Growing up with Mathematics

Do You Know How to calculate ratio:

In mathematics, The magnitude of quantities relative to each other. with the ratio expression Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient.

Example:

For every Spoon of sugar, you need 2 spoons of flour (1:2)

Some Simple Operation in Ratios:
The ration of two numbers a and b(b≠0) is the quotient of the numbers. The numbers a and b referred to as the terms of the ratio.Have you heard about chronometric ratio

1. Compounded ratios
2. Duplicate ratios
3. Triplicate ratios

Compounded ratios:
General format for compounded ratio is
*=
Example for compounded ratios:
Example 1:
How to Find ratios: X = or or 25:4
Amazing is in it also find some interesting topics on Precalculus help

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Let us learn how to draw an ogive
The other name for Ogive curve is cumulative frequency curve.
Cumulative frequency curve or ogive is used to obtain the following information from a set of grouped data.

• median
• lower quartiles
• upper quartile
• inner quartile range

Cumulative frequency table is first step in constructing ogive.
Box and whisker plot can also constructed Using a cumulative frequency curve or ogive.

How to Draw an Ogive - Cumulative Frequency Curve or Ogive

Steps to learn how to draw ogive
Ogive or cumulative frequency curve looks like this:-

The cumulative frequency is the basic step in calculating ogive it is obtained by adding up the frequencies as you go along to give a 'running total'.
Do you Know what is line graph generator
Before drawing the cumulative frequency curve or ogive, we need to work out on the cumulative frequencies. This is done by adding the frequencies in turn.
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Algebra linear calculator is used to find the values of variables without manual calculation. free online algebra tutor. These calculators are very useful for the students who are not well with the math formulas and arithmetic operations. Many websites provides free online linear algebra 2 online equations calculator for solving the problems. When the required values are entered in the online solver, it automatically generates the output value. The picture of linear calculator is shown below,

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Mean formula

Mean Formula

In general sample mean (A.M) or average of n observations x₁, x₂, …, x_n is defined to be the number x such that the sum of the deviations of the observations from x is 0. That is, the arithmetic mean x of n observations x₁, x₂, …, x_n is given by the equation

(x₁ − x) +(x₂ − x) + ^... +(x_n − x) = 0

Hence sample mean formula = x₁+x₂+x₃+…….x_n / n

sample mean formula= sum of elements / number of elements

Would you like to learn about probability mass function

Sample Mean Example

Following steps used to calculate the sample mean value

Step1: find the sum of the numbers

Step2: Calculate the total numbers

Step3: Using the formula finding the mean

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Solving System of Equations

In mathematics, a system of linear equations is a collection of linear equations involving the same set of variables. For example,

is a system of three equations in the three variables . A solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by

since it makes all three equations valid.so this is specially for linear equations in two variables or more than two variables.

In mathematics, the theory of linear systems is a branch of linear algebra, a subject which is fundamental to modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and such methods play a prominent role in engineering, physics, chemistry, computer science, and economics. A system of non-linear equations can often be approximated by a linear system (see linearization), a helpful technique when making a mathematical model or computer simulation of a relatively complex system.This is how linear equations explained ,let's see a example on this now from linear algebra tutoring online.
Question:-

Solve the system of equations

8x-z=4

y+z=5

11x+y=15

Answer:-

8x-z=4 ----- eq1

y+z=5 ---- eq2

11x+y=15 -----eq3

add eq1 and eq2

we get 8x+y=9 ----- eq4

subtract eq4 from eq3

11x+y=15
-8x+y=9
-----------
3x = 6

x =2

putting this value in eq1

8x-z =4

16-z=4

z=12

putting this value in eq2

y+z = 5

y = -7

so x=2 , y= -7 and z=12

How to find the arc length of a curve

The arc length is a topic from 10 grade math geometry,lets see the general definition for arc length after which we can see what is the arc length formula and how to use it.
A curve in, say, the plane can be approximated by connecting a finite number of points on the curve using line segments to create a polygonal path. Since it is straightforward to calculate the length of each linear segment (using the theorem of Pythagoras in Euclidean space, for example), the total length of the approximation can be found by summing the lengths of each linear segment.

This free online tutoring math will discuss this in more detail like,
If the curve is not already a polygonal path, better approximations to the curve can be obtained by following the shape of the curve increasingly more closely. The approach is to use an increasingly larger number of segments of smaller lengths. The lengths of the successive approximations do not decrease and will eventually keep increasing—possibly indefinitely, but for smooth curves this will tend to a limit as the lengths of the line segments get arbitrarily small.

For some curves there is a smallest number L that is an upper bound on the length of any polygonal approximation. If such a number exists, then the curve is said to be rectifiable and the curve is defined to have arc length

The arc length formula is s=rθ

where s is the arc , r is the radius of the circle and θ is the angle .

Commutative and Distributive Number Properties

Number properties are
Associative property applies to both addition and multiplication: a+(b+c)=(a+b)+c, a*(b*c)=(a*b)*c.
Distributive property ties addition and multiplication together. Distributive property can be written as: a*(b+c) = a*b + a*c.
Commutative property means that operands can switch places: a+b=b+a, a*b=b*a.

For Example:
Question 1 :- Distributive PropertyThe property demonstrated in the equation -(3n - 5) = -3n + 5 is:
a. associative b. commutative c. distributive d. Neither side of the equation is equal to the other.
Answer:
-1(3n-5) = -3n+5
(-1) (3n) + (-1) (-5)
= -3n+5 (Distributive Property)

Question 2 :- Associative Property
property demonstrated in the equation (5 + n) - 2 = 5 + (n - 2) is:
Answer:
(5+n)-2 = 5+(n-2)
Here the grouping that is the parentheses has changed.so it a (Associative Property)

Question 3 :- Commutative Property
property is this one 7 - 4 + 2 = 7 + 2 – 4
Answer:
7 - 4 + 2 . 7 + 2 - 4
Here the order - 4 + 2 has become 2 + - 4. So it is a (Commutative Property)