|
In the previous lesson you learned three
vocabulary words used in algebra. Let's quickly review the
algebraic words you have learned so far:
-
Variable
- a letter or other symbol that represents a number. A
variable can represent one specific number, or it can stand for
many different numbers.
-
Constant
- a
number that never changes, is added or subtracted
-
Expression
- is a phrase that contains one or more symbols and numbers and it
does not contain an equal sign
For
this lesson we also need to define the following word:
-
translate
- change words from
one language to another
The two "languages" you will be using
are English words and Algebra words. You are going
to "translate" word, or verbal, expressions into algebraic expressions.
|
Let's start with
some easy expressions with only one variable and
one constant. Although you can use any symbol for your
variable, we will keep it simple by.....
Letting n = "the
number" in all expressions, but the constants will be
different in each expression |
 Let's
start by showing expressions using addition. Notice, because addition is
commutative, order doesn't matter.
|
Expressions using
the addition sign
to connect variable and constant |
|
verbal (word) expressions
|
algebraic
expressions |
| a
number plus 5 |
n + 5
or 5 + n |
| 10
more than a number |
10 +
n or n + 10 |
| 20
added to a number |
20 + n
or n + 20 |
| 8
greater than a number |
n + 8 or
8 + n |
| a
number increased by 4 |
n + 4 or
4 + n |
| the
sum of a number plus ½ |
n + ½ or
½ + n |
 The
following expressions all use subtraction. Notice because
subtraction is NOT commutative, order is important.
|
Expressions using the
subtraction
sign to connect variable and constant |
|
verbal(word) expressions
|
algebraic
expressions |
|
a number minus 10 |
n - 10 |
|
20 minus a number |
20 - n
|
|
5 less than a
number * |
n - 5* |
|
the difference of
a number and 9 |
n - 9 |
|
a number decreased
by 6 |
n - 6 |
|
a number
diminished by 7 |
n - 7 |
*Notice this algebraic expression is not in the
same order as the verbal expression; so be careful with "less than".
You have to really think about that one.
|
 HINT!!
|
If you cannot
decide whether the variable or the constant goes first in a
subtraction expression, try substituting an actual number for
the variable. |
| ex: if the problem
is a number minus 5 |
think:
10 - 5, not 5 - 10, so then you
know the expression must be n - 5, not 5 - n |
And now the easiest to
"translate": expressions using multiplication and division.
|
Expressions using the
multiplication
sign to connect variable and constant |
|
verbal (word) expressions |
algebraic
expressions |
|
three times a
number |
3 x n
or
3n
3n is more
correct, because the times sign looks like an "x" which is
sometimes the chosen variable |
|
Expressions using the
division
sign to connect variable and constant |
|
verbal (word) expressions |
algebraic
expressions |
|
a number divided
by 6 |
n
÷ 6 |
These were the "easy"
ones, because you just had to substitute "n" for "a number".
Lesson II will show you how to translate word problems into
expressions.
Lesson II
|
