last term by the given divisor.

223 + 9/9

223 +1

224

Therefore, the division method for 20016 ÷ 9 is 224.

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Other Example Problem for Easy Way to do Division

Example Problems for Dividing by 9:

Example 2:

Solve the problem using easy way to do division method.

7875 ÷ 9

Solution:

Let us write 7875/9

First find the sum of each digit adding with the next digit and the  total sum got by adding each and every number.

7 (7 + 8) (7 + 8 + 7) last term is (7 + 8 + 7 + 5)

Write the terms as it is and if the total sum has any carry, it can be add it to the before term.

7 (15) (22) last term is (27)

(7 + 10) (5 + 20) (2) Last term is (27)

(80) (70) (2) last term is (27)

(8) (7)(2) Last term is (27)

Divide the last term by the given divisor.

872 + 27/9

872 +3

875

Therefore, the division method for 7875 ÷ 9 is 875.

Algebra Rules Made Easy

Introduction to algebra rules made easy:
As we all know that, algebra consists of constants and variables. There are certain rules and principles for solving algebra problems. Algebra rules really made easy for solving tough algebra problems. Algebra is classified into two categories; they are i) ancient algebra and ii) Modern algebra. There are certain rules to be followed in algebra. These rules are used to solve the problems in algebra. In this article, we are going to see about algebra rules made easy.

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Rules for solving algebra:


The rules for solving algebra is listed below, these rules made easy for solving algebra problems,

Rule 1: All the like terms have to be added/subtracted together on both sides of the given equation.

Rule 2: When there is a multiplication/division operation is to be performed for an equation, then it should be done on both sides.

Rule 3: Change of sign or symbols is applicable in inequalities.

Rule 4: In absolute value, negative sign is altered to positive. Positive value will always remains positive. Negative symbol only changes.

Rule 5: While adding/subtracting polynomials, same degree polynomial is to be added/subtracted in the given problem.

Rule 6: In word problems, translation of word to algebraic expressions is to be done.


Example problems on algebra rules made easy:

Example 1:

Write the equation in slope intercept form,

5y – 4x + 8 = 12

Solution:

Add 4x on both sides,

5y – 4x + 4x + 8 = 12 + 4x

5y + 8 = 4x + 12

Subtract 8 on both sides,

5y + 8 – 8 = 4x + 12 – 8

5y = 4x + 4

Divide 5 on both sides,

5y/y = 4x/5 + 4/5

y = 0.8x + 0.8

The answer is y = 0.8x + 0.8

Example 2:

Solve: (4x ^2 + 9x – 7) + (2x ^2 – 4x + 6)

Solution:

In this problem, we have to add the like terms,

= 4x ^2 + 9x – 7 + 2x ^2 – 4x + 6

= 6x ^2 + 5x - 1

The answer is 6x ^2 + 5x -1.

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Example 3:

Solve 2x + 4 > 10.

Solution:

2x + 4 > 10

Subtract 4 on both sides,

2x + 4 – 4 > 10 – 4

2x > 6

Divide 2 on both sides,

2x/2 > 6/2

x > 3

The answer is x > 3.

Math Help 5th Grade

Introduction to math help 5th grade:
The topics involved in 5th grade math help are number sense, patterns, addition, measurement, subtraction, multiplication, functions,  fractions & mixed numbers, division, algebra, decimals, adding and subtraction of decimals and probability & statistics. In this article we shall discuss about the problems involved in 5th grade math help.

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Math Help 5th Grade Problems:


Example 1:Find the area of a rectangle with base of length is 10 inches and height of 4 inches.

Solution:

Area of a rectangle = length * height

So, Area of a rectangle = 10 *  4

= 40 square inches

Example 2: Find the median of 8, 6, 9, 3, 2, 7

Solution:

Evaluate the total numbers from the given set of values.

From the given set of values, there are totally 6 numbers, Which is even,

Now arrange the total numbers in ascending order,

2, 3, 6, 7, 8, 9

As the given set of numbers is even , Sort out two middle numbers from the above given list of numbers,

Which is  6 & 7 are the two middle numbers,

In order to find the median, add both middle terms and divide by 2,

Adding both numbers `(6+7)/(2)` = 6.5

Therefore median=6.5.

Example 3: Find the value form the expanded form 2 × 10000 + 4× 1000 + 10 × 10 + 8

Solution:  2 × 10000 + 4 × 1000 + 10 × 10 + 8

= 20000 + 4000 + 100 + 8

=> 24108.

Example 4: Find the mode for given set of data. 60, 19, 15, 50, 15, 80, 30

Solution: Mode:The mode is the number that occurs most often in a set of data.

Form the given data set we can say that 15 is the number that has occurred twice.

For the given set of data, Mode = 15.

Example 5: Find the perimeter of a square with length 8.

Solution: The perimeter of a square = 4 * a ( a-> length)

Here length =5, So perimeter of square = 4 * 8 = 32.

Example 6: Find the circumference of a circle with diameter 14.

Solution:  The circumference of a circle = 3.14(pi) * diameter of the circle.

Here diameter = 10, So Circumference of a circle = 3.14 * 14

Therefore the Circumference of a circle =   43.96

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Math Help 5th Grade Practice Problems:


Problem 1:Find the area of a rectangle with base of length is 10 inches and height of 6 inches.

Answer: Area of rectangle =40 square inches.

Problem 2:Find the mode for given set of data. 6, 9, 5, 5, 1, 8, 3

Answer: Mode = 5

Problem 3: Find the value form the expanded form   8× 1000 + 12 × 10 + 10

Answer: 8130

Logic and Set Theory Learning

Introduction to Logic and Set Theory Learning:

Logic theory is a set of sentences in a formal language. The individual sentences of a theory are called as the theorems. A first-order theory is a set of first-order sentences. Many authors require that the theory be closed under logical consequence; a theory with this property can be called a deductive theory. Set theory is the studies of sets, which are collections of objects. Although any type of object can be collected into a set.

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Basic operations of logic and set theory learning


Union in Set theory Learning:
If A and B are different sets then union of A and B denoted as A U B.

For example {3, 4, 5} and {6, 7, 8} is the set {3, 4, 5, 6, 7, 8.

Intersection in Set theory Learning:
If A and B are different sets then intersection of A and B denoted as A n B.

For example {3, 4, 5} and {6, 4, 3} is the set {3, 4}.

Complement in Set theory Learning:
If A and B are different sets then A relative to set b, denoted Ac.

For example complement of {3, 4, 5} relative to {6, 4, 3} is {6}.

Symmetric difference in Set theory Learning:
If A and B are different sets then member of exactly one of A and B.

For example complement of {3, 4, 5} relative to {6, 4, 5} is {3, 6}.

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logic and set theory learning


Negation (NOT) ˜ p in logic learning:
If value of proposition is true then transform into false and vice versa.

Disjunction (OR) p v q in logic learning:
If two propositions are false then the result is false otherwise true.

Conjunction (AND) p ^ q in logic learning:
If two propositions are true then result is true otherwise false.

Conditional (IF…THEN…) p?q in logic learning :
Truth of the proposition p is sufficient to truth of proposition q.

Biconditional (IF AND ONLY IF) p?q in logic learning:
p is sufficient condition for q. q is necessary for p. Unless q not p. Not p unless q. Not p without q.

How to Explain Divide Math

Introduction for explain divide math:

In algebra basic arithmetic operation (addition, subtraction, multiplication, and division) widely used in day to day life. In these articles we are going to see about how to explain divide math. Division can be considered as repeated subtraction or equal distribution.

Simple division teach to find the how frequently one whole number called the divisor, is contain in an additional whole number, called the dividend, or to divide a whole number into some proposed number of equivalent parts, and is a small method of performing frequent subtraction.

The number arise from the procedure is called the quotient; it shows how often the divisor is contain in the dividend, that is into how many equal parts the dividend is divided.

If any thing be over following the division is performing it is called the remainder. The mark for division is ÷ it is name by and shows that the number status previous to the sign is to be divided by the number.


Explain divide math - Definition and steps:


Explain divide math - Definition:

Division is defined as an arithmetic function, which is the opposed process of multiplication. From the process of division, the proportion or ratio of two numbers be capable of be calculated.

Otherwise, the process of decision how many periods of one number is included in a further one. Symbol of division is ‘/’ or ‘÷’. If we divide a number by another number, then

Dividend = (Divisor * Quotient) + Remainder

Explain divide math - Steps:

Step1. Division of two integers by the related signs resolve be positive sign

a) Positive ÷ positive = positive

b) Negative ÷ negative = positive

Step2. Division of two integers by the unlike signs will be negative

a) Positive ÷ negative = negative

b) Negative ÷ positive = negative.


Explain divide math – Example problems:


Problem 1:

The school's Internet connection transferred 646 megabytes of data in 6 seconds. How many megabytes can it transfer in just one second?

Solution:

The school's Internet connection transferred 646 megabytes Data in 6 seconds.

So, therefore total megabytes can it transfer in just one second

= 646 ÷ 6

Step 1: Determine whether the divisor 6 will divide the first digit of the dividend 646. It will since it is not greater than this digit. The result of division is 1, which is placed under the 6.

Step 2: Determine whether the divisor 6 will divide the second digit of the dividend. Since 6 will not divide 4, a zero is placed under the 4.

Step 3: The 4 is now taken with the third digit 6 to become 46. The divisor 6 divides 46 and the quotient 7 is placed under the 7 and remainder 4. The answer is 107.66

= 107.66 megabytes

Problem 2:

There are 48 soft drink machines in the university. They hold 768 cases of soda altogether. How many cases does each machine hold?

Solution:

There are 48 soft drink machines in the university.

They hold 768 cases of soda altogether.

= 768 ÷ 48

= 16

16 cases do each machine hold.

Sixth Grade Math Fractions

Introduction

A fraction is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ?, ¾, etc.) and which consist of a numerator and a denominator, the numerator representing a number of equal parts and the denominator telling how many of those parts make up a whole. Source wikipedia

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Sixth grade math fractions problems:

Sixth grade math problem 1

Add the two fractions `2/3` and `5/3`

Solution:

The given two fractions `2/3` and `5/3`

=`2/3` +`5/3`

Add above the fraction `2/3` and `5/3`

= `(2+5)/3`

We get

=`7/3`

This can be simplified has

=2.33

Answer of the two fraction = `7/3` or 2.33

Sixth grade math problem 2

Add the two fractions `12/3` and `15/3`

Solution:

The given two fractions `12/3` and `15/3`

=`12/3` +`15/3`

Add above the fraction `2/3` and `5/3`

= `(12+15)/3`

We get

=`27/3`

This can be simplified has

=9

Answer of the two fraction = `17/3 ` or 9

Sixth grade math problem 3

Add the two fractions `22/8` and `25/8`

Solution:

The given two fractions `22/8` and `25/8`

=`22/8` +`25/8`

Add above the fraction `22/8` and `25/8`

= `(22+25)/8`

We get

=`47/8`

This can be simplified has

=5.875

Answer of the two fraction = `47/8` or 5.875

Sixth grade math problem 4

Subtract the two fractions `9/3` and `5/3`

Solution:

The given two fractions `9/3` and` 5/3`

=`9/3` -`5/3`

Subtract above the fraction `2/3` and `5/3`

= `(9-5)/3`

We get

=`4/3`

This can be simplified has

=1.33

Answer of the two fraction = `4/3` or 1.33

Sixth grade math problem 5

Multiply the two fractions `2/3` and`5/3`

Solution:

The given two fractions `2/3` and `5/3`

=`2/3` +`5/3`

Multiply above the fraction `2/3` and `5/3`

=` (2*5)/(3*3)`

We get

=`10/9`

This can be simplified has

=1.11

Answer of the two fraction = `10/9` or 1.11

Sixth grade math problem 6

Multiply the two fractions `5/3` and `5/6`

Solution:

The given two fractions `5/3` and `5/6`

= `5/3* 5/6`

Multiply above the fraction `5/3` and `5/6`

= `(5*5)/ (3*6)`

We get

=`25/18`

This can be simplified has

=1.38

Answer of the two fraction = `25/18` or 1.38