Chapter 1
Expressions
A numerical expression consists of numbers and variables. We use variables when we do not know the precise number.
You can convert verbal expression to numeric expressions by identifying important keywords.
| Addition |
increased by
more than
combined, together
total of
sum
added to
|
| Subtraction |
decreased by
minus, less
difference between/of
less than, fewer than
|
| Multiplication |
of
times, multiplied by
product of
increased/decreased by a
factor of (this type can
involve both addition or
subtraction and
multiplication!)
|
| Division |
per, a
out of
ratio of, quotient of
percent (divide by 100)
|
| Equals |
is, are, was, were, will be
gives, yields
sold for
|
source: http://www.purplemath.com/modules/translat.htm
Signed Numbers - Addition
| Rule |
Example |
Results |
| Positive + Positive |
4 + 5
|
always positive (9) |
| Negative + Negative |
-5 + -4 |
always negative (-9) |
| Positive + Negative |
4 + -5 |
varies; see below (-1) |
|
Negative + Positive
|
-5 + 4 |
varies; see below (-1)
|
| Different Signs
|
step 1:find sign of larger magnitude number
step 2:subtract smaller number from larger number
(without regard for sign)
|
|
Signed Numbers - Subtraction
| Rule |
Example |
Results |
| Positive - Positive |
2 - 4 becomes 2 + (-4) |
convert to addition of a negative (see above)
keeping the first operand the same, change the second operand and add it
|
| Positive - Negative |
3 - -3 becomes 3 + 3 |
convert double negative to addition of a positive (see above)
|
| Negative - Positive |
-5 - 6 becomes -5 + (-6) |
convert to addition of a negative (see above) |
| Negative - Negative |
-4 - -7 becomes -4 + 7 |
convert double negative to addition of a positive (see above)
- Do NOT change the first operand ***
|
Signed Numbers - Multiplication/Division
| Rule |
Rule |
| Positive x Positive |
Positive |
| Positive x Negative |
Negative |
| Negative x Positive |
Negative |
| Negative x Negative |
Positive |
this is cool
remember, if you are having trouble with this type of problem, always look at it like an addition problem!!!!!
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