Difference between revisions of "Template:Science-Content"

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== Text ==
 
== Text ==
 +
 +
== Variable ==
 +
 +
In mathematics, a variable is a
 +
value that may change within the scope of a given problem or set of
 +
operations. In contrast, a constant is a value that remains
 +
unchanged, though often unknown or undetermined.[1] The concepts of
 +
constants and variables are fundamental to many areas of mathematics
 +
and its ''<u>applications.</u>''
 +
A &quot;constant&quot; in this context should not be confused with a
 +
mathematical constant which is a specific number independent of the
 +
scope of the given problem.
 +
 +
 +
One may use any letteras m,l,p,x,y,z etc to show a variable . Remeber , a
 +
variable is a number which does not have a fixed value. For ex ,the
 +
number 5 or the 100 or any other given number is not a variable. They
 +
are fixed values.(constant). Similiarly the number of angles of a
 +
triangle has a fixed value i e 3. It is not a variable.The number of
 +
corners of a qudrilateral is fixed (4 ) it is also not a variable.
 +
But the measurement of each side of a qudrilateral is not fixed.
 +
 +
 +
== Dependent and independent variables ==
 +
 +
Variables
 +
are further distinguished as being either a dependent variable or an
 +
independent variable. Independent variables are regarded as inputs to
 +
a system and may take on different values freely. Dependent variables
 +
are those values that change as a consequence to changes in other
 +
values in the system.
 +
 +
 +
== Expressions ==
 +
 +
An expression is a mathematical term or a sum or
 +
difference of mathematical terms that may use numbers, variables, or
 +
both.
 +
 +
 +
=== Example: ===
 +
 +
The following are examples of expressions:
 +
 +
 +
*2
 +
*x
 +
*3 + 7
 +
*2 × y + 5
 +
*2 + 6 × (4 - 2)
 +
*z + 3 × (8 - z)
 +
 +
'''Example:'''
 +
 +
Gangaiah weighs 70 kilograms, and Somanna weighs k kilograms. Write an expression for their combined weight. The combined weight in kilograms of these two people is the sum of their weights, which is 70 + k.
 +
 +
'''Example:'''
 +
 +
A car travels down the highway at 55 kilometers per hour. Write an expression for the distance the car will have traveled after h hours. Distance equals rate times time, so the distance traveled is equal to 55 × h..
 +
 +
 +
Example:
 +
 +
There are 2000 liters of water in a swimming pool. Water is filling the pool at the rate of 100 liters per minute. Write an expression for the amount of water, in liters, in the swimming pool after m minutes. The amount of water added to the pool after m minutes will be 100 liters per minute times m, or 100 × m. Since we started with 2000 liters of water in the pool, we add this to the
 +
amount of water added to the pool to get the expression 100 × m +
 +
2000.
 +
 +
 +
To evaluate an expression at some number means we
 +
replace a variable in an expression with the number, and simplify the
 +
expression.
 +
 +
 +
Example:
 +
 +
 +
Evaluate the expression 4 × z + 12 when z = 15.
 +
 +
 +
We replace each occurrence of z with the number
 +
15, and simplify using the usual rules: parentheses first, then
 +
exponents, multiplication and division, then addition and
 +
subtraction.
 +
 +
 +
4 × z + 12 becomes
 +
 +
 +
4 × 15 + 12 =
 +
 +
 +
60 + 12 =
 +
 +
 +
72
 +
 +
 +
Example:
 +
 +
 +
Evaluate the expression (1 + z) × 2 + 12 ÷ 3 - z
 +
when z = 4.
 +
 +
 +
We replace each occurrence of z with the number 4,
 +
and simplify using the usual rules: parentheses first, then
 +
exponents, multiplication and division, then addition and
 +
subtraction.
 +
 +
 +
(1 + z) × 2 + 12 ÷ 3 - z becomes
 +
 +
 +
(1 + 4) × 2 + 12 ÷ 3 - 4 =
 +
 +
 +
5 × 2 + 12 ÷ 3 - 4 =
 +
 +
 +
10 + 4 - 4 =
 +
 +
 +
10.
 +
 
== Lesson plan ([{{fullurl:{{FULLPAGENAME}}/Lesson Plan|action=edit }} Click to create the subpage]) ==
 
== Lesson plan ([{{fullurl:{{FULLPAGENAME}}/Lesson Plan|action=edit }} Click to create the subpage]) ==
 
Use <nowiki>{{subst:Lesson Plan}}</nowiki> in the newly created subpage.
 
Use <nowiki>{{subst:Lesson Plan}}</nowiki> in the newly created subpage.

Revision as of 17:53, 7 July 2013

Concept Map

Textbook (Click to create the subpage)

Text

Variable

In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined.[1] The concepts of constants and variables are fundamental to many areas of mathematics and its applications. A "constant" in this context should not be confused with a mathematical constant which is a specific number independent of the scope of the given problem.


One may use any letteras m,l,p,x,y,z etc to show a variable . Remeber , a variable is a number which does not have a fixed value. For ex ,the number 5 or the 100 or any other given number is not a variable. They are fixed values.(constant). Similiarly the number of angles of a triangle has a fixed value i e 3. It is not a variable.The number of corners of a qudrilateral is fixed (4 ) it is also not a variable. But the measurement of each side of a qudrilateral is not fixed.


Dependent and independent variables

Variables are further distinguished as being either a dependent variable or an independent variable. Independent variables are regarded as inputs to a system and may take on different values freely. Dependent variables are those values that change as a consequence to changes in other values in the system.


Expressions

An expression is a mathematical term or a sum or difference of mathematical terms that may use numbers, variables, or both.


Example:

The following are examples of expressions:


  • 2
  • x
  • 3 + 7
  • 2 × y + 5
  • 2 + 6 × (4 - 2)
  • z + 3 × (8 - z)

Example:

Gangaiah weighs 70 kilograms, and Somanna weighs k kilograms. Write an expression for their combined weight. The combined weight in kilograms of these two people is the sum of their weights, which is 70 + k.

Example:

A car travels down the highway at 55 kilometers per hour. Write an expression for the distance the car will have traveled after h hours. Distance equals rate times time, so the distance traveled is equal to 55 × h..


Example: 

There are 2000 liters of water in a swimming pool. Water is filling the pool at the rate of 100 liters per minute. Write an expression for the amount of water, in liters, in the swimming pool after m minutes. The amount of water added to the pool after m minutes will be 100 liters per minute times m, or 100 × m. Since we started with 2000 liters of water in the pool, we add this to the

amount of water added to the pool to get the expression 100 × m + 2000.


To evaluate an expression at some number means we replace a variable in an expression with the number, and simplify the expression.


Example:


Evaluate the expression 4 × z + 12 when z = 15.


We replace each occurrence of z with the number 15, and simplify using the usual rules: parentheses first, then exponents, multiplication and division, then addition and subtraction.


4 × z + 12 becomes


4 × 15 + 12 =


60 + 12 =


72


Example:


Evaluate the expression (1 + z) × 2 + 12 ÷ 3 - z when z = 4.


We replace each occurrence of z with the number 4, and simplify using the usual rules: parentheses first, then exponents, multiplication and division, then addition and subtraction.


(1 + z) × 2 + 12 ÷ 3 - z becomes


(1 + 4) × 2 + 12 ÷ 3 - 4 =


5 × 2 + 12 ÷ 3 - 4 =


10 + 4 - 4 =


10.

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