Pre Algebra Period 2 (Monday)

Variables & Expressions 1-1 (continued)

You can translate words into Algebra word by word
just like you translate English to Spanish or French.
5 more than a number
5 + n
the product of 5 and a number
5n
the quotient of 5 and a number
5/n
the difference of a number and 5
n - 5
NOTE: BECAUSE MULTIPLICATION & ADDITION IS COMMUTATIVE, YOU DON'T NEED TO WORRY ABOUT THE ORDER
BUT
FOR SUBTRACTION AND DIVISION, YOU MUST BE CAREFUL ABOUT THE ORDER
GENERALLY, THE ORDER FOLLOWS THE ORDER OF THE WORDS
EXCEPT (counterexample!)
5 less THAN a number
or
5 subtracted FROM a number
Both of these are: n - 5
The order SWITCHES form the words because the words state that you have a number that is more than you want it to be so you need to take away 5 from it.
For word problems like someone's age or the amount of money you have, you should always check your algebraic expression by substituting actual numbers to see if your expression makes sense.
EXAMPLE: Tom is 3 years older than 5 times the age of Julie
Translating: T = 3 + 5J
Does that make sense? Is Tom a lot older than Julie or is Julie older?
Try any age for Julie. Say she is 4 years old.
T = 3 + 5(4) = 23
In your check, Tom is 23. Is Tom 3 years older than 5 times Julie's age?


STRATEGY #2: MAKE A T-CHART
To translate known relationships to algebra, it often helps to make a T-Chart.
You always put the unknown variable on the LEFT side and what you know on the right.
Fill in the chart with 3 lines of numbers and look for the relationship between the 2 columns.
Then, you use that mathematical relationship with a variable.

EXAMPLE: The number of hours in d days
Your unknown is d days so that goes on the left side:

d days number of hours
1 24
2 48
3 72

Now look at the relationship between the left column and the right column.
You must MULTIPLY the left column BY 24 to get to the right column
The last line of the chart will then use your variable d

d days number of hours
1 24
2 48
3 72
d 24d

EXAMPLE: The number of days in h hours (The flip of the first example)
Your unknown is h hours so that goes on the left side:

h hours number of days
24 1
48 2
72 3



(Why did I start with 24 and not 1 hour this time?)


Now look at the relationship between the left column and the right column.
You must DIVIDE the left column BY 24 to get to the right column
The last line of the chart will then use your variable h

h hours number of days
24 1
48 2
72 3
h h/24