Math 6 Honors (Period 6 and 7)

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Mathematical Expressions 1-1

A variable is a symbol used to represent one or more numbers. The numbers are called the values of the variable.


An expression, such as 3 x n, that involves a variable is called a variable expression.


Expressions, such as 3 x 2, that name a certain number are called numerical expressions


When we write a product that involves a variable, we usually omit the multiplication symbol (whether that be written as x or as ∙ or even with parentheses). Thus, 3 x n is written as 3n
and 2 x a x b is written as 2ab

In numerical expressions for products a multiplication symbol must be used to avoid confusion.

9 x 7 may be written as 9 ∙ 7 or even 9(7)

When a mathematical sentence uses an equal sign, it is called an equation. An equation tells us that two expressions name the same number. The expression to the left of the equals sign is called the left side of the equation and the expression to the right of the equals sign is called the right side.
expression = expression

When a number is substituted for a variable in the variable expression and the indicated operation is carried out, we say that the variable expression has been evaluated. For example, if n has the value 6 in the variable expression 3 x n, then 3 x n has the value 3 x 6, or 18
Example: Evaluate the expression 6a when the variable has the following values:
6a; 2, 4, 6, 8
You would substitute in each value for the variable a
6(2) = 12
6(4) = 24
6(6) = 36
6(8) = 48

148 ÷ 4 =
148/4
37


if m = 3 and n = 18
n ÷ m
substitute in
n/m or 18/3 = 6


If y = 18 and x = 8
4y ÷ 3x immediately set this up as
4y/3x

Now substitute in your values
4(18) / 3(8)
72/24 = 3