## Wednesday, March 9, 2011

### Chapter 4: Algebra - An Introduction...constants and variables

In algebra, we make friends with variables & constants... Who are they? How do they look like? Let's get to know VARIABLES first...

Post the definitions of (i) Variable (ii) Constant. In each case provide at least 2 examples.

1. The definitions and examples of
i) Variable: A changing value. It is also a letter that represents an unknown number. Examples are like y+4=11 or y7=21; y is the variable.
ii) Constant: A value that remains the same or unchanged. Such examples are like 5p and 5+p-q: 5 is the constant since its value will never change.

2. i) Variable: A variable is a value/factor that changes. Examples: y+5=11 or 2y=20. In the first equation, y=6 but in the second equation, y=10, so the value of y varies and y is a variable
ii) Constant: A constant is a value that does not change. Example: 5+x=6, 5+y=7. In both equations, 5=5 and does not change, so 5 is a constant

3. i) A variable is a factor or value that will change. The examples is 5y =5 x y = 25 well then in 5+y= 13 Which means in the first one y = 5 and in second one y = 8 ... So the value of y changes. The other example is that, 8 + x = 23 and 8z = 8 x z =32 So in the first scenario z= 15 and in the second one z=4 .. The value of z changes..

ii) A constant is a factor or value that will never change.. The examples are z/5 and x/5 .. In both the number sentence the value 5 does not change.. The other example is that 8+z and 8+y .. The value 8 does not change.. It is constant..

4. i) A variable is a symbol that represents a quantity in an algebraic expression associated with a value and whose associated value may be changed.
Example:
Eq 1: 2x = 4
x = 2
Eq 2: 3 + x = 4
x = 1
Therefore you can see that the algebraic expression x is associated with a value and the value can change as you can see in equation 1 x is associated with the number 2 and in equation 2 x is associated with the number 1.
Eq 1: 3n = 12
n = 4
Eq 2: 3 + n = 12
n = 9
Therefore you can see that the algebraic expression n is associated with a value and the value can change as you can see in equation 1 n is associated with the number 4 and in equation 2 n is associated with the number 9.

ii) A constant is a number that will not change and is fixed.
Example:
Eq 1: x = 2
2 X x = 4
Eq 2: x = 3
2 X n = 6
Therefore you can see that in both equations, 2 is fixed and and the value will not be changed.
Eq 1: x = 2
2 + x = 4
Eq 2: n = 4
2 + n = 6
Therefore you can see that in both equations, 2 is fixed and and the value will not be changed.

5. (i) Variable:Is something that is likely to vary . In math, a variable is a value that may change within the scope of a given problem or a symbol that represents a quantity in an algebraic expression.
e.g.
as x is the variable it can be any number
x=1-9999996
so x+3 may equal to 4-9999999 respectively
(ii) Constant:changeless: unvarying in nature.In Math a Constant is a number that will not change and is fixed.
e.g. 12 is the constant
x=1
12+x=13
x=2
12+x=14
as 12 is the constant its value will never change

6. (i) Variable: It is something that varies. In mathematics, a variable is a value that changes.
For example: x - 10 = 20 and x10 = 60
(x is a variable)

(ii) Constant: It is something that stays the same. In mathematics, a constant is a value that does not change.
For example: 8+x=10 and 8+x=20
(8 is a constant)
(x is a variable)

7. Variable: A quantity or function that may assume any given value or set of values. (In mathematics)

EXAMPLE: y = 10, y = - 3, y = 11 or f(x) = y = 14

Constant: Something that remains unchanged throughout a long period of time or sometimes forever.

EXAMPLE: F (x) = x or F (x) = x2

8. 1 divided by 2=X
2 divided by 1=X

i)something that changes: X

ii)something that remains the same:1 and 2