Study Online Arithmetic

Introduction

Arithmetic is a branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting and many other calculations.

Arithmetic involves the study of the result of combining numbers. It involves in following operation:

Operation                  Symbol

Addition                                +

Subtraction                             -

Multiplication                          X

Division                                     /


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Operations in arithmetic.


Addition

Addition is a mathematical operation that represents combining collections of objects and digits together into a larger collection. It is denoted by plus sign (+).Performing addition is one of the simplest numerical tasks. Addition is written using the plus sign "+" between the terms; that is, in infix notation. The result is expressed with an equals sign.

Example:Add 34 and 14

34+14=48

Addition of 34 and 14 so denoted by (+) sign and result is 48 so denoted by (=) sign

Subtraction

Subtraction is a one of four mathematical operations that represents difference of objects and digits together into a smaller collection. It is denoted by plus minus (-).Performing addition is one of the simplest numerical tasks. Subtraction is written using the plus sign "-" between the terms; that is, in infix notation. The result is expressed with a sign. It’s inverse of addition.

Example:Subtraction of 34 and 21

Given:34 and 21

34-21=13

Subtraction of 34 and 21 so denoted by (-) sign and result is 13 so denoted by (=) sign

The traditional names for the parts of the formula:

C − B= A

Where:C=minuend

B= subtrahend

A=difference

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Multiplication and division of arithmetic problems


Multiplication

Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in arithmetic. It multiplies one number with other and increases or doubles the number.

Denoted by symbol (X or *)

Now  we  study folowing example.

Example:Multiply 2 and 4?

Given: 2 and 4

4X2=8

Division

Mathematics, especially in elementary arithmetic, division is the arithmetic operation that is the inverse of multiplication.

Denoted by symbol (/ or ÷)

a/b=c

Note:b not equal to zero

In the above expression, a is called the dividend, b the divisor and c the quotient

Example:Divide 4 and 2

4/2=2

Solve Online Estimation

Introduction:

Estimation is defined as the method which is used to simply the calculation in easy way. Estimation is the process of values taken for adding and subtracting to change the value into nearest and easier numbers for simplification. In considerations of small values in calculations they are changed to their nearest 10’s and for largest values of calculations they are changed to their nearest 50’s and 100’s.

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Solve Online Estimation – Online Example


Solved Problems:

Example 1: Estimate 84 + 99.

Solution:

84 is changed to the nearest value 80 (i.e. nearest 10’s since it is the smallest value)

99 is changed to the nearest value 100 (i.e. nearest 10’s since it is the smallest value)

80 + 100 = 180

Example 2: Estimate 78 - 62.

Solution:

78 is changed to the nearest value 80 (i.e. nearest 10’s since it is the smallest value)

62 is changed to the nearest value 60 (i.e. nearest 10’s since it is the smallest value)

80 - 60 = 20

Example 3: Estimate 274 + 299.

Solution:

274 is changed to the nearest value 250 (i.e. nearest 50’s since it is the largest value)

299 is changed to the nearest value 300 (i.e. nearest 100’s since it is the largest value)

250 + 300 = 550

Example 4: Estimate 218 - 56.

Solution:

218 is changed to the nearest value 200 (i.e. nearest 100’s since it is the largest value)

56 is changed to the nearest value 50 (i.e. nearest 50’s since it is the largest value)

200 - 50 = 150

Example 5: Estimate 329 - 54.

Solution:

329 is changed to the nearest value 300 (i.e. nearest 100’s since it is the largest value)

54 is changed to the nearest value 50 (i.e. nearest 50’s since it is the largest value)

300 - 50 = 250

Example 6: Estimate 418 - 108.

Solution:

418 is changed to the nearest value 400 (i.e. nearest 100’s since it is the largest value)

108 is changed to the nearest value 100 (i.e. nearest 100’s since it is the largest value)

400 - 100 = 300


Solve Online Estimation - Online Practice


Practice Problems to solve

Problem 1: Estimate 74 + 48

Answer: 120

Problem 2: Estimate 294 – 273

Answer: 50

Quotient Online

Introduction for Quotient:

A quotient is obtained as a result of dividing two integers, where the quotient is the integer part of the result. While dividing two numbers such that 15/3, the quotient would be 5 where the remainder is zero. The quotient has been mainly used to indicate the algebraic structures, sets and spaces where the entities are the equivalence classes of some equivalence relation in a set.

In this article we are going to see some answers for the quotient online.

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Online answers for quotient:


This topic includes some online questions and answers for the quotient.

Example 1: Find the quotient of 1000 / 5.

Solution: As we know already quotient will be obtained by dividing the two given integers.

Given: 1000/5

Here 1000 is referred to as the numerator (dividend) and 5 is said to be the denominator (divisor).

1000/5 = 200

Thus the result of division of two integers 200 is called as the quotient.

Example 2: Find the quotient, remainder of 9/2

Solution: Here 9 is called as the dividend and 2 is the divisor, when the dividend is not exactly divided by the divisor then it yields a remainder.

Given: 9/2

9/2 = 4

4*2 = 8

9-8 = 1.

After the completion of the division process 1 remains which is said to be the remainder.

Here the quotient is four.

Example 3: Find the quotient of 12/4

Solution:

Here 12 is said to be the dividend and 4 is said to be the divisor

When we divide the two integers then we get the quotient.

12/4 = 3

Hence the quotient is 3

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Practice problems for online quotient:


Here there some practice problems given online fir the topic of quotient.

1) Solve the following and find the quotient of 125 / 5

Solution: The quotient is 25.

2)  Find the quotient of 111/10 and also the remainder

Solution: Quotient: 10, Remainder: 1

Solve Algebra Word Problems Online

Algebra, which is derived from the Arabic word al–jabr. In Arabic language, ‘al’ means ‘the’ and ‘jabr’ means ‘reunion of broken parts’. The usage of the word algebra can be understood by a simple example. In the equation x + 5 = 9, the left hand side is the addition (sum) of two parts x and 5. If we add (unite) (–5) to each side of the equation, we get

(x + 5) + (–5) = 9 + (–5) or x + [5 + (–5)] = 9 – 5 or x + 0 = 4 or x = 4.

Here 9 and -5 are reunited to get 4. This type of mathematics is called algebra.

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Problem 1:


The sum of twice a number plus 13 is 75.  Find the number.

Solution:

Given : The sum of twice a number and 13 equals 75.

By using the numbers and a variable that represents something, N in the case (for number),

You can write the equation with the given problem

2N + 13 = 75

By solving the equation we can get the value for variable

2N + 13 = 75     Equation.

- 13 = -13     Add (-13) to both sides.

______________

2N      =  62

N       =  31     Divided both sides by 2.

So, the answer is N= 31

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Problem 2:


The number which is decreased by 24 is 5 times its opposite. find number.

Solution:

opposite means negative.By the given question we can make an equation and it describes the problem

N - 24 = 5(-N)        Equation.

N - 24 = -5N          Multiplied out.

5N + 24    5N + 24     Add (5N + 24) to

_______________________     both sides.

6N      =       24

N = 4            Divide both sides

by 6 to isolate N

So the answer is N= 4

Practice College Algebra Online

Introduction :

College algebra is one important topic in mathematics. College algebra is used for the known quantities to determine the unknown quantities. In place of numbers, sometimes letters can be used. It includes the different topics such as polynomials, equation, expression, equation of a line, Cramers rule and slope of a line. Let us discuss some practice problems in college algebra through online.


Example problems for practice college algebra online:


Example 1:

Factorize: 45xy -18ya + 60xb -24ab using factor by group

Solution:

Step 1:

Given expression 45xy- 18ya + 60xb -24ab

Step 2:

Given expression in the standard form ax² + bx + c = 0

45xy- 18ya + 60xb -24ab = 0

Step 3:

Groups the terms

45xy- 18ya + 60xb -24ab = 0

(45xy + 60xb) - (18ya – 24ab) = 0

Step 4:

Determine the greatest common factor for the expression given

15x (3y – 4b) – 6a (3y – 4b) = 0

(15x – 6a) (3y – 4b) (3y – 4b) = 0

Solution to the given equation is (15x – 6a) (3y – 4b) = 0.

Example 2:

Find the slope of a line for the given points (4, 6) and (8, 9)

Solution:

For finding the slope of a line, we use this formula

`m = (y_2 - y_1)/(x_2 - x_1)`

Here the given points of (x1 , y1) and (x2, y2) are substituted in the formula.

`m = (9 - 6)/(8 - 4)`

`m = (3)/(4)`

`m = (3)/(4)`

Solution to the slope of a line is m = 3/4.

Example 3:

Find the equation of a line which passes through the line (-3,4) with slope of -3.

solution:

Given:

x1= -3, y1 = 4 and slope m = -3

Equation of a point slope form equation is

y - y1 = m (x - x1)

y - 4 = -3(x - (-3))

y - 4 = -3(x + 3)

y - 4 = -3x -9

y = -3x -5.

Solution to the equation of a line is y = -3x - 5

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Practice problem for college algebra online:


Some example practice problems for college algebra online

1). Factorize the given expression by using the factor by group method.

30xy + 40xb - 12ay - 16ab

Solution: (10x – 4a) (3y – 4b) = 0.


2). Solve the system of equation with two variables equations.

x + y = 10                       → (1)
3x - y = 6                       → (2)
Solution of the equation is (x and y) is (4, 6)

3). Find the slope of a line for the given points (5, 6) and (8, 9)

Solution: m = 1

4). Find the equation of a line which passes through the line (-5,6) with slope of -2.

Solution: y = -2x -4

Learn Online Range

Introduction :

Learn online range is the set of values that numbers can have particular starting and ending point of the value that is maximum and minimum value. In between the numbers of maximum and minimum these values said to be with in the range of given set of numbers. For example consider the set of number 1 – 5. learn online range maximum value is 5 and the minimum value said to be 1. The range will be in between the 1, 2, 3, 4, and 5.

Formula for the range = Maximum value – minimum value

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Example problem for learn online range:


Example problem :1

A student took 10 math tests in his school. What is the range of the student score in his test?

Test             Marks obtained

1                    56                                                                     

2                    85

3                    55

4                    96

5                    80

6                    65

7                    88

8                    70

9                    75

10                   76

Solution for learn online range:

Given marks are 56, 85, 55, 96, 80, 65, 88, 70, 75, and 76

Order the given test marks

After ordering the given marks: 55, 56, 65, 70, 75, 76, 80, 85, 88, 96

Formula for the range = Maximum value – minimum value

= 96 – 55

= 41

Example problem: 2

A marathon race there is 5 members are participated in the race. They have reached the destination with different timing. Calculate the range of the different timing they have reached the destination in the marathon race.

6.2 hr, 5.5 hr, 4.8 hr, 7.9 hr, 5.0 hr

Solution for learn online range:

Given

6.2 hr, 5.5 hr, 4.8 hr, 7.9 hr, 5.0 hr

Order the given times

4.8 hr, 5.0hr, 5.5hr, 6.2hr, 7.9hr

Formula for the range = maximum time – minimum time

= 7.9 hr - 6.2 hr

= 1.7 hr

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Practice problem for learn online range:


1.The Michal family has spent the hotel for their vacation in different place with the different cost. Calculate the range of the cost they have spent in the different place and the cost.

The cost in dollars 200, 300, 100, 500, 600.


2.A football team has scored their goal in the match that has shown. Find the range of the different game.

The goals are 10, 7 , 4, 5, 4

Learn Online Polynomials

Learn polynomials in online very easy. Online polynomials are mathematical expression, which comprises of sum of terms each and every term including a single variable or more variables raised to the powers and it is multiplied by coefficients. A simple online polynomial has only one variable. Polynomials are of different types that is two, three, or more variables. A two-variable polynomial is called bi-variate and three-variable polynomial is called trivariate.


Learning problems on polynomials online:


Learn an Example For Factor Polynomial online:

Factorize 3x3 – 4x2 – 13x – 6.

Solution for factor polynomial:

Sum of the coefficients of all terms: 3 – 4 – 13 – 6 = 20 ≠ 0.

Therefore, learn (x – 1) is not a factor.

Sum of the coefficients of even degree terms = –4 – 6 = –10.

Sum of the coefficients of odd degree terms = 3 – 13 = –10.

Since they are equal (x + 1) is a factor.

By synthetic division,

-1   |      3    -4    -13     -6

|            -3     +7    +6

|____________________

3      -7     -6   | 0

|_____

Remainder is 0.

Therefore the online polynomials (x + 1) is a factor.

Factorizing the quotient,

3x2 – 7x – 6 = 3x2 – 9x + 2x – 6

= 3x (x–3) + 2 (x–3) = (x–3) (3x+2)

Therefore 3x3 – 4x2 – 13x – 6 = (x+1) (x–3) (3x+2)

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Learn sample problems on polynomials online:


Example:

Find out the G.C.D. of the following online polynomials x3 – 9x2 + 23x – 15 and

4x2 – 16x + 12

Solution:

Let f(x) = x3 – 5x2 + 13x – 10 and g(x) = 4x2 – 16x + 12 = 4 (x2 – 4x + 3)



x-5

____________________

x2 – 4x + 3 |      x3 – 9x2 + 23x – 15

|      x3 – 4x2 + 3x

| ___________________

|          – 5x2 + 20x – 15

|          – 5x2 + 20x – 15

| ____________________

0

_____________________

G.C.D. = x2 – 4x + 3

Problem for factorization:

Determine the value of m and learn the factorization, if x + 1 is a factor of x3 + mx2 + 20x + 13

Solution:

Let P(x) = x3 + mx2 + 20x + 13

P(–1) = (–1)3 + m(–1)2 + 20(–1) + 13 = –8 + m

By learn factor theorem since the polynomial (x + 1) is a factor P(–1) = 0 or –8 + m = 0 or m=8