Math Function 5th Grade

Introduction to math function 5th grade:

In the level of 5th grade the math functions are, algebra, fractions, decimals, place values, comparing, and division using decimal numbers, multiplication using decimal numbers, geometry, coordinate graph, measurement, probability and statistics. In this article we learn about the math functions of multiplication, division, subtraction, and addition math function sin the 5th grade.

Addition problems using decimal numbers for the math functions of 5th grade:


Problem 1:

Add the given decimal numbers 15.06 and 12. 11

Solution:

The same addition process is used in the decimal addition; put the decimals in the correct location.

15.06

+ 12.11

__________

27.17

___________

The given numbers are two digit decimal numbers, so we put decimal point before two digits.

The answer of the given term 15.06, and 12.11 is 27.17

Problem 2:

Add the given decimal numbers 23.14 and 52.64

Solution:

Arrange the given decimal numbers in the form of vertical, and put the decimal points in the correct place. The given decimal problem is a two digit decimals.

23.14

52.64

______________

75.78

________________

Place the decimal point in the correct place.

Answer of the given decimals 23.14 and 52.64 = 75.78.

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Subtraction problems using decimal numbers for the math functions of 5th grade:


Problem 1:

Subtract 24.01 from 57. 68

Solution:

Arrange the given decimal numbers in the form of vertical

57.68

24.01

Subtract the given terms in usual format and put the decimals in the correct place

57.68

24.01

___________

33.67

__________

The answer of the given decimal terms is 33.67

Problem 2:

Subtract 35. 23 from 68.56

Solution:

The given terms are arranged in vertical form

Then subtract the terms in usual format.

68.56

35.23

__________

33.33

____________

The answer of the given term is 33.33


Multiplication problems using decimal numbers for the math functions of 5th grade:


Problem 1:

Multiply 16.14 x 2

Solution:

1614 x 2

____________

3228

_____________

Steps:

Multiply the given terms in usual multiplication. Place the decimals in the correct place, in the given term is a two digit decimal points, so we put the decimal point before two digit from the right hand side. So, the answer is 32.28

The answer of the given term is 32.28

Math Division Fraction

Introduction to math division fraction:

As division of whole numbers shows how often one integer is contained in another integer, to division of fraction shows how often one fraction is contained in another. If the numerator of any fraction be made a denominator, and the denominator a numerator, the fraction of made is called the reciprocal of the former. Thus `4 / 3` is the reciprocal of `3 / 4.`

In division * as the divisor is to the dividend, of is a unit of the quotient (both in whole numbers and fraction).


Math division fraction – Steps and methods:


To dividing algebraic fraction, follow these steps:

Write the given fractions.
Change the division sign to a multiplication sign and invert the second fraction.
Write the given fraction and cancel any common factors.
Multiply the numerators.
Multiply the denominators.
We will get final answer.
Math division fraction – Methods:

Dividing common fraction
Dividing a fraction and a whole number
Dividing mixed number

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Math division fraction– Three methods and example problems:


Dividing common fractions:

To divide common fraction, follow these steps:

Invert the divisor.
Then multiply the numerator by the numerator and the denominator by the denominator.
Reduce to lowest terms if possible.
Example 1:

Find the dividing fraction

(`4 / 6` ) `-:` (`5 / 8` )

Solution:

(`4 / 6)` `-:` (`5 / 8` ) (divisor)

= (`4 / 6` ) * (`8 / 5` )

= `(4 * 8) / (6 * 5)`

= `32 / 30`

= `16 / 15`

Example 2:

Find the dividing fraction

(`5 / 9` ) `-:` (`4 / 9` )

Solution:

(`5 / 9` ) `-:` (`4 / 9` ) (divisor)

= (`5 / 9` ) * (`9 / 4` )

= `(5 * 9) / (9 * 4)`

= `45 / 36`

= `5 / 4`

Math division fraction and a whole number:

To divide a fraction and a whole number, follow these steps:

Change the whole number to a fraction by the placing the whole number over one.
Invert the divisor.
Then multiply the numerator by  numerator and  denominator by denominator.
Reduce to lowest terms if possible.
Example 1:

Find the dividing fraction

12 `-:` (`3 / 7` )

Solution:

12 `-:` (`3 / 7` )

= (`12 / 1` ) `-:` (`3 / 7)`

= (`12 / 1` ) * (`7 / 3` )

= `(12 * 7) / (1 * 3)`

= ` 84 / 3`

= 28

Example 2:

Find the dividing fraction

8 `-:` (`12 / 5` )

Solution:

8 `-:` (`12 / 5` )

= (`8 / 1` ) `-:` (`12 / 5` )

= (`8 / 1` ) * (`5 / 12` )

= `(8 * 5) / (1 * 12)`

= `40 / 12`

= `10 / 3`

Dividing mixed number fraction:

To divide mixed numbers, follow these steps:

Change the mixed number to an improper fraction
Invert the divisor.
Then multiply the numerator by numerator and denominator by denominator.
Reduce to lowest terms if possible.
Example 1:

Find the dividing fraction

(2 `6/5` ) `-:` (`7 / 2`

Solution:

(2 `6/5` ) `-:` (`7 / 2` )

= (2 `6/5` ) = `((2 * 5 + 6) / 5)` = `16 / 5`

= (`16 / 5` ) `-:` (`7 / 2` )

= (`16 / 5` ) * (`2 / 7` )

= `(16 * 2) / (5 * 7)`

= `32 / 35`

Example 2:

Find the dividing fraction

(4` 7/3` ) `-:` (`6 / 5` )

Solution:

(4 `7/3` ) `-:` (`6 / 5` )

= (4 `7/3` ) = `((4 * 3 + 7) / 3)` = `19 / 3`

= (`19 / 3` ) `-:` (`6 / 5` )

= (`19 / 3` ) * (`5 / 6` )

= `(19 * 5) / (3 * 6)`

= `95 / 18`

Word Problems Slope Math

Introduction to word problems slope math:

Slope of line is a number that tells about the slant characteristics of a given equation. If the line is perfectly level the slope is at origin that is 0. If, the line gets up, we say it is sloping up or positive slope. Slope is based on the ratio of the "rise" divided by the "run" between two points on a line, and the ratio of the altitude change to the horizontal distance between any two points on the line.

If y is a linear function of x, after that the coefficient term of x is the slope of the line shaped by graphing the function. Therefore, if the equation of the line is known in the form

The slope, y = mx + b

Where m = slope.

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Word problems slope math – Example problems:


Example 1:

The average lifespan of American women has been tracked, and the model for the data is y = 0.2t + 75, where t = 0 corresponds to 1960.  Explain the slope and y-intercept.

Solution:

The average lifespan of American women has been tracked, and the model for the data is y = 0.2t + 75,

Where t = 0 corresponds to 1960.

y = mx + b

y = 0.2t + 75

y = 0.2(0) + 75

y = 0 + 75

y = 75

In 1960 (when they started counting), the average lifespan of an American woman was 75 years.

Example 2:

Fisherman in the Finger Lakes Region has been recording the departed fish they encounter while fishing in the region. The number of fish deaths y for a specified pollution index x is y = 8.607x + 121.96. What is the slope and y-intercept?

Solution:

Slope: It is m = 8.607. These values tell that, for each increase by 1 in my input variable x, I get an increase of 8.607 in my output variable y.

It means for every one increase in the pollution index by one unit, there are nine or ten more fish deaths during the year.

y = mx + b

y = 8.607x + 121.96

When x = 0, what is the value of y

y = 8.607(0) + 121.96

y = 0 + 121.96

y = 121.96

Looking at the equation, I see that y = 121.96

The y intercept means that, even if the index were zero, there would still be about 122 fish deaths a year anyway.

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Word problems slope math - Practice problems:


Word problems slope math problem 1:

The average life span of Russian men has been tracked, and the model for the data is y = 5.2t + 85, where t = 0 corresponds to 1980.  Explain the slope and y-intercept.

Answer: y = 85 average lifespan of Russian  men

Word problems slope math problem 2:

The equation for the speed (not the height) of a ball that is thrown straight up in the air is given by y = 115 – 25t, where v is the velocity (in feet per second) and t is the number of seconds after the ball is thrown. With what initial velocity was the ball thrown? What is the slope and y intercept?

Answer: It was launched upward at 115 feet per second.

Maths Properties Learning

Introduction for learning maths properties:

In maths, we can see many properties for learning. There are three basic properties present in maths they are associative, commutative and distributive property. These three properties of maths are used in wide area.  Along with these properties we can simplify the expressions given. In this article let us start learning about the maths properties.


Properties in maths for learning:

The properties that are used for learning is given here,

Associative property
Commutative property
Distributive property
Additive identity
Multiplicative identity

Learning properties in maths:

Here we start learning about all the properties in the math.

Associative property:

In this property it does not matter how we group the numbers but the answer obtained in the end is same. Hence this associative property is very efficient. This is same for both addition and multiplication. The associative property for learning is given as,

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

(a * b) * c = a * (b * c)

For example,

(2 + 3) + 5 = 2 + (3 + 5)

5 + 5 = 2 + 8

10 = 10

Commutative property:

When we change the order of the operation it does not changes the answer obtained in evening. This property is also common for both the addition and multiplication. The commutative property for learning is given as,

a + b = b + a

a * b = b * a

For example,

4 * 2 = 2 * 4

8 = 8

Distributive property:

In this property we can do the addition and also the subtraction in combined forms. The parenthesis that is used in this property is used to separate the operation. The distributive property for learning is given as.

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

For example,

5 (2 + 3) = 5 * 2 + 5 * 3

= 10 + 15

= 25.

Additive identity:

In this property when any number is added with the number zero we get the same number as the answer.

a + 0 = a = 0 + a

For example,

3 + 0 = 3 and 0 + 3 = 3

Multiplicative identity:

When we multiply the number with 1 we get the same number as the answer. Thus this is referred as multiplicative identity.

a * 1 = a = 1 * a

For example,

2 * 1 = 2 and 1 * 2 = 2.

Solve Inequality Math

Introduction of solve inequality math:
In mathematics, an inequality is a statement about the relative size or order of two objects or about whether they are the same or not (See also equality).

The notation a < b means that a is less than b.

The notation a > b means that a is greater than b.

The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other one.

Source: Wikipedia


Properties of solve inequality math:


Trichotomy property for solve inequality math:

For any real number, a and b, exactly one of the following statements is true:

pq

The trichotomy property indicates that exactly one of the following statements is true about any two real numbers. Either

The first is less than the second
The first is equal to the second, or
The first is greater than the second one.


Transitive property for solve inequality math:

If p,q and s are real numbers with p
If p,q and s are real numbers with a>b and b>c, then a>c.

The first part of the transitive property indicates that:

If a first number is less than a second number and the second is less than a third, then the first number is less than the third.

The second part is similar, with the word “is greater than” substituted for “is less than”.

Addition property for solve inequality math:

Any real number can be added to (or subtracted from) mutually sides of an inequality to produce another inequality with the same direction.

To solve the addition property, we add 6 to both sides of the inequality 2<6 br="" get="" to="">
6+2<6 br="">
8<12 br="">
We note that the < sign is unmovable (has the similar direction).

Subtracting 6 from both sides of 36<46 br="" change="" direction="" does="" either.="" inequality="" not="" of="" the="">
36-6<46-6 br="">
30<40 br="">
Multiplication property for solve inequality math:

If both sides of an inequality are multiple (or divided) by a positive number, another inequality results wilt the same direction as the original inequality.

To solve the multiplication property, we multiply both sides of the inequality -3<6 3="" br="" by="" get="" to="">
3(3)<3 br="">
9<18 br="">
The < symbol is unaffected.

Dividing property for solve inequality math:

Dividing both sides by 4 does not change the direction of the inequality either.

`-8/4`<`12/4`

-2<3 p="">
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Example for solve inequality math:


To solve the inequality -12≤6a+3<7 br="">
Solution:

This inequality means that 6x+3 is between -12 and 7. We can solve it by isolating a between the inequality symbols.

-12≤6a+3<7 br="">
-15≤6a<4 br="">
-15≤6a<4 br="">
The solution set is {a|-15≤6a<4 br="" in="" interval="" notation="" or="">

Formal Problem Statement

Definition of formal problem statement:

Problem arises as wrong clients will confirm up in split monthly files are wrong intended for further one month. So, Julie has to generate further than one delayed notice, which corresponds to every month, for each one customer. Followed by, Rhonda is dependable to recognize these replacement notices and combine them into one. This condition produces two grave problems. First, the workload increases considerably. Second, the separate letters infrequently slip along with a customer can receive some late notices. Please express your views of this topic Sum of Two Normal Distributions by commenting on blog.


Sample formal problem statement:


The popular of the problems, because they are described in the prescribed problem statements, mostly perform with clerical and recording errors.

Here is enhancing in workload the last half of every month. This problem occurs as the cost of seven of the relations is due on the first of the month. This condition causes problems to further office events in to time period. The human resources have a set of work to do preparing and meting out the expenses, which effect in the belated or unfinished process of the rest assignments.

Continuous problems occur commonly in applications such as representation appropriate, adaptive control, neural network training, indication processing, and trial design. Discrete optimization is a large subject unto resource allocation, network routing, policy planning.

A main issue in optimization is distinctive between global and local optima. Every other factors being equivalent, one would forever want a globally optimal solution to the optimization problem. It might not be possible to get a global solution and one should be fulfilled with obtaining a restricted solution.


Examples for formal problem statement:


Example 1: Air Conditioning in ECU Dormitories

According to the ECU operation of formal problem statement, the university seeks to supply students with a safe, healthy education environment.  Dormitories are one significant of that learning environment, because 55% of ECU students live in campus dorms and mainly of these students spend a important amount of time working in their dorm rooms.

Example 2: Safe Rides Program (from a past student group)

According to the ECU police operation of formal problem statement, the goal of the university is to support student’s logic and staff in maintaining a secure location and to improve the excellence of life at East Carolina University. Accordingly each weekend numerous students venture downtown to enjoy a good time crowded with dancing partying and drinking.

Third Grade Solve Problem

Introduction:

The third grade math consists of addition, subtraction, multiplication and division. There third grade math problems are very easy and simple, it can be easily understood by the third grade kids. It forms the basic for the fourth grade math. If we practice well and good in the third grade then its very easy for us to solve fourth grade problems. In this article we shall discuss about the problems involved in third grade solve problem. Having problem with Inverse Property of Addition keep reading my upcoming posts, i will try to help you.


Solve third grade math problem - Examples


Third grade math addition problems:

Example 1: Add the two numbers,

a) Solve: 8 + 9

Solution:

8
(+) 9
_____
17

b)Solve: 45 + 12

Solution:

45
(+)12
______
57

Third grade math Subtraction problem:

Example 2: Subtract the two numbers,

a) Solve: 56 – 26

Solution:

56
(-) 26
______
30
b) Solve: 5 – 4

Solution:

5

(-)  4
______
1


Third grade math multiplication problems:

Example 3: Multiplying two numbers,

a)      3 * 2

Solution:

3 * 2
___________
6

b)      2 * 4.

Solution:

2 * 4
______
8

Example 4: Jessica has 35 pens. Her sister has 5 times as many pens as she. How many pens do they have altogether?

Solution:

Step 1: Find the number of story pens Jessica’s sister has.

Jessica = 35 pens

Jessica sister =?

35 x 5 = 175

Jessica’s sister has 175 pens.

Step 2: Find the total number of pens they have

35 + 175 =?

35 + 175 = 210

They have 210 books together.

Example 5:Alex bought 8 boxes of orange. Each box contained 50 oranges. He then put the oranges equally into 10 bags. How many oranges did he put in each bag?

Solution:

Step 1: Find the total number of oranges Alex bought.

1 box = 50 oranges

8 boxes =?

50 × 8 = 400

Alex bought 416 oranges altogether.

Step 2: Find the number of oranges he put in each bag.

Oranges = 416

Bags =?

400 ÷ 10 = 40

He put 40 oranges in each bag.

Example 6: Andrew saved $1680. Jercy saved $1856 more than Andrew. How much did they save altogether?

Solution:

Step 1: Find how much Jercy saved.

Andrew = 1680

Jercy = 1856

1680 + 1856= 3536

Jercy saved $3536.

Step 2: Find how much they have saved altogether.

1680 + 3536 = 5076

They saved $5216 altogether.

Solve third grade math problem - practice questions

Practice problem 1: Devin bought 8 boxes of mangos. Each box contained 62 mangos. He then put the mangos equally into 12 bags. How many mangos did he put in each bag?

[Answer: 40].

Practice problem 2: Aden saved 1554Jercysaved1754 more than Aden. How much did they save altogether?

[Answer: 4862]

Practice problem 3: Jay has 42 pencils. Her sister has 7 times as many pencils as she. How many pencils do they have altogether?

[Answer: 336]

Business Math Problems

Introduction to business math problems :

Business mathematics is mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis. The Main categories in business math are,

Money math
Paying taxes
Interest
Investing
Saving
Profit and loss  and etc.,
In this article we will see few basic business math problems. I like to share this Simplifying Radical Expressions with you all through my article.

(Source: Wikipedia)


Example business math problems:


Business math problems Example 1:

A Computer Sales and services center sells pendrives for `$` 30 and laptops for `$` 2500 each.  In June, total sales were `$` 10720.  Customers bought 6 times as many pendrives as laptops. How many of each did the centre sell?

Solution:

Let L = number of laptops

Then 6L = number of pendrives.


Selling price of each laptops (L)   = `$` 2500

So, `$` 2500L

Selling price of each pendrives (6L) = `$` 30

6L (`$` 30) = `$` 180

Together, they sold for:  2500L + 180L = 2680L dollars.

But we know that the total sales were `$` 10720

Hence,

2680L = 10720

L = `10720/2680`

l= 4, 6L = 6(4) = 24


Therefore, they sold:  4 laptops and 24 pendrives.

Business math problems Example 2:

An invoice dated July 15 for products Sara bought added up to `$` 750. The terms were 3/10, n/60, f.o.b. shipping point. When the goods arrived, she paid shipment amounting to `$` 5.50. On July 20 she returned goods billed at `$` 22, and received credit therefore. Sara paid the bill on July 24. Find the amount of her check?

Solution:


Sara paid shipment in cash.

The shipment bill is outside of the invoice of `$` 750.

She returned goods worth `$` 22, so

The balance payable = `$` 750 - `$` 22

= `$` 728

Sara paid on July 24 (within 10 days), so she gets a 3% discount ( as  3/10, n/60 shipping point)

Sara pay = 728 - (728* `3/100` )

= `$` 706.6

Additional example problems for business math :

Business math problems Example 3:

John purchased a car by obtaining a simple interest loan. The car costs `$` 120000, and the interest rate on the loan is 8%. If the loan is to be paid back in monthly installments over 2 years, what will be the,

1. The interest amount paid over the 2 years,

2. The total amount to be paid back,

3. The monthly payment amount.

Solution:

Given,

Principal = P= `$` 120000

Interest rate = R= 8% =` 8/100` = 0.08

Time = T = 2 years

By formula,

Simple interest = P*R*T

1. The interest amount paid over the 2 years,

I= 120000 * 0.08 * 2

= `$` 19200

2. The total amount to be paid back,

Total payment = Principal +interest

= `$` 120000 +`$` 19200

= `$ ` 139200

3. The monthly payment amount.

= Total payment / payment time in months

= `139200 / (2 * 12)`    ( 1 year = 12 months)

= `$` 5800 per month

Exact Value of Pie Math

Introduction to exact value of pie in math:

Pie can be defined as an arbitrarily constant whose value has been given which is equal to the circumference ratio of any circle to its diameter.

Pie can also be given as a value which is equal to the ratio of a area of circle to its radius square (`pi` =A/r2).

Pie is almost equal to 3.141593 in the universal decimal notation.

Pie is absorbed in many formulae of math.

It is one of the most considerable mathematical and physical constants.

Pie is a dimensionless number i.e.) just a number without physical units.

The symbol for pie in math can be denoted as `pi`


What is the exact value of pie in math?


We can’t define the exact value of pie. The exact value can be given only by ratio.

Pie is the ratio of 22 to 7 i.e.) pie =22/7

The decimal characterization of pie which is not the exact value is as follows

pie=3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803

482534211706798214808651328066470938446095505822317253594081284811174502841027019385211055596

446229489549303819644288109756659334461284756482378678316527120190914564856692346034861045432

664821339360726024914127372458700660631558817488152092096282925409171536367892590360011330530

548820466521384146951941511609...

The value shown below for pie is to be truncated to 5 decimal places.

Pie= 3.14159

In math trigonometry the exact value of pie is equal to the value of 180 degrees. Understanding Images of Obtuse Angles is always challenging for me but thanks to all math help websites to help me out.


Example problems for exact value of pie in math:


Example 1:

Solve the following (22/7) +pie+7-76+87

Solution:

We know that the pie is the ratio of 22/7.

So, (22/7) + (22/7) +7-76+87 = 2(22/7) +22

= 44/7 +22.

28.28.

Example 2:

Solve the following 24+pie+78-76+817

Solution:

We know that the pie is the ratio of 22/7.

So, (24) + (22/7) +78-76+817 = 24+ (22/7) +78-76+817

= 24+3.14+2+817

846.14

Example 3:

Solve the following (17) +pie+pie+pie-87

Solution:

We know that the pie is the ratio of 22/7.

So, (17)+pie+pie+pie-87 = 17+3pie-87

= 104+3pie

= 104+3(22/7)

113.4

Example 4:

Solve the following pie+pie+pie+pie+pie+pie+pie

Solution:

We know that the pie is the ratio of 22/7.

So, pie+pie+pie+pie+pie+pie+pie = 7pie

= 7(22/7)

= 22

Example 5:

Solve the following (67) +pie+pie+pie-87

Solution:

we know that the pie is the ratio of 22/7.

So, (67)+pie+pie+pie-87 = 67+3pie-87

= 154+3pie

= 154+3(22/7)

163.4

Example 6:

Solve the following (7) +pie+pie-pie-7

Solution:

We know that the pie is the ratio of 22/7.

So, (7) +pie+pie-pie-7     = 7+2pie-pie-7

= pie

= (22/7)

Solving Math Problems

Introduction to solving math problems:

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. In this article we shall discuss about solving math problems. (Source: wikipedia)

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Solving math problems example


Example:

Solving the inequalities 6x – 10 > 4x +16

Solution:

The given inequalities is

6x – 10 > 4x +16

Adding the 10 on both side of equation

6x -10+10> 4x +16+10

6x>4x+26

Subtract 4x on both side of the inequality equation

2x>26

Simplifying the x

x>24/2

x>12

Example:

Solve the coefficient of the given equation

1 - 2 / (x - 3) = 12

Solution:

This equation in the form of rational expression, multiply the given expression by the denominator (x -3)

(x - 3) (1 - 2 / (x - 3)) = (x - 3)12

Simplify the above expression we get

(x - 3) - 2 = 12 (x - 3)

Multiplying the factors value and grouping the like terms in the expression.

x - 5 = 12x – 36

Add value -12x to both sides of equation and simplifying the equation

-11x - 5 = - 36

Add value + 5 to both sides of the equation

-11x = - 31

Solve for x

x = 31 /11.

Example:

Isolating the variable x in equation

2x + 12 = x + 4y

To isolating the variable x, to get all the x terms on one side of the equation

So we need to subtract x from both sides of the given equation

2x + 12 - x = x + 4y - x

x + 12 = 4y

Get rid of the 12 on the left side of the equation

x + 12 - 12 = 4y - 12

x = 4y – 12

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Solving math practice problems


Problem:

Solving the coefficient of the equation

1 - 2 / (x - 6) = 14

Answer:

x = 92 /13.

Problem:

Solving the inequalities 5x – 12 > 4x +12

Answer:

x>24

Problem:

Isolate the variable x in equation
2x + 10 = x + 8y

Answer:

x = 8y – 10

Variables in Math

Introduction to variables in math:

A variable is a symbol that stands for a value that may vary; the term usually occurs in opposition to constant, which is a symbol for a non-varying value, i.e. completely fixed or fixed in the context of use.The concepts of constants and variables are fundamental to all modern mathematics, science, engineering, and computer programming(SOURCE:WIKIPEDIA).

Having problem with linear equations and inequalities in two variables keep reading my upcoming posts, i will try to help you.

Example problems of variables in math:

Variables in math problem 1:

Twice the sum of a number and 3 equals 18 added with the same number. Find the number using algebraic equation.

Solution:

Let y be the unknown number.

For the given statement, we have following algebraic equation

2* (y+3) =18+y

2y + 6= 18 +y

Subtracting y on both sides,

2y-y +6 = 18-y+y

y+6= 18

Subtracting 6 on both sides,

y= 18-6

y= 12

Therefore, the 12 is the number.

Answer: 12

Variables in math problem 2:

Solve the following system:

m + n = 16

2m - n = 8

Solution:

We can solve m and n by using substitution method.

Given         m + n = 16……………. (1)

2m - n = 8……………... (2)

Solve the equation (1) for n,

m+ n= 16

Subtract to the value m on both sides,

n= 16-m ………. (3)

Substitute the value n into the second equation. Then we get,

2m-(16-m) =8

2m-16+m=8

3m-16= 8

Add to the value 16 on both sides.

3m-16+16= 8+16

3m= 24

Divide by the value 3 on both sides.

m=8

Substitute the value of m into the equation (1).

8+n=16

Add the value -8 on both sides.

n= 16-8

n=8

Answer: m=8 and n=8

Variables in math problem 3:

Solve the equation 7(-5y - 3) - (5y - 4) = -6(4y + 6) + 3

Solution:

Given the equation 7(-5y - 3) - (5y - 4) = -6(4y + 6) + 3

First we can multiply the factor variables for both left and right hand side.

-35y - 21 - 5y + 4 = -24y - 36 +3

Here we can group the like terms on both sides.

-40y - 17 = -24y – 33

Add 20y+15 on both sides.

-40y-17+24y+33=0

-16y+16=0

Subtract 16 on both sides.

`-16y= -16`

Divide -16 on both sides.

`y= (-16)/-16`

`= 1`

Answer: y =1

Please express your views of this topic Statistical Distributions by commenting on blog.

Practice problems of variables in math:

Find x: 5x+3x-6=74
Solve: 3(y -3) + 5z - 4(y -2z -3) + 8
Answer:

x= 10
13z-y+11

Sequence Alignment

Introduction for free sequence alignment:

In this article, we will discuss about the free sequence alignment. Sequence alignment is a method of arranging the sequences. It has two types of sequences.

1. Arithmetic sequence and

2. Geometric sequence.

Arithmetic sequence means that, the sequence of numbers such that the difference between two consecutive members of the sequence is a constant. Geometric sequence means that, the sequence of numbers such that the ratio between two consecutive members of the sequence is a constant. The free sequence alignment formulas and example problems are given below. I like to share this Sum of Arithmetic Series Formula with you all through my article.


Formulas for free sequence alignment:


Sequences formulas are given below.

Formula for arithmetic sequence:

nth term of the sequence : an = a1 + (n - 1)d

Series of the sequence: sn = `(n(a_1 + a_n))/2 `

Formula for geometric sequence:

nth term of the sequence: an = a1 * rn-1

Series of the sequence: sn = `(a_1(1-r^n))/(1 - r)`

Example problems for free sequence alignment:


Example problem 1:

Find the 10th term of the given series 11, 31, 51, 71,.....

Solution:

First term of the series, a1 = 11

Difference of two consecutive terms, d = 31 - 11 = 20

n = 10

The formula to find the nth term of an arithmetic series, `a_n = a_1 + (n-1)d`

So, the 10th term of the series 11, 31, 51, 71,.... = 11 + (10 - 1) 20

= 11 + 9 * 20

= 11 + 180

After simplify this, we get

= 191

So, the 10th term of the sequence 11, 31, 51, 71,... is 191.

Example problem 2:

Find out the 6th term of a geometric sequence if a1 = 55 and the common ratio (C.R) r = 2

Solution:

Use the formula `a_n = a_1 * r^(n-1)` that gives the nth term to find `a_6` as follows

`a_6 = a_1 * r^(6-1)`

= 55 * (2)5

= 55 * 32

After simplify this, we get

= 1760

The 6th term of a geometric sequence is 1760.

The above examples are helpful to study of free sequence alignment.

Free Algebra Advice

Introduction to free algebra advice:

Branch of mathematics deals through variables and constants are called Algebra. In free Algebra advice use letters like a, b, x and y to indicate numbers. Performing addition, subtraction, multiplication, division or extraction of line on these signs and real numbers, find free algebra advice terms. Symbols in free advice algebra term are called variables of term. If two free algebra advice terms are equated, we get free algebra advice equations.


Free algebra advice : Simultaneous linear equations


Set of linear equations having regular answer set is called system of instantaneous linear equations. In earlier classes, learnt different methods of solving instantaneous linear equations in two variables. Linear equation in three unknowns declare x, y statement of equality of form ax + by + c = 0 where a, b, c are real numbers with a ≠ 0, b ≠ 0. For example 5x – 2y = 5 linear equation in 2 variables.

Solving two linear equations in x, y

Eliminate variable y.
Gain for equations in x.
Solve common manner in previous cases.
Substitute value of x in any one of two equations to obtain value of y.
Values of x and y are find out.


Understanding Identity Property of Multiplication is always challenging for me but thanks to all math help websites to help me out.

Example problem


Example:

Sum of three numbers is 24. One number is equal to half of sum of other two numbers but four times difference of them.

Solution:



Let the numbers be x, y, z.



Sum of numbers is 24  x + y + z = 24                                                     ------------ (1)



One number is equal to half of sum of other two  x = ½ (y + z)                ----- (2)



Same number is four times difference of them  x = 4(y–z) or x–4y+4z=0 ----- (3)



Let solve the equations (1), (2) and (3)



(1) + (2)  3x = 24 or x = 8



(1)  y + z = 24 – x = 24 – 8 = 16 or y + z = 16 ---------------(4)



(3) 4y – 4z = x = 8 or y – z = 2 --------------- (5)



(4) + (5)  2y = 18 or y = 9. (4)  9 + z = 16 or z = 7



Numbers are 8, 9 and 7.