Math Definitions

Mathematics is one of the vast and most important concepts in education. From primary school mathematics is taught as a major subject introducing numbers, calculations and mathematical operations. In order to gain an in depth knowledge in mathematics, one needs to understand the various definitions or meaning of topics in Mathematics.

• Addition: The mathematical operation where two or more values are added is called addition. For example: She bought kids’ kitchen sets for Rs. 350 and stuffed cloth toys online for Rs.220. Therefore, she paid Rs. 350 + 220 = Rs. 570 while buying kids’ kitchen sets and stuffed cloth toys online.
• Subtraction: The mathematical operation where a part is subtracted from a whole is called subtraction. For example: Mahesh bought woodcraft construction kit online for Rs.1500. Seema contributed Rs. 580 in buying the woodcraft construction kit online. Therefore, Mahesh paid Rs. 1500 – 580 = Rs. 920 from his own pocket.
• Division: The mathematical operation where a value is distributed, it is called division. For example: Ram bought 8 apples which he needs to distribute among 4 kids equally. Therefore, 8 apples / 4 kids = 2 apples. Each kid gets 2 apples.
• Multiplication: The mathematical operation where a value is scaled by another value, it is called multiplication. For example: John earns $50 per day. Therefore, his earning per month is 50 * 30 = $1500.
• Algebra: Algebra is a branch in mathematics where one needs to find out the value of variables.  For example: 2X = 8. Therefore, X = 4.
• Fraction: Fraction is a part of a whole. For example: 7/9, 2/7 etc. are fractions.
• Proper Fraction: A proper fraction is a fraction where the numerator is smaller than the denominator. For example: 2/5, 3/9 etc.
• Improper Fraction: An improper fraction is a fraction where the denominator is greater than the numerator. For example: 5/7, 9/2 etc.
• Mixed Fraction: Mixed fraction is a combination of a whole number and a fraction. For example 3 ½ , 4 ½  etc.
These are some of the basic math definitions.

Free Algebra Equation Solver

Introduction:
Branch of mathematics deals with equations are called Algebra. In free Algebra equation solver we use letters like a, b,c.... y and z to denote numbers. Performing addition, subtraction, multiplication, division or extraction of roots and real numbers obtain free algebraic expressions. Symbols in free algebraic equation solver expression are called variables of expression. If two algebraic equation solver expressions are equated, we get free algebraic equations.


Simultaneous Equations


In free Algebra equation solver a set of linear equations having a common solution set is called a system of simultaneous linear equations. In earlier classes, have learnt different methods of solving simultaneous linear equations in two variables. linear equation in three unknowns x, y, z is a statement of equality of form ax + by + cz + d = 0 where a, b, c, d are real numbers with a ≠ 0, b ≠ 0 and c ≠ 0. For example 2x – 3y + 6z = 5 is a linear equation in 3 variables. Find values of three unknowns, given three linear equations in three unknown variables.

Solving given linear equations in x, y, z

Take any two equation solver.
First we are going to eliminate the z.
Now,we get 2 linear equations with x and y.
Solve them in common way learnt in previous cases.
By substitute x and y values in the equation,we get z value.
Finally we get x,y and z values.

I have recently faced lot of problem while learning System of Equations Solver, But thank to online resources of math which helped me to learn myself easily on net.

Practice Example


Example :

Solve:

x - 3y =12 ----------(1)
2x + 6y = 4 ----------(2)

SOLUTION:

(1) x 2 => 2x – 6y = 24
(2)      => 2x + 6y =   4   (+)
___________
4x + 0 = 28
___________

4x = 28

Divide by 4 on both sides,

(4x/4) = (28/4)

x = 7

Plug x = 7 in ( 1 ),

7 - 3y = 12

Subtracting 7 on both sides,

7 -3y - 7 = 12-7
-3y = 5

y = -(5/3)

Solution for this Algebra problem is x = 7 & y = -(5/3)

What Is Ratio In Math

Introduction for ratio in math:

In our daily life, by learning ratio and proportion many a times we compare two quantities of the same type. Thus, in convinced situations, comparison by division makes better sense than comparison by taking the difference. The comparison by division is the Ratio. We denote ratio-using symbol ‘:’. If two ratios are equal, we state that they are in proportion and use the symbol ‘:’ or ‘=’ to equate the two ratios.

Ratio in math - Definition and example problems:


Definition of ratio:

The learning ratio is a comparison by division method. We compare the two quantities in terms of ‘how many times’. This comparison is known as the Ratio. We denote ratio-using symbol ‘:’

A : B

Ratio in math – Example problems:

Example 1:

If 5 pounds of grains cost $0.82, how much would 45 pounds of grains cost at the same rate?

Solution:

`(5 pounds) / ($0.82) ` = `(45 pounds) / (x)`   (Cross multiply)

(5 pounds) * (x) = (45 pounds) * ($0.82)

Divided by 5 pounds on both sides,

x = (9 pounds) * ($0.82)

x = $7.38

45 pounds of grains cost $7.38

Example 2:

The ratios of good scores to bad scores are 5 to 1. If there are 25 good scores, how many were bad?

Solution:

`(5 good scores) / (1 bad scores)` = `(25 good scores) / (x bad scores)`

5 * x = 25

X = `25 / 5`

X = 5

5 bad scores

Example 3:

Find the value for x,

`16 / 8 ` = `8 / x`

Solution:

`16 / 8` = `8 / x`

16 * x = 8 * 8

16x = 64                           (16 multiply 4 = 64)

x = `64 / 16`

x = 4

Example 4:

Find the value for x,

`8 / 13` = `8 / x`

Solution:

`8 / 13` = `8 / x`

8 * x = 8 * 13

8x = 104                           (13 multiply 8 = 104)

x = `104 / 8`

x = 13

Understanding Number and Operations is always challenging for me but thanks to all math help websites to help me out.

Ratio in math – Practice problems:


Practice problem 1:

Fine the value for x,

`12 / 8` = `6 / x`

Answer: x = 4

Practice problem 2:

Fine the value for x,

`14 / 7` = `6 / x`

Answer: x = 3

Practice problem 3:

In a backyard, the ratio of birds to squirrels is 8 to 2. If there are 16 squirrels in the backyard, how many birds are there?

Answer: 64 birds

Free Online Tutoring for Geometry

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Free Algebra Online

Introduction for free algebra online:
‘Free Algebra Online’ is a math tool which helps the students to get more knowledge in math. Also it supports to perform well in their exams. The student can come at any time though online and can get excellent help without any hesitation. Free algebra online covers the following basic operations such as addition, subtraction, multiplication and division. Also free algebra online cover the basic properties such as commutative, associative, identities and inverse. I like to share this free math solver algebra with you all through my article.


Most important term in free algebra online:


Free algebra online describes the terms such as variables, constant, coefficients, exponents, terms and expressions.

Variables

Algebraic variables are the alphabets where we are assigning the values. While solving the algebraic equation value of the variable will be changed. Widely used variables are x, y, z

Constant

Algebraic constants are the value whose values never changes while solving the algebraic equation. In 43y + 33, the value 33 is the constant.

Expressions

An algebraic Expression is the mixture form of variables, constant, coefficients, exponents, terms which are combined together by the following arithmetic operations such as Addition, subtraction, multiplication, and division. The example of an algebraic expression is given below

5y + 6

Term

Terms of the algebraic expression is used to form the algebraic expression by the arithmetic operations such as addition, subtraction, multiplication and division. In the following example 8n2 + 9n the terms 8n2, 9n are combined to form the algebraic expression 8n2 + 9n by the addition operation ( + )

Coefficient

The coefficient of an algebraic expression is the value present just before the terms. From the following example, 8n2 + 9n the coefficient of 8n2 is 8 and 9n is 9

Equations

An algebraic equation balances the numbers or expressions. Most probably algebraic equation is used for the value of the variable. The example of the equation is given below

9n +9 = 6


Order of the operation in Free algebra online


1. First, Reduce the algebraic expression whatever inside the parentheses.

2. Next, Reduce the exponents.

3. Next, Reduce the multiplication or division operations.

4. Finally, Reduce the addition or subtraction operations.

Having problem with Combinatorics Problems keep reading my upcoming posts, i will try to help you.

Examples for Free algebra online:


Example 1:

2(a-2)+4b-2(a-b-2)+10

Solution:

=  2(a-2)+4b-2(a-b-2)+10

= 2a–4+4b–2a+2b+4+10

= 2a–2a+4b+2b-4+4+10

= 6b+10

= 3 ( 3b – 5)

Example 2:

5x - 15 = 4x - 30

Solution:

5x - 15 = 4x - 30

5x – 15 + 15 = 4x – 30 + 15 (Add 15 on both sides)

5x =4x -15

5x – 4x =4x -4x - 15 (Add -4x on both sides)

x = -15

Angle of Depression Problems

Introduction to Angle Of Depression problems:

The word “depression” means “fall” or “drop”.

Angle of depression problem is the angle which is between the horizontal and the line of sight to an object beneath the horizontal. The angle of Depression is similar to angle of elevation.

The angle of depression problem is below the horizontal that an observer must look to see an object that is lower than the observer.The angle of depression is similar to the angle of elevation (this assumes the object is close to the observer so that the horizontals for the observer and the object are parallel; this would not be the case for an astronaut in orbit around the earth observing an object on the ground).

Please express your views of this topic What is the Angle of Depression by commenting on blog.

Angle of depression problem:1

A man who is 2 meter tall stands on horizontal ground 30 meter from a tree. The angle of elevation from the top of the tree from his eyes is 28˚. Find the height of the tree.

Angle of depression problem solution:

Let the height of the tree be h.
Tan 28o=(h-2)/30
h – 2 = 30 tan 28˚
h = (30 ´ 0.5317) + 2 ← tan 28˚ = 0.5317
= 17.951
The height of the tree is approximately 17.95 meter.

Angle of depression problem:2

An Bird is flying at an altitude of 1000 m. The angle of depression from the bird of a tree on the ground is measured as 15°. What is the distance from the bird to the tree?
Choices:
A. 3,864 m
B. 3,732 m
C. 1,035 m
D. 1,000 m
Angle of depression problem solution:
Step 1: Let x be the distance from the bird  to the tree.
Step 2: Here the horizontal lines are parallel; the angles of elevation is equal to angle of depression Step 3: sin 150=1000/x
Step 4: x=1000/sin 150
Step 5: x = 3,864 m
Step 6: the distance from the bird to the tree is 3,864 m.

Learn Algebra 2

Definition of algebra:

Algebra is the division of arithmetic to the study of the regulations of operations and dealings, and the concept arising from them, together with all possible algebraic sub topics. Algebra is easy to learn and to solve the problems when the concept is understood very well.

An algebraic term represent a scale, what is ready on one side of the scale with a number is also ready to the other side of the range. The numbers are the constants. Algebra consist of real numbers, complex numbers, matrices, vectors etc.

Free answers to algebra problems:

Q1:  A person crosses a 500 m long street in 7 minutes. What is his speed in km per hour

Solution:

Given,

Distance = 500m

Time = 7minutes

Formula:

Speed = distance / time

Speed = 500 / (7*60)

Speed = 1.2m/sec

Converting m/hr to km/hr, we get

=1.2*18/7

=3.08km/hr

Answer:

The final answer is 3.08km/hr

Q2: The ratio between the speeds of two trains is 5 : 6. If the second bus runs 300 km/s in 2 hours, then find the speed of the first bus in km/hr.

Solution:

Given ,

The speed of two bus be 5x and 6x

Distance = 300km

Time = 2hours

Speed formula:

Speed = distance/ time

First take 5x,

5x = 300 / 2

= 150

X = 150/5

= 30 km/hr

Answer:

Speed of first bus=30*6=180km/hr

Q3: A man complete a journey in 8 hours. He appointments first half of the journey at the rate of 20 km/hr and second half at the rate of 22 km/hr. Find the total journey in km.

Solution:

(½) x / 20+ (1/2) x / 22 = 8

After simplifying, we get

X / 20 + x / 22 = 8

Take lcm for 20 and 22, we get

Lcm is 220

21x = 220*8

21x = 1760

Divide by 21 on both the sides, we get

X = 1760 / 21

= 83.8km

Answer:

The final answer is 83.8 km. Understanding Inverse Matrix Calculator is always challenging for me but thanks to all math help websites to help me out.


Practice questions for free algebra:

Question 1:

The rectangle of a two digit integer is divided by half the number. After 36 is added to the measure, this sum is then divided by 2. The digit of the resulting numbers are the equal as the new number, but they are in reverse order. The tenth place of the number is equal to twice the difference between its digits. What is the number?

Answer:- 46

Question 2:

In one hour, a ship goes 11 miles per hour along the stream and 5 miles per hour next to the river. The rate of the ship in still stream (in miles per hour) is:

Answer: - 8 miles per hour