Pre Algebra (Period 2 & 4)

Evaluating Expressions 1-3 (continued)


STRATEGY #1: 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 ---> 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 ---> 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 -> 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 -> days
24 --->1
48 ---> 2
72 ---> 3
h --->h/24


The number of inches in y yards
You know that there are 36 inches in 1 yard.
y yards is the unknown so that must go on the left

y yards -> inches
1 ---> 36
2 --->72
3 ---> 108

Ask yourself
"What did I do to 1 to get 36?"
"What did I do to 2 to get 72?"
"What did I do to 3 to get 108?"
Answer for all three multiplied by 36

so what do you do to y ?
multiply by 36

y yards -> inches
1 ---> 36
2 --->72
3 ---> 108
y ---> 36y

36y is the expression you are looking for!!

How about the number of yards in i inches.
This time i inches is the unknown
i inches -> y
36 ---> 1
72 --->2
108 ---> 3

This time when you ask the question it is
"What did I do to 36 to get 1?"
What did I do to 72 to get 2?"
"What did I do to 108 to get 3?"

With each of these your answer is you divided by 36.

So what must you do to i... divide by 36
i inches -> y
36 ---> 1
72 --->2
108 ---> 3
i ---> i/36

so i/36 is your expression


We drew a grocery bag with the following info:
Food -> Calories
Bread ---> 55
Apple ---> 70
Banana --->100
Egg ---> 110


3 apples + 2 bananas
3(70) + 2 (100)
210 + 200 = 410 calories
a apples + b bananas
becomes 70a + 100b

e eggs + 1 slice of bread?
110e + 55