plot line

Let us learn about plot line

A line plot is defined as a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer numbers.

• A line plot shows data on a number line with the symbol x or other marks to show frequency.

• In the applications of line plot, we have also created the scatter plot analysis. I we go in the wrong path or plotting the extra values or plotting the values in different place or leaving some values when we plotting make great difference in the diagrams.

Line Plot Maker - Making a Number Line Plot:

• To define the scale which we use, if the data is described as 100 the scale is increased by 10. So that we define the scale as 10 for 100

• Next we have to draw the horizontal line to across the paper.

• Break the grid as per the required scale.

• Place the data values of x in the x-axis and y in the y-axis.

X

X X

X X X

X X X X X X

0 1 2 3 4 5 6 7 8 9 10

In our next blog we shall learn about converting 1 meter to feet

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fraction reducer

Let us learn about fraction reducer

The word fraction has been derived from the Latin word fractus, means broken

A Fraction means a part of a group or a region or a whole.

Fractions having the same(common) denominators but different numerators are known as like fractions.

Fraction is defined as an element of quotient field. Fraction can be represented as " a / b " here fraction variable 'a' denotes the value called as numerator and fraction variable 'b' denotes the value called as denominator and the denominator 'b' is not equal to zero.

Fractional functions:

The fraction rule is used in following functions,

1. Addition
2. Subtraction
3. Multiplication
4. Division

In our next blog we shall learn about misleading graphs

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change of base formula

Let us learn about "change of base formula"

The solving change of base formula is known as formulas which it permits us to rework a logarithm by means of the logs that may be is written with different base.

The change of base formula is given by,

Log _a x = log _b x / log _b a

Here, assume that a, b and x are positive where a≠1 and b≠1.

Problem

Solve log ₁₆ 32

Change of base formula => log_a x = log_bx / log_ba

log ₁₆ 32 = log ₂ 32 / log ₂ 16

= 5 / 4

Thus a formula that allows you to rewrite a logarithm in terms of logs written with another base. This is especially helpful when using a calculator to evaluate a log to any base other than 10 or e.

In our next blog we shall learn "how to simplify radicals"

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Factors of 72

Hi Friends, Good Morning!!!

In our previous blog we learned about Factor of 28. Today let us learn about "Factor of 72"

Like concepts presented throughout the Montessori classroom, even those more abstract concepts of Mathematics have been made concrete for the children in our classrooms. Beginning with simple number concepts like understanding quantity and identifying numerals, the Math materials include advanced presentations in cubing numbers, factors, fractions, and mathematical operations.

Factor Tree can be started by taking Different factors. The factor trees can be different but we will see that the Prime Factorization will remain same.

Steps to draw the Factor Tree of 72

Step 1: We start by building a Factor Tree of 72 by dividing 72 by smallest prime number that is 2.

Step 2: since 72 is 2 x 36 we write both these factors under 72 and circle 2 since it is prime.

Step 3: Since 36 is even number so we divide 36 again by 2 we get 2 x 18

Step 4: writing both factors 2 and 18 under 36 and circling 2 as it is again prime

Step 5: Then splitting 18 as 2 and 9 and writing the factors under 18 again circling the prime factor 2.

Step 6: Since now 9 is not divisible by 2 so we see next prime number that is 3

Step 7: On dividing it by 3 we get 3 which is the last and final factor.

Note: we keep on continuing these steps until we get all prime numbers in bottom row.

The Graphical representation of the factors of any number is called a Factor Tree

Factor Tree can be started by taking Different factors. The factor trees can be different but we will see that the Prime Factorization will remain same.

Steps to draw the Factor of 72

Step 1: We start by building a Factor Tree of 72 by dividing 72 by smallest prime number that is 2.

Step 2: since 72 is 2 x 36 we write both these factors under 72 and circle 2 since it is prime.

Step 3: Since 36 is even number so we divide 36 again by 2 we get 2 x 18

Step 4: writing both factors 2 and 18 under 36 and circling 2 as it is again prime

Step 5: Then splitting 18 as 2 and 9 and writing the factors under 18 again circling the prime factor 2.

Step 6: Since now 9 is not divisible by 2 so we see next prime number that is 3

Step 7: On dividing it by 3 we get 3 which is the last and final factor.

Note: we keep on continuing these steps until we get all prime numbers in bottom row.

In the above figure on the left side we see all the prime factors

So the prime factorization can be written as product of all Prime factors

72= 2 x 2 x 2 x 3 x 3

In simplified form it can be written in form of Exponents

72= 2^3 x 3^2

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vertex formula

Hi Friends, Good Afternoon!!!

Let us learn about "vertex formula".

Introduction to write quadratic function in vertex form

General form of a quadratic equation is y= ax²+ bx +c where a,b and c are real numbers and a 0.The graph of the quadratic equation is a parabola (either up or down). Let us assume that this parabola has its vertex at (h,k), then we can write the quadratic equation in vertex form as y= a(x-h)²+k.

There are 2 methods to write quadratic equation in vertex form.

Click on the link to learn about "quadratic equation formula"

1. Using completing the square method

2. Using vertex formula

VERTEX : For any two edges that meet at an end – point, there is a third edge, that also meets them at that end – point. This point of intersection of three edges of a cuboid is called a vertex of the cuboid.

The vertices of the cuboid in the figure are A, B, C, D, E, F, G, H.

Clearly, a cuboid has 8 vertices.

Thus, we see that the twelve edges of a cuboid can be grouped into three groups such that all edges in one group are equal in length. This means that twelve edges of a cuboid can have only three distinct lengths. Usually, the longest of these is called the length of the cuboid and out of the remaining two, one is called the breadth or width and the other height of the cuboid.

BASE AND LATERAL FACES : Any face of a cuboid may be called the base of the cuboid. In that case, the four faces which meet the base are called the lateral faces of the cuboid.

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Antiderivative Calculator

Hi Friends, Good Afternoon!!!

Let us learn about "Antiderivative Calculator" and as you know in previous blog we learned about "Molarity Calculator" which was very interesting.

Antiderivative Calculator allows users to enter an integrand in order to return the indefinite integral. Does anybody know something about antiderivative solver online? Integral Calculator calculates an antiderivative (indefinite integral) of a function with respect to a given variable using analytical integration. The first thing is the antiderivative you will usually learn, when you begin your study of integral calculus.

As simple we can say, antiderivative finding is the exact opposite process of finding the derivative of any given function. So, before beginning a study of integral calculus, you must have a firm foundation in differential calculus. For an algebraic equation solver, antiderivative finding process is not very complex.

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Exterior of the triangle and Interior of the triangle

Hi Friends

Good Afternoon!!! In our previous blog we learned about Triangles. Now let us learn about "Exterior of the triangle and Interior of the triangle"

Interior of the triangle:

The region enclosed by the sides of a triangle is called the interior of the triangle.

In the figure, the points P, Q, R and X lie in the interior of QUOTE /\ABC.

Exterior of the triangle:

Any region outside the triangle is called the exterior of the triangle.

In the figure, points X, Y, Z and M lie in the exterior of /\ PQR.

I hope the above explanation was useful.

In our next blog we shall learn about 7 types of triangle. keep reading and leave your comments.

Factors of a number

Let Us Learn About Factors of a number

Consider the number 6, we have 6 divisible by 1, 2, 3, and 6.

Which means after division of 6 by any of 1, 2, 3, and 6, we get the remainder as zero.

These numbers 1, 2, 3, and 6 are called as factors of 6.

Factors of a number: factors of a number are those numbers which when divide the given number, leaves zero remainder.

Examples:

(i)3 and 5 are factors of 15 as 3x5 = 15

Also, 1x15 = 15

or, 1 and 15 are also factors of 15.

Thus, as we discussed above; 1, 3, 5 and 15 are factors of 15 as each of these numbers (1, 3, 5 and 15) divides number 15 exactly.

Let Us Learn On Methods Of Factorization

* Common Factor
* Prime Factor
* Highest Common Factor

Let Us understand About Common Factor
10 = 2 × 5 = 1 × 10

Thus, the factors of 10 are 1, 2, 5 and 10.
15 = 1 × 15 = 3 × 5
Thus, the factors of 15 are 1, 3, 5 and 15.
Clearly, 5 is a factor of both 10 and 15. It is said that 5 is a common factor of 10 and 15.

We shall Learn About Prime Factor in our next blog


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