Steps for solving word problems

Word problem plays an important role in mathematic. Before i take you through on steps for solving word problems. let me help you understand what is word problem and how does it help mathematic.

What is word problem?

In mathematics education, a word problem is a mathematical question written without relying heavily on mathematics notation. Word problems commonly include mathematical modelling questions, where data and information about a certain system is given and a student is required to develop a model.This also plays an important role in algebra word problems.

Steps for solving word problems:-

Now let me help you go through the important steps to be followed in solving word problems before i take you through with the help of examples.

1) The problems are to be thoroughly read

2) The information given is to be listed and what is asked in the problem is to be clearly understood. An equation is to be formed with the information given. While forming equation key words are to be correctly noted for defining the correct operation like addition/subtraction/multiplication/division.

3) The equation is to be solved for knowing the variables.

Key words	Operation
Increased by, more than, combined together, total of, sum , added to	Addition
Key words	Operation
Less than, fewer than, reduced by, decreased by, difference of	Subtraction
Of, times, multiplied by	Multiplication
Per, a, out of, ratio of, quotient of, percent	Division

This was just a brief introduction to word problems. May be in the next lesson let me help you with a example so that you understand word problems in a better way. keep reading and leave your comments. And even if you have any doubts feel free to share with me .. i will be able to help you.

Decimal Number System in Math

Introduction to Math Decimal System:

The concept of math decimal system is also deals with the fractions whose denominators are 10, 100 or 1000 etc. In this section, a decimal can be expressed as a fraction and vice-versa. A math decimal system may contain a whole number part and a decimal part. In a decimal system, if whole number part is not given, we indicate it by writing a zero on the left of the decimal point.In math, decimal value is represented by the point.

Decimal Number System in Math:

In math decimal number system, the value of a digit depends upon its place, or position, in the number. Each place has some value of 10 times the place to its right.

To the left of decimal point are:

Ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, etc

To the right of the decimal point are:

Tenths, hundredths, thousandths, ten thousandths, hundred thousandths, and so on.

Example on Decimal Number System in Math: -

Example :

Write the following as a decimal:

34+

Solution:

34+

=34.23 is decimal form

How do you feel now?...Did i help you understand on number system.. Keep reading and give me your valuable comments or even if you need any help on math...

Understanding Polygons : Types of Polygon

A polygon is a two dimensional plane figure, bounded by line segments called as sides. A polygon can be classified as regular or irregular polygon, based on their sides. If all the sides are equal, then it is called as a regular polygon. An irregular polygon has unequal sides.
Hear are the few types of polygons -

1. Regular polygon,
2. Irregular polygon,
3. Convex Polygon,
4. Concave polygon,
5. Crossed polygon and
6. Equiangular polygon

Polygons can be classified as,
1. Convex and Concave polygon
2. Regular polygon
3. Congruent polygon
These are the types and classification of polygons..... I understand you still require a detailed explanation on all the types of polygons. keep reading.. we will try to learn that may be in the next lesson.

Examples of Congruent Triangles

we just learned on congruent triangles and now let me also help understand better with some examples on congruent triangles.

Examples of Congruent triangles:
The definition of congruent triangles describes only when the triangles are said to be congruent, and here are some examples of congruent triangles.

• If two line segments each measure 20 units, they are congruence segments.
• If two angles each measure 80 degrees, they are congruent angles, even if they are in different locations and facing different directions.
• If two triangles have sides measuring 4, 6, and 8 units, and their equivalent angles are congruent, then the triangles are congruence too
• If two polygons have 20 sides, and the corresponding sides and angles are congruent, then the polygons are congruent too.

I hope you got a good knowledge on congruent triangles. keep reading...... and if you are really keen on leaning math's and need help on any topics then leave your comments. I can help you understand better with my examples....

Note on Congruent Triangles

we were been trying to understand more on number sense and now.. let me help you understand on congruent Triangles.

Introduction:

The triangles are said to be congruent when all the subsequent sides and interior angles are congruent. The triangles will have same shape and size, but one may be a mirror image of other in the definition of triangles

Congruent Triangles:
Probably the most generally used example of congruence is the congruence of two triangles. Congruence in triangles is able to be proven using one of several rules. The rules for the definition of congruent triangles include side-angle-side, angle-side-angle, side-side-side, or angle-angle-side. The below definition gives the meaning of the congruent triangles.

• Side-angle-side – If the two sides and the included angle of one triangle are said to be congruent to two sides and the included angle of another triangle, the triangles are congruent.
• Angle-angle-side – If the two sides and then a non-included angle of one triangle are congruent to two sides and a non-included angle of another triangle, the triangles are congruent

Now you got an good understanding on congruent triangles. keep reading and leave your comments... may be on the next lesson.. let me share my knowledge on Examples of Congruent Triangles.

procedure to draw hyperbola graph

Dear readers.. as we discussed about properties of hyperbola and now let me help you understand more on the procedure to draw hyperbola graph.

Before we learn on drawing... let me help you on the important steps involved in it

• First we have to plot the intercepts The four points are (a,0), (-a,0) and (0,b), (0,-b)
• Using this four points draw the rectangle
• Draw two lines forming diagonals of the rectangle .It represents the asymptotes of the hyperbola
• Now draw the hyperbola that with the vertices's (a,0) and (-a,0)

Procedure to draw a graph -
Two variables x and y are connected by an equation of the form y = ax2 + bx + c then it is called a quadratic polynomial. We have already seen in Algebra that the equation ax2 + bx + c = 0 is a quadratic equation. This is the reason why we call y = ax2 + bx + c as a quadratic graph. For each value of x the equation y = ax2 + b x + c gives a value of y and we obtain an ordered pair (x, y) of real numbers. The set of all such ordered pairs define the graph of y = ax2 + bx + c called the quadratic graph.

The following procedure is used in drawing quadratic graphs:

• By substituting selected values for x in the equation y = ax² + bx + c, we get corresponding values for y and then we form a table.

• Draw x-axis and y-axis on the graph sheet and choose a suitable scale on the co-ordinates axes. The scale for both the axes are chosen depending on the values of the co-ordinates obtained.

• Plot the points in the Cartesian plane of the graph sheet.

• Join these points by a smooth curve, then we get the required quadratic graph of y = a x² + bx + c

I hope you got an idea on this lesson. Keep reading and i will help you also go through on Different Line Graphs on hyperbola graph

Properties of hyperbola

Introduction to hyperbola learning:

A hyperbola learning is a conic section obtained on slicing a double napped cone by a plane parallel to the axis of the cone.

The locus of a point from a fixed point is at a constant ratio and it is greater than one of its distance from a fixed line is called a Hyperbola.

Standard form of a hyperbola

x²/a² – y²/b² = 1

Learning Properties of hyperbola

Properties of hyperbola is the lines from the foci to any point on a hyperbola make equal angles with the tangent at that point. Hence if the surface of a reflector is generated by revolving a hyperbola about its transverse axis, all rays of light converging on one focus are reflected to the other, along with hyperbolic functions

The hyperbola is symmetric about x-axis, y-axis and hence the hyperbola is symmetric about the origin.

The hyperbola does not pass through the origin.

The tangent from any point (x₁, y₁) to the hyperbola is xx₁/a² – yy₁/b² = 1

learning the above properties will help to solve many problems

This is only the brief introduction to properties of hyperbola. Let us try to learn more on this topic. may be in the next lesson let me help you go through on Procedure for Draw the Hyperbola Graph.

Rational and Irrational Numbers

In among number theory.... Rational and Irrational Numbers plays an important role... This will help us understand all about number system and its functions in mathematical terms.

Rational Number -

The rational numbers can be expressed as terminating or recurring decimals.
Decimal fraction has denominator as 10 or a power of 10. A recurring decimal is denoted by placing dots or a bar over recurring digits.

Irrational Number -

Under number theory, numbers which are not rational are called irrational numbers. When expressed as decimals, they are non-terminating and non-recurring. We can obtain infinite number of irrationals between two irrational numbers

Summary -

1. Problems involving rational numbers are simplified using 'BODMAS' rule.

2. A rational number can be represented in the decimal form.

3. When a rational number is represented as a decimal, it will be either a terminating decimal or a recurring decimal.

4. All rational and irrational numbers can be marked on the number line.

5. Numbers with surds in the denominator are supposed to be simplified by rationalising their denominators

This is only the brief introduction to number theory. After reading this .. i am very sure that .. you would love to learn more and get help on math... keep reading and leave your valuable comments.... may be in the next lesson let me help you go through on Algebra Problems