a x b = ab = product
a + a + a + a = 4a
a ÷ b = a/b = quotient
GROUPINGUSE OF PARENTHESES
Occasionally a combination of symbols must be
treated as a single symbol. When this occurs, the group
is set apart by use of parentheses.
In order to symbolize 5 times the sum of a + b, you
should write 5(a + b).
The quotient of a + b divided by 2 is written
REMOVAL OF COMMON FACTORS
FROM AN EXPRESSION BY USE OF
In the expression 2a + 2b + 2c: the common factor
may be removed and the remainder combined in paren-
theses: 2(a + b + c) or in the following: 4ab + 2ac + 6ax.
All the terms contain the factor 2a. The expression
may be changed to read 2a(2b + c + 3x).
Since the parentheses indicate that each term within
is to be multiplied by the factor outside the parentheses,
the parentheses may be removed by multiplying each
term by the common factor.
Expression: 2x(2y + 3Z + m)
Multiply: 4 x y + 6 x z + 2 x m
SUBSTITUTION OF NUMERICAL
VALUES FOR GROUPED SYMBOLS
Consider the expression:
5(a + b)
This means to first: add a and b. Second: multiply the
sum by 5. Third: divide the product by 2.
Assign numerical values to a and b.
Let a = 4 and b = 2.
Perimeter and circumference have the same mean-
ing; that is, the distance around. Generally, circumfer-
ence is applied to a circular object and perimeter to an
object bounded by straight lines.
PERIMETER OF A POLYGON
The perimeter of a triangle, quadrilateral, or any
other polygon is actually the sum of the sides.
Write an equation for the perimeter(P) of the quad-
P = a + b + c + d
If this figure were a rectangle,
the formula P= a + b + c + d would still apply, but since
opposite sides are equal, we could substitute a for c and
b ford and write
P = 2a + 2b
If the figure were a square, the formula would
P = 4 a
We may, by the same reasoning, establish that the
formula for the perimeter of any regular polygon of n
sides having a sides is:
P = n(s)