Download 2 - Mr. Hilli

Algebra is a form of mathematics that combines letter and
numbers with arithmetic operations.
These letters represent unknowns values and are called
variables. They are called variables because they can be
used to represent different numerical values.
For example:
a
is a variable that represent an unknown number.
Properties of variable
Variables have the same properties as regular digits (Integers,
fractions, etc.) Let’s look at some:
1. Addition and subtraction:
Examples:
a+1=a+1
a–1=a-1
Here, because a is an unknown, the
operation remains as is.
a + a = 2a
Here, you can imagine that there is a 1 in
front of the variable and that it can be
added onto another identical variable.
Same story
2a + 3a = 5a
1. Addition and subtraction:
Examples:
a–a=0
Again, we have two similar variable.
4a – 1a = 3a
4a – 7a = -3a
5a + 6b = 5a + 6b
5a - 6b = 5a – 6b
In this, case, there are two different
variables and hence, they cannot be
added or subtracted.
2. Multiplication:
Examples:
2 x a = 2a
Since a is an unknown variable that
represents a numerical digit, it can
multiply the 2.
a x b = ab
2a x b = 2ab
So two variables that represent unknown
digits can be multiplied as usual.
2a x 2b = 4ab
In this case, the numerical digits multiply
and it’s status quo for the variables.
a x a = a1+1 = a2
As in multiplication with exponents, the
exponents are added together.
2. Multiplication:
Examples:
2ab x 3ab = 2 x 3 x a x a x b x b In this case, identical
= 6 a1+1b1+1
variables multiply.
= 6a2b2
2. Division:
Examples:
2÷a= 2
a
Again, Here, because a is an unknown,
the operation remains as is.
2a ÷ a = 2 x a1-1
= 2 x a0
=2x1
=2
Only the identical variables perform the
operation.
4a2b ÷ 2a = 4 ÷ 2 x a2 ÷ a x b
=2
x a2-1 x b
=2
xa
xb
= 2ab
3. Fractions:
Examples:
2
a
x
3
a
= 2 x 3
a x a
=
6
a1+1
=
6
a2
3. Fractions:
Examples:
a
2
x
3
a
= a x 3
2 x a
=
3a
2a
=
3
2
Things to know before we get started.
1. Algebra involves the use of variables such
as x or y or z or any other letter that can designate any number.
1. Imagine that algebraic equations are scales. A scale can be tilted if
you add, subtract, multiply or divide either side.
2. So what you do on one side of the equation must be done on the
other.
3. Let’s look at the following example.
So:
1. 2x + 2 = 8
My objective is to solve for x. To do so, I have to isolate x i.e. have
x by itself on one side.
2. We’ll start by subtracting the 2 being added because that will
eliminate the 2. But remember that what you do one side you
must do on the other.
2x + 2
-2
= 8
-2
So:
0= 6
=6
3. 2x +
2x
4. Now, I have to eliminate the other 2 that is multiplying the x. To
do so, since it is multiplying the x, I will divided it by 2 because the
opposite of multiplication is division. Again, what you do one side,
you must do on the other.
6
2 2
2x =
So:
5. x =
3
6. Now, try solving the following equation by your self:
7. 3x + 5 = 14