Solve Using Addition Method

Introduction to solve using addition method:

The method of addition is the basics for mathematics. By using the addition method we can solve equations. By adding terms on the equations, we can solve the given problem. This addition method is also used for solving two set of equations.  We are going to see some example problems to solve using addition method. I like to share this Binary to Decimal Converter with you all through my article.

Example Problems to Solve Using Addition Method:

Example: 1

Solve the equation x – 5 = 25.

Solution:

Given equation is x – 5 = 25.

We need x value. For that add the number 5 on this equation x – 5 = 25

x – 5 + 5 = 25 – 5

x + 0 = 20

x = 20

Thus we can solve the given equation using addition method.

Example: 2

Solve:

x + y = 12

x- y = 2

Solution:

Given equations are,

x + y = 12 ----- (1)

x- y = 2 ---------(2)

Step 1:

For solving the equations, first add the given equations.

x + y = 12

x – y = 2

________

2x + 0 = 14

________

2x = 14

`2/2` x = `14/2`

x = 7

Step 2:

Substitute the x = 7 on equation (1)

x + y = 12

7 + y = 12

Now add -7 on the above equation.

7 + y – 7 = 12 – 7

y = 5

Answer: x = 7 and y = 5.

Example: 3

Solve the equations x + y = 3 and x – y = 7 using addition method.

Solution:

Given,

x + y = 3 ----- (1)

x – y = 7 ------ (2)

Step 1:

First add the two given equations.

x + y = 3

x – y = 7

__________

2x + 0 = 10

__________

2x = 10

`2/2` x = `10/2`

x = 5

Step 2:

Substitute the value of x = 5 on equation (1)

x + y = 3

5 + y = 3

Add -5 on above equation.

5 + y – 5 = 3 – 5

y = -2

Answer: x = 5, y = -2


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Practice Problems to Solve Using Addition Method:

Problem: 1

Solve: y -12 = 24

Answer: 36

Problem: 2

Solve:

x + y = 11

x – y = 1

Answer: x = 6, y = 5

Mathematical Symbol X

Introduction for mathematical symbol X:

Mathematical symbol X denotes unknown values in an equation.In algebra we substitute variables for representing numbers. Also  we have  learnt, how to use place holders to represent unknown numbers. Instead of place holders, we can use mathematical symbol like X to represent the unknown numbers. These  variables or letters  are said to be Literals. Mathematical symbol x denotes the unknown value or numbers in mathematical problems or an equation which has to be determined. I like to share this formulas for math with you all through my article.

Examples for Mathematical Symbol X:

Ex 1: Katie says that she has 10 more marbles in her collection than nicole. Nicole has 20 marbles, then Katie has 30.
We have to find exactly how many marbles nicole has.
Sol:
But we know that, Katie's marbles = nicole's marbles + 10.
We shall denote nicole’s marbles by the letter x. Here, x  is a un known variable,   which can may be  any value 1, 2, 3, 4,.,10,... ,20,... ,30,.
Using x, we write Katie's marbles = x + 10. Nicole has 20
Then  expression (x + 10)
x is 20, (x + 10)
=20+10 =30. katie has 30 marbles.

Ex 2: Tom and Leo are brothers. Leo is younger than Tom by 3 years.Now Tom is 12 years old,  Leo is 9 years old.
Find leo's age when Tom is 15 years old.
Sol:
Let x denote Tom’s age in years, x is a variable.
If Tom’s age in years is x, then  Leo ’s age in years is (x – 3).
The expression (x – 3) = 15-3
=12

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Problems Using Mathematical Symbol X:

Ex 1: What number added to 10 will give 15?

Sol :
10 + X = 15
X=15-10
X=5

Ex 2: Kim has 18 Dollars. She buys Apples  for 8 dollars. Find the remaining dollars with her.
Sol :
We can write it as 18 – 8 = X
X=10
Ex 3: When a number is multiplied by 9, the product is 36
Sol :
X `xx` 9 = 36.

X=`36/9`
X=4

Total Equality

Introduction to total equality:

The individuality relation is the model of the extra universal idea of a similarity relation on a set: those binary relationships which are automatic, symmetric, and transitive. The connection of equality is in addition anti symmetric. Let us see about the topic total equality are given below content. I like to share this Absolute Value Equations with you all through my article.

Example Problem for Total Equality with Expression:

Example 1:- using total equality

Let us see about the topic is total equality are given below some example problems,

Evaluate the expressions are same to another expression 1 x 10?

Solution:

The given expression is 1 x 10, we can calculate the same equality to given expression.

The term 1 x 10 is equal to 5 x 2.

Example 2:

Evaluate the expressions are same to another expression 18 x 2?

Solution:

The given expression is 18 x 2, we can calculate the same equality to given expression.

The term 18 x 2 is equal to 9 x 4.

Example 3:

Evaluate the expressions are same to another expression 1 x 10?

Solution:

The given expression is 1 x 10, we can calculate the same equality to given expression.

The term 1 x 10 is equal to 5 x 2.

Example 4:

Evaluate the expressions are same to another expression 9 x 8?

Solution:

The given expression is 9 x 8, we can calculate the same equality to given expression.

The term 9 x 8 is equal to 6 x 12.

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Practice Problem for Total Equality:

Let us see about the topic is total equality are given below some practice problems with key solution,

Problem 1:- using total equality

Evaluate the expressions are same to another expression 15 x 3?

Solution: 9 x 5

Problem 2:

Evaluate the expressions are same to another expression 20 x 5?

Solution: 4 x 25

Problem 3:- using total equality

Evaluate the expressions are same to another expression 15 x 5?

Solution: 25 x 3

Problem 4:

Evaluate the expressions are same to another expression 10 x 4?

Solution: 20 x 2

Numeric Equivalent Problems

Introduction to numeric equivalent problems
The term numeric can be viewed  as numbers especially the characters from 0 to 9.Generally the numeric equivalent problems deals with arithmetic operations like ( + ,`-`, ÷ `xx` ). based on this operation we going to see the problems like  order of operation problems and fraction problems. Here we are going to see about the article called numeric equivalent problems I like to share this What is a Equivalent Fraction with you all through my article.

Solved Numeric Equivalent Problems

Problem 1:

Find the solution for numeric equivalent  problem 9 (s – 17) – 19s - 27 = 31(s + 35)
The Solution follows below:

Given expression is,

9 (s – 17) – 19s - 27 = 31(s + 35)

Multiplying the integer terms

9s `-` 153 – 19s ` -` 27 =31s + 1085

Grouping the above terms

`-` 10s `-` 180= 31s + 1085

Add 180 on both sides

`-` 10s + 180 – 180 = 31s + 1085+180

Grouping the above terms

`-` 10s = 31s + 1265

Subtract  31s by on both sides

`-` 10s  – 31s = 31s ` -` 31s + 1265

Grouping the above terms

`-` 41s = 1265

s = `-1265/41`

The required solutions is s = s = `-1265/41`


Problem 2:

Calculate the given equation  95 `n` = – 95`n` – 1681 to find the solution for `n`.
Solutions:

Step 1: Consider the given equation,

95 `n` = – 95`n` – 1681

Step 2: Add 95 `n` on either side

95`n`+ 95`n` = – 95`n`+ 95 `n` – 1681

Step 3: Simplify the above expression, we get

190`n` =  – 1681

Step 4: Divide by 190 on either side

` (190n)/190 = (-1681)/ 190`

`n = (-1681)/ (190)`

Thus, the solutions for        `n = -8.67`

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Solved some more Numeric Equivalent Problems

Problem 3:

Solve the fraction problem
142x = `13774/142`

Solution:

The given equation is 142x = `13774/142`

To simplify an equation

142x = `13774/142`

142x = 97

Divide by 142  on both sides, we get

x = `97/142`

Answer:  The required fraction is   x = `97/142`

Problem 4:

Solve the problem 33 + 10( 36 +12) ÷ 48– 77  in method of order of operation

Solution:

Given:

`=>`  33 + 10( 36 +12) ÷ 48– 77

Step 1: we need to simplify the parentheses

`=>` 33 + 10  `xx` 48 ÷ 48 – 77

Step 2: We need to simplify the multiplication

`=>` 33 + 480 ÷ 48 – 77

Step 3: We need to simplify the division

`=>` 33 + 10 – 77

Step 4: We need to simplify the addition

`=>` 33 –  67

Step 5: We need to simplify the subtraction

`=>` – 34

Answer: 33 + 10( 36 +12) ÷ 48– 77   =  – 34.

Solve for X Percentage

Introduction to solve for x percentage:

Percentages are applied to state great or small one number is, comparative to a different amount. The first number typically characterizes a division of or modify within, the following number, that must be larger than zero. For instance, an increase of $ 0.22 for price on $ 2.00 is an increase through a fraction of 0.22 / 2.00 = 0.11. Articulated as a solve for percentage, this is therefore a 11% increase. I like to share this Solve Proportions with you all through my article.

Solve for X Percentage:

Homogeneous are method of a combination to identify how to be separated in comparatively wholesome as of other method by definite process such like centrifugation. Mathematical sums to be not a whole number.

A percentage is a technique of correspond an amount as a fraction of 100 that can be solve for percentage. It is often represent through the percent symbol %.

Uses of Percentage:

Commission
Discount
Markup
Sales tax
Price with sales tax
Shipping and handling
Simple interest
Simple interest and principal

Example Problem for Solve Percentage:
Example 1:

Solve the x percent of increase from 80 to 100.

Solution:

Step 1: 100 - 80 = 20

Step 2: change in amount = increase amount - original amount.

Step 3: Percent of change = amount change / original amount

Step 4: x = 20 / 80 = 0.25

Step 5:x =  25%

Step 6: the percent of increase x is 25%

Example 2:

Solve the x percent of decrease from 42 to 20.

Solution:

Step 1: change in amount =  original amount - decrease amount

Step 2: 42 - 20 = 22

Step 3: Percent of change =  amount change / original amount

Step 4: x = 20 / 42 = 0.48

Step 5: x = 48%.

Step 6: the percent of decrease x  is 48%. Please express your views of this topic how to find area of a trapezoid by commenting on blog.

Example Problem for Solve Percentage:

Example 3:

Solve the x percentage of decrease from 60 to 40.

Solution:

Step 1: change in amount = original amount - decrease amount

Step 2: 60 - 40 = 22.

Step 3: Percent of change = amount change / original amount

Step 4: x = 20 / 60 = 0.33.

Step 5:x =  33%.

Step 6: the percent of decrease x is 33%.

Example 4:

Solve the x percent of increase from 80 to 120.

Solution:

Step 1: 120 - 80 = 40.

Step 2: change in amount = increase amount - original amount.

Step 3: Percent of change = amount change / original amount

Step 4: x = 40 / 80 = 0.5.

Step 5: x = 5%.

Step 6: the percent of increase x is 5%.

Put Numbers in Order Calculator

Introduction to Put numbers in order calculator:-

Putting numbers in order is a math activity which starts from grade 1 up to grade 5
First graders are asked to put the one digit or two digit numbers in order.
The terms used for 1st graders are step up the numbers, step down numbers, climb up numbers, climb down numbers, numbers from small to big, numbers from big to small, numbers before, number after, number between.
For 3rd and 4th graders the terms used are ascending order and descending order.
The put up numbers  for 1st graders  are   one to two digit and for graders 2and 3 it is three digit and  four digit numbers  and for grade 5,it becomes higher order digits. I like to share this Dividing Whole Numbers with you all through my article.

Put Numbers in Order for Grade 1 by Calculator :

Grade one students are given simple numbers.
# step  up these numbers 5,3,8,1,9
Solution :- The student writes 1,3,5,8,9
#Step down these numbers 0,9,7,3,8
Solution:- the student starts counting backwards :- 9,8, 7, 3 ,0
#What comes before?
-----, 15  The student must fill up the blank.  His answer is 14
-----, 21  The students fills the blank as 20
-----, 90   The student writes  89
#What comes after ?
59,----  Here the student fills up as 60
78,-----  Here the answer would be  79
99,----- The student  knows the next number is the three digit 100
# What comes in between?
14,-----, 16    The student fills the missing number as 15
79, ----, 81     The student  fills the gap with the number 80

Put Numbers in Order for Graders 2 and 3 by Calculator

The put numbers in order for graders 2  are usually  three digit numbers
# put numbers  from small to big.
238, 345, 761, 121, 100
Solution:
Step 1: the student  looks up at the hundreds place and chooses the small number .  It is 1, there are two  number 121 and 100.
Since 100 is smaller than 121 , he puts 100, 121
Step 2: The student now looks for the number 2 in hundreds place.  The next number is 238
Step 3 : Now he looks for the number 3 in the hundreds place.  It is 345
Step 4 : The only number that is left out is 761
Step 5 : Hence he write the  small to big  order as 100,121,238,345,761
# Write the same numbers  from  big to small.
Solution : It becomes easy for the student.  He reverses the order as 761,345,238,121,100
For grade 3 it would usually be 4 digit numbers
# Put numbers in order from small to big   4,321; 6,710; , 2,111; 9,985
Solution:-
Step 1 : The student looks at the thousands place and picks up the small number 2.  Now he writes 2,111
Step 2 : The student now checks for the number 3 in thousands place. There is no such number.  SO he check for number 4 in                      thousand's place.  It is 4,321.
Step 3 :  Next he looks for any number in 5 thousands.  It is not there. so he searches for the number in 6 thousands.  It is 6,710
Step 4 : The remaining number is 9,985
Step 5 : Now the student writes the order as 2,111; 4,321 ; 6,710 ; 9,985
The same numbers can be written from big to small in reverse order as 9,985; 6,710 ; 4,321; 2,111
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Put Numbers in Order for Grader 4 and 5 by Calculator

Put numbers in order calculator for grade 4 would be numbers in ten thousand order
# Write the following numbers in ascending order:- 54,345; 53,331; 72,589; 99,999
Solution:-
Step 1: The student looks at the ten-thousands digit.  The smallest has 5 in ten thousands place.  There are two numbers.
They are 54,345 and 53,331. To choose the smaller of the two, he must look at the thousand's place.  53 is
smaller  than 54.  Hence the numbers are 53,331 and next comes 54,345
Step 2 : He looks at the other two numbers  and finds 7 comes before 9.  So the next number is 72,589
Step 3 : That places the number 99,999 in the last place
Step 4 : The student now puts the number in order as  53,331; 54,345; 72,589; 99,999
These numbers can be written in descending order as 99,999 ; 72,589 ; 54,345 ; 53,331
Now the 5th graders must deal with big numbers .
Put the numbers  in descending order:- 123,456 ;  23,456 ;  987,123;  555,555
Solution:
Step 1 : The student must count the digits first and finds three numbers have 6 digits an one number has only 5 digits.
Step 2 : In the 6 digit numbers, he looks for the bigger number in the ten-thousands place. It is 987,123
Step 3 : The next smaller number  would be 555,555
Step 4 : That leaves only the six digit number 123, 456.  So that is put in the third place
Step 5 :  The five digit number occupies the last place.  That is 23,456
Step 6 :  Hence the descending order is  987,123 ;  555,555 ; 123,456;  23, 456
The same numbers are put n ascending order as 23,456; 123,456; 555,555 ; 987, 123

Solve Complimentary Events

Solve Complementary Events

Probability is the chance of the outcome of an event of a particular experiment. An event is a one or more possible outcomes of an experiment. Probabilities are occurs always numbers between 0(impossible) and 1(possible). The set of all possible outcomes of a particular experiment is called sample space.

Complementary Events:

When one event occurs if and only if the other event does not occur, they are called complementary events. The sum of probabilities of complementary events = 1. i.e P(A) + P(A') = 1

Solve Complementary Events - Example Problems

See these solved problems to understand about complementary events.

Example 1: A bag has 9 green balls and 11 blue balls, if 3 balls are drawn at random, what is the probability of not getting all  the 3 are green balls?

Solution:

Let S be the sample space = 9 + 11 = 20

A be the event of getting all the 3 are green balls.

n(S) = C(20,3) = 1140

n(A) = C(9,3) = 84

P(A) = `84/1140` = `7/95`

P(A') = 1 - P(A)

= 1 - `7/95` = `88/95`.

Therefore the probability of not getting all the 3 are green balls is `88/95` .

Example 2: If the probability of a complementary event is `2/7`, what is the probability of an event occurring?

Solution:

P(A) = 1 - P(A')

= 1 - `2/7` =  `5/7`.

Therefore the probability of an event occurring is `5/7`.

Example 3: A bag has 7 fifty dollar bills and 10 hundred dollar bills, if 2 bills are drawn at random, what is the probability of getting both are hundred dollar bills and its complementary event?

Solution:

Let S be the sample space = 7 + 10 = 17

A be the event of getting 2 hundred dollar bills.

n(S) = C(17,2) = 136

n(A) = C(10,2) = 45

P(A) = `45/136`

P(A') = 1 - P(A)

= 1 - `45/136` = `91/136`. I have recently faced lot of problem while learning multiplication table chart, But thank to online resources of math which helped me to learn myself easily on net.

Solve Complementary Events - Practice Problems

Solve these following practice problems.

Problem 1: A bag has 8 green balls and 7 blue balls, if 3 balls are drawn at random, what is the probability of not getting all  the 3 are blue balls?

Problem 2: If the probability of a complementary event is `3/10`, what is the probability of an event occurring?

Answer: 1) `1/13` 2) `7/10`

Different Forms of Numbers

Introduction to different forms of numbers:

Let us study about different forms of numbers. The different form of numbers in mathematics refers to the various types of numbers as natural numbers, whole numbers, real rational and irrational numbers, complex numbers, integers, etc.I like to share this Real Number Definition with you all through my article.
All these forms of numbers are used in all kinds of calculations. Involving some forms of numbers in calculations will give another form of results.
Some examples with different forms of numbers are discussed below.
Different Forms of Numbers:

Different forms of numbers – natural numbers:

In mathematics the natural numbers are defined as the numbers that are with the set of positive integers starting from the value ‘1’ and ends with infinity.


Example:

N = {1, 2, 3, 4, 5, 6, 7, 8, 9……}


Different forms of numbers – whole numbers:

In mathematics the whole numbers are defined as the numbers that are with the set of positive integers starting from the value ‘0’ and ends with infinity.


Example:

W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9……}


Different forms of numbers – real numbers:

In mathematics the real numbers are defined as the numbers that are with the combination of rational and irrational numbers.


Rational numbers:

In mathematics the rational numbers are defined as the numbers that can be able to represent them in the form of simplest ratios with two integers as` p/q` , where ‘q’ should not be equal to ‘0’ at any case.


Example:

R = {`1/2` , 0.75, `-2/3` , `4/5` , `-6/7` , `8/9` , `3/10` ……}

Irrational numbers:

In mathematics the irrational numbers are defined as the numbers that cannot be able to represent them in the form of simplest ratios with two integers but it will in the form of infinite decimal values, etc.


Example:

R = {0.365489….., `sqrt(7)` , 10/3……}


Different forms of numbers – complex numbers:

In mathematics the complex numbers are defined as the numbers that are in the form ‘a + bi’, where ‘a’ and ‘b’ are real numbers and ‘i’ is the imaginary part.


Example:

C = {(1 + 1i), (2 +2i), (3 + 3i)……}


Different forms of numbers – integers:

In mathematics the integers are defined as the numbers that are with the set of both positive and negative numbers that all starts from negative side infinity and ends with positive side infinity.


Example:

I = {…..-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9……}

Comparing rational numbers

Rational numbers, sometimes abbreviated as RN are those numbers which can be expressed in the form of p/q, where q ? 0. Since 1 also can be considered for ‘q’, all whole numbers are included in this category. . Since it is only an option to include whole numbers, we will refer in the numbers in fraction form as rational numbers.

It is a natural tendency that when you see two (or more) quantities, you start comparing. Even if you those are given for any other purpose, you do compare them mentally by intuition. Similarly the RNs are also are required to be compared. With the given RNs you can identify and arrange them in order by comparing rational numbers.

Now let us see how to compare rational numbers. To compare two rational numbers, the first step is to compare the denominators and numerators. If the denominators are same, then the RN with a greater value in the numerator is greater. For example, between ¼ and ¾ , ¾ is greater among the two. On the other hand, if the numerators are same, then the RN with a lower value in the denominator is greater. For example, between 1/8 and 1/16 ,1/8 is greater among the two.

From what we explained so far, comparing the numbers with same denominator or with same numerators is very easy and mostly done mentally. However in cases of numbers with different numerators and denominators, the comparison may not be that apparent. The process of comparing RN is a bit laborious. What needs to be done first is to rewrite the equivalents of the given numbers with same denominators and now compare the numerators. But how do you find a ‘common denominator’ (which is also called as least common denominator, LCD)?

The LCD of two given RN is the lowest common multiple (LCM) of their denominators. Now take the given fractions and write their equivalents with this LCM as the denominator. Now the transformed numerators are compared for actual comparison of the given fractions. Let us explain this with an example. I have recently faced lot of problem while learning Finding the least Common Denominator, But thank to online resources of math which helped me to learn myself easily on net.

Suppose we need to compare (3)/(4) and (5)/(6). It is not apparent which is greater of the two. The LCM of the denominators 4 and 6 is 12. The equivalent fraction of (3)/(4) with denominator 12 is (9/12). The equivalent fraction of (5)/(6) with denominator 12 is (10/12). Now by comparing the numerators we find is (10/12).is greater of the two. Accordingly we conclude that (5)/(6) is greater among (3)/(4) and (5)/(6).

Geometric Distribution Expected Value

Introduction to geometric probability distribution expected value:

The geometric probability distribution is one method in statistics. The probability of possible is determined by this method and it is giving the result between 0 to 1.The expected value is in geometric probability distribution is reciprocal of the success probability. Now we are going to see about geometric probability distribution expected value. I like to share this What is Geometric Mean with you all through my article.

Explanation for Geometric Probability Distribution Expected Value

Expected value of geometric probability distribution:

The expected value is differed based on probability distribution. In geometric probability distribution, the expected value is based on probability of success. The expected value means whole probability of success.

Expected value formula in geometric probability distribution:

The expected value in single success is E(X) = `1/p` .
The expected value in geometric probability is E(X) = Σx .P(X).

more about Geometric Probability Distribution Expected Value

Example problems for geometric probability distribution expected value:

Problem 1: Find out the expected value from the probability of success p =` 3/36` .

Solution:

The given probability of success is p = `3/36` =` 1/12` .

The formula for geometric probability distribution expected value is E(X) = `1/p` .

E(X) =` 1/(1/12)` = 12.

Therefore, the expected value of geometric probability distribution is 12.

Problem 2: Find out the expected value from probabilities of getting less than 6 in dice throw.

Solution:

The probability of getting less than 6 is

x     :  1    2   3   4   5

P(x):   `1/6`   ` 1/6`   `1/6`   `1/6`   `1/6`

The expected value of geometric distribution is E(X) = Σx .P(X)  .

E(X) = 1 x `1/6` + 2 x `1/6` + 3 x `1/6` + 4 x `1/6` + 5 x `1/6` = `1/6` + `2/6` + `3/6` + `4/6` + `5/6` = `(1 + 2+ 3+ 4+ 5)/6` = `15/6` .

Therefore, the expected value of geometric distribution is `15/6` .

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Exercise problems for geometric probability distribution expected value:

1. Find out the expected value from probability of success p = `2/3` .

Solution: Expected value of geometric probability distribution is E(X) = `3/2` .

2. Find out the expected value from probability of getting 3 or 4 in dice throw.

Solution: Expected value of geometric probability distribution is E(X) = `1/3` .