Math Division Chart

Definition of Dividend, Divisor ,Quotient ,Remainder

Dividend →
 
                   A quantity which is to be divided by another quantity is known as dividend.
e.g. 6 divided by 3, 6 is the dividend.

Divisor →
                  The quantity by which the dividend is to be divided is known as divisor.

e.g. 6 divided by 3, 3 is the divisor.

Quotient  →

                    The number resulting from the division of another number.
              Dividend ÷ Divisor = Quotient

e.g.  2 is the quotient of 6 divided by 3.
Remainder →
                           When an integer m is divided by a positive integer n, and a quotient q is obtained for which  m=nq+r

 Then r is the remainder.

    Math Division chart

Greek Alphabet In Math

Introduction :

The Greek alphabet is a set of twenty-four letters that has been used to write the Greek language since the late 9th or early 8th century BCE. It is the first and oldest alphabet. The Greek alphabet is descended from the Phoenician alphabet, and is not related to Linear B or the Cypriot syllabary, earlier writing systems for Greek.


Now we are going to see about the Greek alphabet in math.

About Greek alphabet in math:
                    Now we will see about the Greek alphabets and its symbols which are used in math.
In math, various symbols are required to represent the various functions such as in the set theory, numbers, functions and spaces.

However at the time of introduction, many of them seem to use some of the notations and the letters in the math.

Now it is familiar in all countries and many formulas in math and in other subjects are using the Greek alphabets only.

The lower case numbers are used often for variables, complex numbers etc.

Greek alphabets and its symbols in math:
                      Now we see Greek alphabets and symbols in math.

1.    α is the symbol used to represent the number and the name is alpha(Α)

2.    β is the symbol used to represent the number and the name is beta(Β).

3.    γ is the symbol used to represent the number and the name is gamma(Γ).

4.    δ is the symbol used to represent the positive number and the name is delta(Δ).

5.    ε is the symbol used to represent a positive number and the name is epsilon(Ε)

6.    ζ is the symbol used as seldom and the name is zeta(Ζ).

7.    η is the symbol used as seldom and the name is eta(Η)

8.    θ is the symbol used for an angle and the name is theta(Θ)

9.    ι is the symbol used hardly and the name is diota(Ι)

10.     κ is the symbol used to represent the kappa(Κ).

11.     λ is used to represent a constant multiplier and the name is lambda(Λ).

12.     μ is used to represent a constant multiplier and the name is mu(Μ).

13.     ν is used to represent number and called as nu(Ν)

14.     ξ is used and the called as xi(Ξ)

15.    ο is used hardly and called as do micron(Ο)

16.    π is used to denote invariably and called as pi(Π)

17.    ρ is used for radius rho(Ρ)

18.    σ is used for and called as sigma(Σ)

19.    τ is used and called as tau(Τ)

20.    υ is used and called as dupsilon(Υ)

21.    φ is used for an angle, called as phi(Φ)

22.    χ seldom used as chi(Χ)

23.    ψ is used for an angle psi(Ψ)

24.    ω is used rare and called as omega(Ω)

Coordinate Plane Slope Math

 Slope in a coordinate plane:

Slope:

In mathematics the slope of the line shows the steepness of the line. Slope is also defined as rise by run. We can find the slope from the equation of the line or form the coordinates. The positive slope has + sign and negative slope has – ve sign. Here we are going to see about slope in coordinate plane.

The formula to find slope is

Slope m = `(y2 - y1) / (x2 - x1)`

Slope in the coordinate plane is determined by rise in y axis by run in x axis.

consider the following figure.



Here the rise in y axis is -15 units

run in y axis is 30 units

Slope = `-15/30`

slope = `-1/2`

`and it can be also calculated using the coordinates from the above formula.`


Slope in a coordinate plane - Examples:


1). Find the slope of the line containing the coordinates (5, 12) and (7, 10).

Solution:

Given:

x1 = 5     x2 = 7

y1= 10    y2 = 12

Slope m = `(y2 - y1) / (x2 - x1)`

= `(10-12) / (7 -5)`

=` -2 / 2`

m = 1

Hence the slope of the given points are m = 1

2). Find the slope of the line containing the coordinates (14, 8) and (18, 9)

Solution:

Given: x1 = 14    x2  = 18

y1 = 8      y2 = 9

Slope m = `"(y2 - y1) / (x2`

=`" ( 9 - 8 ) / ( 18 - 14 `

= `1/4`

m = `1/4`

Hence the slope of the given points m =` 1/4 `

1)Find the slope of the line having the coordinates (6, 10) and (9, 11)
Solution:

Given:            x1 = 6     x2 = 9

y1 = 10    y2 = 11

Slope   m =` (y2-y1) / (x2-x1)`

= `(11 -10) / (9 - 6)`

= `1/3`

2) Find the slope of the line having the coordinates (7, 11) and (12, 14)

Solution:

Given:            x1 = 7     x2 = 12

y1 = 12    y2 = 14

Slope   m = `(y2-y1) / (x2-x1)`

= `(14 -11) / (12 - 7)`

= `3/5`

3) Find the slope of the line having the coordinates (11, 14) and (16, 23)

Solution:

Given:            x1 = 11     x2 = 16

y1 = 14    y2 = 23

Slope   m =` (y2-y1) / (x2-x1)`

= `(23 -14) / (16 - 11)`

= `9/5`.

What Does Area Mean in math

Introduction to calculate area of building:

Area is the measure of surface occupied by an object. The standard unit for measurement of area is meter square (m2)however the areas of smaller dimensions can be expressed in mm2or cm2.The areas of large amount of dimensions can be expressed in acre or hectare. Here we have study about how to calculate the area of the building shape image and its example problems.

Calculate area of the building example problems:

Example: 1

Calculate the area of the building which is in the form of square with side length is 6.

Solution:

First we have to draw the image and mark the side length.



Here the building shape is square

We know that area of the square = a 2

a = 6

Substitute a value in the formula we get

Area = (6)2

=36 meter square

Area of the given building is 36 meter square.

Example: 2

Calculate the area of the building which is in the form of rectangle with base is 8 meter and the height of the rectangle is 7 meter.

Solution:

Figure:



Mark the all measurements.

Here the shape is rectangle so we have to find the area of the rectangle

Formula = base *height

Here the given b = 8 meter and h= 7 meter

Substitute the b and h value in the above formula we get

Area = 8*7

= 56 meter square

Example: 3

Calculate the area of the building which is in the form of triangle with base is 12 feet and the height of the rectangle is 9 feet.

Solution:

Draw the diagram for the given measurement and mark the all data.


Here the building shape is a triangle so we have to find the area of the triangle

Formula:

Area = 1/2 (b*h)

Here base is 12 feet and height is 9 feet substitute the above formula we get

Area = 1/2 (12*9)

= 108 / 2

The simplest form is 54

The area of the given triangle shaped building is 54 feet square

Bar Diagrams for Math

Introduction :

In math a bar diagram is a pictorial representation of numerical data in the form of rectangles or Bars  of equal widths and various heights. These rectangles are drawn either horizontally or vertically.It should be remembered that bar diagram is of one Dimension.The height of bar represents the frequency of the corresponding observation.The gap between two bars is kept the same.


Steps for drawing bar diagram of math:


STEP 1 :- If the given frequency distribution is in inclusive form, convert it into an exclusive form.

STEP 2 :- Taking suitable scales, mark the class-intervals along x-axis and frequencies on y axis.

Note that the scales chosen for both the axes need not be the same.

STEP 3 :- Construct rectangles with class intervals as bases and the corresponding frequencies as heights.


Example for bar Diagram of math:


Draw the bar diagram following data that is the monthly expenditures of jack’s family on various items

Items                     Expenditure (In Rs.)

House Rent                  3000

Food                               4500

Education                       600

Electricity                       350

Transport                       800

Miscellaneous              500

Procedure to Draw a Bar diagram




Step: 1

First we have to take a paper and draw the horizontal line at the bottom of the paper the horizontal line is called x axis. And draw another line perpendicular to the horizontal line which is called y axis.

Step: 2

With  the horizontal axis, we take the information ‘item’ and in the vertical axis, we take the corresponding other information namely ‘the Expenditure

Bar diagram:

The following diagram is the bar diagram for the given data.

Bar diagram is showing the monthly expenditures of jack’s family on various items.

Questions for the bar diagram of math:

1) What is the information given by the bar diagram?

2) What is the number of items shown in the bar diagram and list them.

3) In which Item the maximum amount was spent.

4) In which Item the minimum amount was spent

Solution:

1) The information given by the bar diagram is the monthly expenditure of jack’s family on various items.

2) There are 6 items listed in the bar diagram. The six items are house rent, food, education, Electricity, transport and miscellaneous.

3) Food is the item where the maximum amount is spent.

4) Electricity is the item where the minimum amount is spent.

Ancient Symbols In Math

The two cultures that laid the groundwork for modern western civilization left us a legacy of symbols that is woven through every aspect of modern life. Many of these symbols were even used to build our modern world. 

Where would math, science and engineering be today without the Greek alphabet? There are 25 Greek letters that are used today to represent individual concepts. Here are just a few.
Alpha is used to represent the angle opposite of side A in a triangle, one root of a quadratic equation, an alpha particle, and angular acceleration.

Delta is used to represent a finite difference. Theta is used to represent a plane angle and potential temperature. Kappa is used to represent thermal conductivity. Mu is used to represent dynamic viscosity. Pi is used to represent Archimedes' constant, the ratio of a circle's circumference to its diameter.

From just these few samples, it's clear that modern mathematical and scientific expression is highly dependent on Greek symbols.

Greek mythological symbols have also come down through the ages.

Owl: Athena was the Goddess of wisdom. One of her symbols was an owl. Today, the owl is probably the most widely recognized symbol for wisdom.

Grape vine: Dionysus was the god of wine. One of his symbols was the grape vine. We still use the grape vine today as a symbol of wine.

Winged boots: Hermes was the messenger of Zeus. One of his symbols, the winged boot has made its way through the ages as a symbol for messengers.

Thunderbolt, eagle and oak: These are all symbols that have survived the ages to represent power and strength, attributes of Zeus.

But what about our Roman legacy? Science as we know it would not have developed without Roman nomenclature. It is the single most organizing factor in modern science.

Armor: Mars (god of war) and Minerva (goddess of war) were both represented by armor, a symbol still used today to represent war.

Scales: Them is was the goddess of justice. She actually originated as Ma' at from Egyptian mythology. Her scales symbolize the weighing of the hearts of man. She now stands as a universal symbol of justice blindfolded and holding a sword in one hand and scales in the other.

Ancient Greek and Roman symbols surround us in the modern world. They are not likely to go away any time soon. Our written language is deeply rooted in ancient symbols that represent sounds. Our ideas are nearly parallel to the ideas that inspired the symbols used by the ancients. Why wouldn't they be? Their cultures laid the groundwork for modern western civilization.

Velocity Problems And Solutions

Introduction:

Normally rate of change of position in math is known as velocity.  It is one of the vector quantities because when we mentioned the velocity it will indicate the direction also. Velocity is normally defined by the ratio between the distance and time. In velocity problems we can measure the time and distance. Velocity problems are used to find the solutions for the distance problems. We can find the solutions for maximum height of the object traveled. velocity problems and solutions are one of the main application in physics.

Velocity problems and solutions:


Problem 1:

    A submarine descends 90 miles in 10 seconds. Find the velocity of the submarine.

Solution:

Step1:

    We know the velocity formula V = Distance (d) / Time (t)

Step2:

   Here distance d = 90 miles

  And the time t = 10 seconds.
Here the submarine is descending so the velocity will be negative velocity.

Step 3:

 So velocity = - 90 / 10 miles / sec

 Velocity V = - 9 miles / sec.

We can find the distance travelled by the object using the velocity problems.


Problem 2:


   A ball is thrown upwards in the air from the ground. The distance travelled by the ball is

 h = 16t2 - 64t + 6. Find the maximum height of the ball.

Solution:

 The distance traveled by the ball is h = 16t2 - 64t + 6

 We want to find the maximum height. When the ball is maximum height the velocity will be zero. To find the velocity function we have to differentiate the distance function with respect to t.
 V = d h / d t = d / d t (16t2 - 64t + 6)

   V = d h / d t =32t - 64

   If the ball is at maximum height velocity v = 0         

   32t - 64 = 0

    32t = 64

   t = 64 / 32

   t = 2

   So when time t = 2 the ball will beat maximum height.

   h = 32 (2)2 -64(2) + 6

  h = 128 – 128 +6

 h = 6           

From the above problem we used the velocity to find the solutions for the maximum height.