Math Decimal System

Introduction to Math Decimal System:

The concept of decimal system  is also deals with the fractions whose denominators are 10, 100 or 1000 etc. In this section, a decimal can be expressed as a fraction and vice-versa. A math decimal system may contain a whole number part and a decimal part. In a decimal system, if whole number part is not given, we indicate it by writing a zero on the left of the decimal point.In math, decimal value is represented by the point.

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Decimal number system in math:


In math decimal number system, the value of a digit depends upon its place, or position, in the number.
Each place has some value of 10 times the place to its right.

To the left of  decimal point are:
Ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, etc

To the right of the decimal point are:
Tenths, hundredths, thousandths, ten thousandths, hundred thousandths, and so on..

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Decimal Conversions math:


Fractions as decimals:
A  fraction with denominator 10 can be expressed  using decimals.here we are going to convert fractions into decimals
Let us try to find decimal representation.

Example 1:
Covert the  ` 22/10`  into decimal

Solution:
We know that
`22/10` =`20+ 2/10 `

= `20/10 +2/10`

= 2 +`2/10`

= 2.2

Therefore, `22/10` = 2.2 is the decimal form

Example 2:
Write the following as a decimal:
34+ `2/10+3/100`

Solution:
34+`2/10+3/100`

=34.23 is decimal form

Example 3:
Convert the following  72+`2/100+3/1000` into decimals

Solution:
72+ `0/10 +2/100+ 3/1000 `

=72.023

Decimals as fractions:
Till now we have to know, how to write fractions with denominators 10, 2 or 3 as decimals.  we  can write a decimal number  like 2.5 as  fraction.
Take numerator as the number obtained by removing the decimal point from the given decimal.
Take denominator as number obtained by inserting as many zeros with 1  ex. 10, 100 or 1000 ,etc. as there are
number of places in decimal  number part.

Example,    Let us see 1.2 = 1+`2/10`

Example 1:
Write the terms into fractions
7.02
Solution:
Here after point placed 2 digits so the fraction is 100
=`702/100`

Example 2:
Write the terms into fractions  0.81

Solution:
Here after point placed 2 digits so the fraction is 100
= `81/100`

Example 3:
Write the terms into fractions  0.125

Solution:
Here after point placed 3 digits so the fraction is 1000
0.123 = `123/1000`

Math Division Help

Introduction to division for kids:

Division is one of the mathematical operations. The process of splitting the whole part into equal parts is called as division. The division process is indicated by a symbol ‘÷’ or ‘/’.  The first term of division is termed as dividend and the second term is termed as divisor. The answer of the division process is termed as quotient. For example, 4 ÷ 2 or 4/2 means, we have to split 4 into 2 equal parts. Here, 4 is dividend and 2 is divisor. This division process is the opposite operation of multiplication. For example, a x b = c is the multiplication operation where as c/a = b or c/b = a are division operations. This article helps to teach the division process for kids by giving simple steps for division. We are also going to see some example problems for division which helps the kids to learn division easily. I like to share this what is the algebraic expression with you all through my article. I like to share this what is the algebraic expression with you all through my article.


Explanation to help the division for kids:


The general form of division is,

Dividend ÷ divisor = quotient

Step 1:

First, we have to subtract the divisor from the dividend. If we get the subtracted answer 0 then stop the process. Other wise, again we have to subtract the divisor from the previous subtracted answer.

Step 2:

Now, we have to count the number of subtraction operation. This count is equal to the quotient.

The above steps help the kids to easily understand the division.

Example:

Consider 6 balls. If we want to split it into 3 equal groups then we need to do division operation.

6 ÷ 3

Step 1:

First, we have to subtract 3 from 6.

6 – 3 = 3

The subtracted answer is 3. So, again we need to do subtraction of divisor 3 from the previous subtracted answer 3.

3 – 3 = 0

Step 2:

We get the subtracted answer 0. So, we can stop this process. The count of subtraction process is 2.

Therefore, 6 ÷ 3 = 2


We can split the 6 balls into 3 equal groups and each group has 2 balls.

Division by 1:

The division of any number by 1 results the same number.

a ÷ 1 = a

Example: 3 ÷ 1 = 3

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Example problems to division for kids help:


Example: 1

Divide: 10 ÷ 5

Solution:

Given: 10 ÷ 5

Step 1:

First, we need to subtract the divisor 5 from 10.

10 – 5 = 5

The answer of subtraction is 5. So, again we have to subtract the divisor 5 from the previous subtracted answer 5.

5 – 5 = 0

The subtracted answer is 0.

Step 2:

The number of steps of subtraction is 2. So, when we are dividing 10 by 5, we get 2.

10 ÷ 5 = 2

Example: 2

Ram has 20 chocolates. If he wants to share it for 5 members then how many chocolates each member has?

Solution:

Given:

Total number chocolates = 20

We have to split into 5 equal groups.

20 ÷ 5

Step 1:

First, we need to subtract the divisor 5 from 20.

20 – 5 = 15

The answer of subtraction is 15. So, again we have to subtract the divisor 5 from the subtracted answer 15.

15 – 5 = 10

Again, we need to subtract the divisor 5 from the previous answer 10.

10 – 5 = 5

Again, we need to subtract the divisor 5 from the previous answer 5.

5 – 5 = 0

The subtracted answer is 0.

Step 2:

The number of steps of subtraction is 4. So, when we are dividing 20 by 5, we get 4.

20 ÷ 5 = 4

So, Ram can share 30 chocolates to 5 members and each member has 4 chocolates.


Practice problems to helps kids for division:


Problem: 1

8 ÷ 4

Answer: 2

Problem: 2

4 ÷ 1

Answer: 4

Math Integer Practice

Introduction to math integer practice:

In mathematics, integer is one important topic in number representation. Integer contains a set of numbers in which there are two types of integer which are non negative integer and negative integer. Integer has a complete entity or unit. No fractional part in integer. Integer performs the arithmetic operations of addition, subtraction, multiplication and division. Let us solve some example problems and also some practice problems for integer in math.

Example for integer:

2254, - 5164, 0 etc,


Math integer practice - Example problems:


Some example problems for integer in math are,

Example 1:

Using addition operation, simplify the given integers

1452 + 3567

Solution:

Given two integer numbers are

1452 + 3567

Given integers are positive so the result is also a positive integer

Here we add 1452 into 3567, and we get the result

1452 + 3567 = 5019

Solution: 5019

Example 2:

Using subtraction operation, simplify the given integers

1858 – 964

Solution:

Given two integer numbers are

1858 – 964

Given integers are positive so the result is also a positive integer

Here we subtract 1858 into 964, and we get the result

1858 – 964 = 894

Solution: 894

Example 3:

Using multiplication operation, simplify the given integers

5467 × 2487

Solution:

Given two integer numbers are

5467 × 2487

Given integers are positive and the result is also a positive integer

Here we multiply 5467 into 2487, and then we get the result

5467 × 2487= 3596429

Solution: 13596429

Example 4:

Using division operation, simplify the given integers

1856 ÷ 32

Solution:

Given two integer numbers are

1852 ÷ 32

Given integers are positive and the result is also a positive integer

Here we divide 1852 by 32, and then we get the result

1852 ÷ 32 =  58

Solution: 58

Example 5:

Using multiplication operation, simplify the given integers

3275 × - 137

Solution:

Given two integer numbers are

3275 × - 137

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

Here we multiply 3275 into - 137, and then we get the result

3275 × - 137 = - 448675

Solution: - 448675

Example 6:

Using addition operation, simplify the given integer

- 1206 + (- 2752)

Solution:

Given two integers is

- 1206 + (- 2752)

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

Here we add - 1206 into - 2752, and then we get the result

- 1206 - 2752 = - 3958

Solution: - 3958.

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Math integer practice - Practice problems:


Problem 1:

25056 + 10745

Answer: 35801

Problem 2:

7856 – 3745

Answer: 4111.

Problem 3:

526 × 415

Answer: 218290

Problem 4:

`3350/134`

Answer:  25

Problem 5:

- 1006 + 63

Answer: - 943

Problem 6:

- 56 – 2045

Answer:  - 2101.

Problem 7:

- 199 × 2451

Answer:  - 487749

Problem 8:

`1972/34`

Answer:  58

Average Formula Math

Introduction of average:

In mathematics,when the addition of given terms is divided by the total number of terms, it is called average. The other name of average is mean. It is used in educational institutions and in industries. In educational the student performance is calculated by using this average.If the average is high then the object is good other wise it is bad. Understanding Calculate Weighted Average is always challenging for me but thanks to all math help websites to help me out.


Average formula in mathematics:


Average formula in mathematics:

Formula for average is,

Average=Addition of given terms/ Total number of terms

Consider if there are n terms and if we want to find the average of first terms means then the formula of average in maths in written as follows.

Average=`(n_1+n_2+n_3+n_4+n_5)/n`

It also produces the mean value of the given numbers. If the given number set is odd, then the centre value is the mean or average value of the given set. For the above formula the average value may be n3


Examples for average in maths:


Examples for average in maths:

Example:1

Neha got the marks as follows. Tamil:93, English:88, Maths:100, Science:99, Social science:96 Find the average of Neha.

Solution:

Given,

Step 1: Total number of subjects are 5

Step 2:

Tamil (T)=93

English(E)=88

Mathe(M)=100

Science(S)=99

Social science(SS)=96

Step 3: Formula for finding average is,

Average=`(T+E+M+S+SS)/(Total)`

=`(93+88+100+99+96)/5`

=`476/5`

=95.2

Average of Neha is 95.2. The average of this student is high hence the performance of the student is good.

Example:2

Find the average of given set of values. 22,55,33,44

Solution:

Step 1:Given numbers are 22,55,33,44

Step 2:Total number of terms are 4

Step 3: Formula for finding average=Sum of given terms/Total number of terms

=`(22+55+33+44)/4`

= `154/4`

= 38.5

Average of the given numbers 22,55,33,44 is 38.5

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Practice problems for average in maths:


Problem:1

Find the average of n numbers. The numbers are 89,56,23,100,58,48,79,84

Ans:67.125

Problem:2

Find the average of n numbers. The numbers are 98,65,32,85,97,80,63

Ans:74.28

Problem:3

Calculate average for the given numbers. 1,1,3,17,19,25

Ans:11

Simple Solutions Math

Introduction to simple solutions math:

The simple solutions include the algebraic solutions using the simple operations like addition, finding the factors for the equation and also find the values for the linear equations. The simple solutions for the math include the basic operations for the complex numbers. The basic operations include the addition, subtraction, multiplication and also the division. Please express your views of this topic Absolute Value of a Complex Number by commenting on blog.


Examples for simple solutions math:


Example 1 for simple solutions math:

Find the value of x for the linear equation 2x +80 =12.

Solution:

The given linear equation is 2x +80 =12.

Subtract 80 on both sides of the equation to get the value of x.

2x+80-80 =12-80

2x= -68

x= -34

The value of x for the linear equation x+54 =10 is -34.

Example 2 for simple solutions math:

Find the values of x and y from the equation 2x+ 2y =5 and x - 2y = 10.

Solution:

The given equations are 2x+ 2y =5 and x - 2y = 10.

For finding the values for the equations, first remove x or y from the two equations.

2x+ 2y =5

x - 2y = 10

-----------------

3x =15

-----------------

Divide by 3 on both sides of the equation.

`(3x)/3` =`15/3`

x =5

Substitute the value of x in the equation (1) to get the value of y.

2 (5)+ 2y =5

10+ 2y =5

Subtract by 10 on both sides of the equation.

10+ 2y-10 =5-10

2y =-5

y =-`5/2`

The values of x and y for the equation 2x+ 2y =5 and x - 2y = 10 are x=5 and y=-`5/2` .

Example 3 for simple solutions math:

Find the value for the complex number (2+10i) + (3+16i).

Solution:

The given complex number is (2+10i) + (3+16i).

In this we have to add two complex numbers. Add the real part separately and add the imaginary part separately.

(2+10i) + (3+16i) = (2+3) + (10i + 16i)

(2+10i) + (3+16i) = 5 +26i

The value for the complex number (2+10i) + (3+16i) is 10+26i.

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Practice problem for simple solutions math:


Find the value for x+31= 182.
Answer: 151

Find the roots for the algebraic equation x2+5x +15=0.
Answer:  x= -3, -5

Math The Easy Way

Introduction of math the easy way:

Mathematics plays an important role in the human life. The math is generally a simple subject which saves the time for working. The persons who understand the math in step by step manner feels the math has a easy way of subject. Those who neglect the math will sure losses the part of knowledge in their life. If we go for a purchase we should count the amount of money we have in our pocket. So the math is the easy way for solving. Please express your views of this topic Formula for Pythagorean Theorem by commenting on blog.


The easy way of math:


Math is the easy way for understand. The math is the universal acceptance of the language throughout the world. The c, c++ is the languages which are similar to math. The math involves in every fact in our life. The math can’t be changed due to the changes for the location or the weather variation in the area.

The equal sides intersect and center of the edge is made opposite to this vertex. The two angles are made to join with the edges. The three sides are same, which goes the angles are made same. In equilateral triangles there are mostly symmetric which we take it through any corner to corner and any side to side. The shape is mentioned as regular shape.

Some of the rules which make math easy are,

Multiplication:

Negative * Positive = Positive

Positive *Negative = Negative

ADDITION:

Positive + Positive = Positive

Negative + Negative = Negative

Dividing Rules:

Positive ÷ Positive = Positive: 12 ÷ 3 = 4

Negative ÷ Negative = Positive: (-12) ÷ (-3) = 4

Negative ÷ Positive = Negative: (-12) ÷ 3 = -4

Positive ÷ Negative = Negative: 12 ÷ (-3) = -4

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Example for math the easy way:


Compute the simplest form of the fraction 10/14.

10/14 = (2 x 5)/ (2 x 7)

Example:            What is 5+ (-2)?

From above: + (-) becomes a negative sign.

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

Answer: 5+ (-2) = 3

Example: What is -6+ (+3)?

From above: + (+) becomes a positive sign.

-6+ (+3) = -6 + 3

Start at -6 on the number line, move forward 3, and you end up at -3

Answer: -6+ (+3) = -3.

Constant Ratio Math

Introduction to constant ratio math:

The constant ratio in math is the ratio of the two numbers. Take any two numbers a and b, the ratio of those two numbers is represented as a: b, in this b must be the non zero number. The multiplication and division of the terms of the ratio by the same number does not affect the ratio. The constant ratio can also be represented as a/b. Please express your views of this topic Math Ratios by commenting on blog.


Examples for constant ratio math:


Example 1 for constant ratio math:

The mixture contains the water and the oil in the ratio 3:8. The water is 100 liters. What is the quantity of the oil?

Solution:

The  ratio of the water and the oil is 3:8.

The amount of the water is 100 liters.

Let oil be x liters.

Water/ oil= 3/8

100/ x= 3/ 8

Perform cross multiplication. We get,

100 x 8= 3x

800 = 3x

Divide by 3 on both sides of the equation. We get,

x= 800/3

x=266

The quantity of the oil in that mixture is 266.

Example 2 for constant ratio math:

Divide 200 in the ratio of 2:3.

Solution:

The given ratio is 2:3.

The sum of the ratio is 2+3 =5.

For the ratio 2,

200 x (2/5) = 80.

For the ratio 3,

200 x (3/5) = 120.

Example 3 for constant ratio math:

Find the simplified ratio for 121: 169.

Solution:

The given ratio is 121: 169

The above ratio can be written as 11^2: 13^2.

The ratio can be simplified as 11: 13.

The ratio 121: 169 can be simplified as 11: 13.

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Practice problem for constant ratio math:


Divide the amount 100 in the ratio 1: 4.
Answer: for 1 the amount is 20, for 4 the amount is 80.

The mixture contains water and alcohol in the ratio of 1: 9. The quantity of the water is 20 liters. Find the quantity of the alcohol in liters.
Answer: 180 liters.

Simplify the ratio 64: 216.
Answer: 4:6