Formulas for measurement

In the previous post we have discussed about Problems in measurements and In today's session we are going to discuss about Formulas for measurement.
Formulas for measurement
There are different shapes for which measurement formula is applied
Shape 1 Rectangle Measurement is done in the form of Area and Perimeter


Properties of rectangle:

In a  angle right angle triangle and lines are parallel to each other. Opposite sides are equal to each other .In the above figure L=Length and B=Breadth
Rectangle:
Area = Length X Breadth
A = L*B

Perimeter = 2 X Lengths + 2 X Breadth
P = 2L + 2B
P=2(L+B)
Shape 2:

In  the parallelogram opposite sides are equal a , b are the length of the two sides with the height as H where comes the 90 degree angle

Parallelogram Area:
Area = Base X Height
A = b*h


Shape 3
The triangle have three sides  a , b , c  with a height ‘h’ and b as base
Triangle
Area = 1/2 of the base X the height
a = 1/2 (B*H)
Perimeter = a + b + c
(add the length of the three sides)
 Learn Formulas for measurement with the help of examples

Examples: Find the area and perimeter of a rectangle with sides 4cm, 2cm?
Solution: Area =Length * breadth
Area = 4 * 2
Area =8 cm²
Perimeter=2(L+B)
P=2(4+2)
P=2*6
P=12 cm

Example: Find the area of the parallelogram where base =3 cm and height =8cm?
Solution: Area =Base * height
Area =3* 8
Area =24 cm²

 (know more about icse board, here)

Example :Find the area and perimeter of the triangle with Dimensions in centimetres  (3 , 4 , 6) and height as 3cm ?
Solution : Area = 1/2 of the base X the height
a = 1/2 (4*3)
Area =12/2
Area =6 cm²

Perimeter = a + b + c
P= 3+4+6
P=13 cm

Example: Find the length of a rectangle where area is 24cm² and breadth is 4 cm ?
Solution : Area =L*B
24=L*4
6cm =L

Example :Find the height of a triangle where base is 5 m and area is 35 m^{2?
Solution :}  Area =(b*h)/2
35= (5*h)/2
70=5*h
14m=h

Problems in measurements

Problems in measurements are very common problems that are mostly encountered while doing math calculations on a daily basis. This part of measurement can be broadly classified into three types of problems:
1.Distance : It  generally includes problems with mm, cm, km...
2. Time: It generally includes problems with seconds, minutes, hours...
3.Mass: It generally includes problems with Milli gram, gram, kilo gram...
This part is specially designed for Grade VII and now, we will move to word problems measurement:
Problems 1: If One liter is equal to 1000 cubic centimeter and we have a Milk container containing 34.6 liters of milk, how much does this in cubic centimeters?
Solution 1: 1 Lit = 1000 cc.
34.6Lit = 34.6 * 1000 = 34600 cc.
Problem 2 : If we increase the Radius of a circle by 200 %, how many times will the area be increased for that particular circle?
Solution 2 : Area of circle = ∏r>2. That is the area is directly proportional to the square of the value of radius, when we increase the value of the radius by 200 % that means that now the radius is 3r from earlier r and when we square this 3r it will give us 9r>2, making the value of circle increase by 9 times.
Problem 3: It takes 30 minutes to pile up the bundle of 100 files, there are 2000 files in the store room. How much time will it take? (know more about cbse sample papers, here)

  Solution 3: It takes 30 min to pile 100 files, which means to pile 1000 files it will take 300 min and similarly to pile 2000 files it will take 600 minutes, which is equal to 10 hours.
Thus we, hope that now things related to this topic are more clear with the pupils. In the next session we will discuss about Formulas for measurement.

Measurements in Mathematical World

Measurements in maths play a very crucial role in our day to day life. In earlier times, we used to calculate the distance and lengths by feet or palms, which was not a standard unit of measurement. To overcome this difference, standard scale of measurements was developed. It can be represented in form of a scale as follows:
Milli
Centi
Deci
Unit
Deca
Hecto
Kilo
The above scale shows that milli is the smallest unit and kilo represents the largest unit.  For length measurements meter is the standard unit and the above table can be written as:
Milli Meter
Centi Meter
Deci Meter
Meter
Deca Meter
Hacto Meter
Kilo Meter
In Grade VII, we will learn about converting one unit to another. When we do certain mathematical operations on measurements, the units must be same. So for this reason we need to convert one unit to another. Suppose we need to add 13 mm and 4 cm. In such cases as the units are not same, we need to convert either of the units. If we convert mm to cm, we need to divide it by 10 and if we convert cm to mm, we will multiply it by 10.
So 13 mm becomes 13/10 cm
= 1.3 cm
Now 1.3cm and 4 cm can be added easily.
= 1.3 + 4 cm
= ( 1.3 + 4.0 ) cm
= 5.3 cm Ans
we conclude that in the above table if we convert from upper to lower form the  digits are divided by 10 every time. Eg if mm is to be changed to cm, then divide by 10, mm to deci meter then divide by 100... and so on
Similarly if we move from bottom to top, then we need to multiply by 10 every time. eg: if km is to be converted to hectometer then the digits are multiplied by 10, km to deca meter, then multiply by 100 ... and so on.
In the next topic we are going to discuss Problems in measurements

Graphing solutions of inequalities

Today we will be studying Graphing Solutions Of Inequalities, Graph Solution Of Inequalities, Measurements-
To understand Graphing solutions of inequalities, Graph solution of inequalities, Measurements we must first understand the meaning of inequalities, inequalities can be defined as that one expression can be greater than or less than some other expression, the mathematical symbols used in inequalities are less than(<), greater than (>), less than equals to (≤) and greater than equals to (≥). The inequalities can transformed in many other ways. The direction of inequalities does not change if any number is added to both sides or if number is subtracted from both sides or both sides are multiplied and divided on both sides.
An inequality is of the form y > mx + b or y < mx + b, here x and y are the coordinates and 'm' is the slope and 'b' is the intercept.
Examples of inequalities-
y ≤ 2x + 3 or 2x – 3y < 6
As we have understood the meaning of inequalities, so now we will try to plot some of the inequalities on a graph. The examples are show below-

1)Let us take an example y ≤ 2x + 3 and plot it on the graph.
First we will plot the equal part of inequality that is y = 2x + 3, it is a straight line so after plotting
the graph will look like

                                                     This graph is for the equality part that is y = 2x + 3 but we also have to plot less than part of the inequality. To plot the less than part that is y < 2x + 3 we just shade the region.
So either we shade the region below the line on region above the, in this inequality we will shade the region below the line as 'y' is less than 2x + 3 .So after shading the region below the line graph will look like:                                                     

                                                            
                                   





So this is how we see Graph solution of inequalities.
In the next session we are going to discuss Measurements.

Relation between objects in space

SPACE:

• space is a three dimentional structure
• space is boundless and limitless.
• space contains object exist in space
• many events exist in space

objects:

• object is a physical body which is a collection of masses.

mass and weight of an object:

Mass is a measure of how much material is in an object, but weight is a measure of the gravitational force exerted on that material in a gravitational field; thus, mass and weight are proportional to each other, with the acceleration due to gravity as the proportionality constant. (know more about icse board papers 2013, here)
w=m*g
w is the weight
m is the mass.
g is the acceleration due to gravity.
g=9.8 m/sec>2

 Relation between objects in space
Relation between objects in space follows the newtons  gravitational law of gravitational
Newton's Universal Law of Gravitation states that any two objects exert a gravitational force of attraction on each other. The direction of the force is along the line joining the objects
Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of electrical force between two charged bodies and this signifies the Object And Space Relationship.

.The magnitude of the force is proportional to the product of the gravitational masses of the objects, and inversely proportional to the square of the distance between them .
F(1,2)=(G*m1*m2)/r>2
m1 & m2 are the objects in space
m1 exerts  force F12 on m2
m2  exerts force F21 on m1
G is  the gravitational contant which is 6.67 x 10>- 11 N m>2/kg>2

• The inertial mass of an object determines the amount of force needed to produce a given acceleration of that object.
•  The gravitational mass determines the force of gravitational attraction between two bodies.

Gravitation is a natural phenomenon in which physical bodies attract with force propotional to the mass.
it is resposible for keeping all the object  in the universe in there orbit , otherwise all objects would have collide

In the next session we will discuss about Graphing solutions of inequalities. 

Congruence in Grade VII

Hello students today we are going to discuss Congruence. In mathematics you have to deal with many topics, congruence is one of them. If there are two or more objects or figures that have the same size and same shape, they are called congruent objects or figures. In other words the figures are called isometric, i.e. they have same size and same shape. In congruence we can reposition the objects in other shapes than they known as translation, rotation and reflection and combination of all called is transformation. Let’s take an example of triangle that will surely help you to understand this:-If      Two triangles have same corresponding size and same corresponding shape than they are congruent. As shown in figure we have two triangles ABC and DEF and in first triangle AC=7, CB=6 and in second triangle DF=7, FE=6. This implies both the triangles have same size and same shape so we can show their relationship in this way:-

∆ABC≅∆DEF

To determine congruence we have some comparisons, they are:-

-Angle side angle.

-Angle angle side.

-Side angle side.

-Side side side.

-Right angle hypotenuse side.

If any one of the comparisons exists in any figure than they are said to be congruent figures. Generally congruence may be defined in many fields like:-

-In relation.

-In modular arithmetic.

-In groups and subgroups.

-In number theory.

-In general relativity.

-In graphs.

And congruence is present in those shapes where equality is there; like in figures, objects, relations, groups and in many fields.

 

The above described congruence information will surely helpful for grade VII students. In the next topic we are going to discuss Relation between objects in space.

Pythagorean Theorem in Grade VII

In Euclidean Geometry, Pythagorean theorem is given for three sides of right triangle. Right triangle is described as a triangle whose one angle is a right angle i.e. 90'. Pythagorean theorem states that square of the side opposite to the right angle known as hypotenuse is equal to the sum of the square of other two sides of the right triangle. We can define it by an equation known as the Pythagorean Theorem Worksheet as:
If a right triangle have three sides a , b and c then according to the Pythagorean theorem of maths the relation between the sides is A² + B² = C² where C is a hypotenuse of right triangle and A and B are two other sides of right triangle .
If the two sides of the right triangle are given then we can calculate other third side by using the Pythagorean theorem.  (To get help on cbse syllabus click here)
Let us assume that A side has the length of 3 centimeters and side B has the length of 4 centimeters then the length of the hypontenuse is A² + B² = C²

So according to the Pythagorean theorem, length of c is 3² + 4² = c² . By solving this equation we get the value of C is 5 as C = ( 3² + 4² )^½
= ( 9 + 16 )^1/2 = ( 25 )^1/2
= 5 centimeters.
Example: If we have the length of hypotenuse as 13 centimeter and one of its side is 5 centimeter then calculate the length of other remaining side.
Solution: We are given that A=5, C=13. We have to find B.
5² + B² = 13² then value of B as B² = 13² – 5² then
B² = 169 – 25
B = ( 144 )^1/2
B = 12 centimeters
So In the next topic we are going to discuss Congruence and In the next session we will discuss about Congruence in Grade VII. 

math blog on grade VII

Dear kids,Previously we have discussed about how to simplify rational numbers and in this session we will talk about inequalities and problem related to inequalities and graphing inequalities problems, of grade VII of gujarat state education board.  We will learn here how to graph any inequality on the number line and how to solve them, You can take inequality solver help if needed.

An inequality is a type of linear equation in which there are two different expressions on both sides of a particular symbol either equality or the symbol of inequality. This symbol shows the relationship between these two expressions that how they are related to each other whether they are equal or have some comparative relation in them. In inequality, there are some of the symbols which are used in inequalities to show the relationship between the expressions. Say in equation 2x = 3y, here is the relation of equality between two expressions 2x and 3y. In a similar way the inequality 2 x > 3 y, shows that the value of left side expression is larger than that of right side of expression.

If an expression is greater than any other expression then in the notation, it will come in the right and smaller expression will come in the left of the inequality symbol. The inequality is also same as the number line notation. The symbol less than (<) is used to represent comparatively less value and (>) is used for larger value.

We can say here, that 4 is greater than -1, because 4 is on the right side of -1 (or -1 is on the left of 4). We write it as 4 > - 1 or as − 1 < 4. Let say for basic purpose two different expressions are as x and y, then:
                y > x       left side expression is greater than that of right side of expression.
                y < x       left side expression is less than that of right side of expression.
                y = x       both expression are of same value.
                y >= x          both of the function may be same or y may have greater value than that of value of the x.
                y <= x          both of the function are either of same value or y have less value than that of value of x.

Sometimes equality is also included with inequality. For example: Inequality       y >= - x + 1.
Just for example we can draw an inequality y>= (2/3) x - 4 on the plane as:                                                  

The graph shows the equations as per the inequality where they are true on the number line and what values they can grab.(want to Learn more about inequality, click here),
To solve any inequality and get exact solution, we go through the graphing problem on number line. Graphing inequalities problem is the best way to solve any of the inequality. In inequality having one unknown, there may be more than one possible solution (sometimes may be infinite) for a particular inequality. Solving any of the linear inequalities involves the finding of solutions of expressions where variables are not equal on the number line. To solve any inequality we have to graph the inequality on the number line, it is similar to the graphing of linear functions.
This is all about the graphing inequalities problems and if anyone want to know about Graph and Slope of Lines in Grade VIII then they can refer to Internet and text books for understanding it more precisely. Read more maths topics of different grades such as Multistep problems in the next session here.    

Properties of lines

In the Earlier sections we have discussed about converting whole numbers to fractions and also discussed about Math problems related to it and now we are starting with a new topic that is Properties of lines which is an important part of every education board, When a Line segment extends endlessly in both the directions such that it has no starting or end point and has no fixed length is called a line.(want to Learn more about Line, click here),
Some of the properties of lines are:
1. A line cannot be drawn on a paper as it extends endlessly. So to represent any line we mark arrow signs at both its ends.


Represents a line
2. Intersecting lines: Two lines are called intersecting lines when they both meet at a point. This point is called the point of intersection of two lines.

Lines m and n are intersecting lines.                       
3.  Parallel lines: Two lines are called parallel, if they do not meet at all, which means that the perpendicular distance between the two lines is equal at all the points. It is said that the two parallel lines never meet.
                               <------------------------------------------> m
                                <------------------------------------------> n
Here, we have lines m and n as the pair of parallel lines.

4. A line has no fixed length.
5. When two lines are parallel and they both are intersected by any third line, then this intersecting line is called a transversal.
 6. When a pair of angles combine together to form a straight line, i.e. the sum of two angles is 180 degrees then it is called a linear pair.

Here ∠AOC + ∠COB = 180
So   ∠AOC and ∠COB form a linear pair

 7. Following properties are true for a pair of parallel lines, if there is a transversal passing from a pair of parallel lines
     a) Interior Alternate angles are equal
     b) Corresponding angles are equal
     c) Interior consecutive angles are supplementary
This is all about the Properties of lines and if anyone want to know about Geometry then they can refer to Internet and text books for understanding it more precisely. You can also refer Grade 8th blog for further reading on Representations of data.