Download n - Haiku

Algebra: THE RECAPUsing Symbols for un-knows
• Objective: To recap
algebra rules and
simplify expressions
Must symbols for
unknowns
Should Simplify
expressions
Could Simplify
expressions with
powers
1
Using symbols for unknowns
Look at this problem:
+ 9 = 17
The symbol
stands for an unknown number.
We can work out the value of
.
=8
because
8 + 9 = 17
2
Using letter symbols for unknowns
In algebra, we use letter symbols to stand for numbers.
These letters are called unknowns or variables.
Sometimes we can work out the value of the letters and
sometimes we can’t.
For example,
We can write an unknown number with 3 added on to it as
n+3
This is an example of an algebraic expression.
3
Writing expressions
Here are some examples of algebraic expressions:
n+7
a number n plus 7
5–n
5 minus a number n
2n
2 lots of the number n or 2 × n
6
n
6 divided by a number n
4n + 5
4 lots of a number n plus 5
n3
a number n multiplied by itself twice or
n×n×n
3 × (n + 4)
or 3(n + 4)
a number n plus 4 and then times 3.
4
Collecting together like terms
Remember, in algebra letters stand for numbers, so we
can use the same rules as we use for arithmetic.
In arithmetic,
5+5+5+5=4×5
In algebra,
a + a + a + a = 4a
The a’s are like terms.
We collect together like terms to simplify the expression.
5
Collecting together like terms
When we add or subtract like terms in an expression we
say we are simplifying an expression by collecting
together like terms.
An expression can contain different like terms.
For example,
3a + 2b + 4a + 6b = 3a + 4a + 2b + 6b
= 7a + 8b
This expression cannot be simplified any further.
6
Collecting together like terms
Simplify these expressions by collecting together like terms.
1) a + a + a + a + a = 5a
2) 5b – 4b = b
3) 4c + 3d + 3 – 2c + 6 – d = 4c – 2c + 3d – d + 3 + 6
= 2c + 2d + 9
4) 4n + n2 – 3n = 4n – 3n + n2 = n + n2
5) 4r + 6s – t
Cannot be simplified
7
8