Algebra (Period 1)

WORD PROBLEMS--REVIEW
Writing algebraic expressions will NOT have an equal sign and you will NOT be able to solve them!

CHAPTER 1-6: WRITING ALGEBRAIC EXPRESSIONS
STRATEGY #1: TRANSLATE WORD BY WORD
Many times you can translate words into Algebra word by word just like you translate English to Spanish or French.

5 more than a number

n + 5
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 are both commutative, when solving for a solution the order will not matter for the solution BUT I require that you translate accurately-- similarly to when you speak another language you are required to learn the proper order of words... AND, 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. If you aren’t sure about the order with these, I suggest that you try plugging in an actually number and see what you would do with the phrase.
For example, if the phrase was
“5 subtracted from 12”
you would immediately know to write
12-5

For word problems like someone's age or the amount of money you have, you also 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: 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.

3 + 5(4) = 23

In your check, Tom is 23.
Is Tom 3 years older than 5 times Julie's age?

YES!
You're algebra is correct!



STRATEGY #2: DRAWING A PICTURE

I have 5 times the number of quarters as I have dimes.

Let’s say I first translate to: 5Q = D
I
check: If I assume that I have 20 quarters, then 5(20) = 100 dimes

Does this make sense? That would mean I have a lot more dimes than quarters.

The original problem says I have a lot more quarters!

My algebra is WRONG!
I need to switch the variables.

5D = Q

I check: If I assume that I have 20 quarters, then 5D = 20
D = 4

Does this make sense? YES!
I have 20 quarters and only 4 dimes.

Sometimes it helps to make a quick picture.

Imagine 2 piles of coins.

The pile of quarters is 5 times as high as the pile of dimes.

You can clearly see that you would need to multiply the number of dimes
to make that pile the same height as the number of quarters!



STRATEGY #3: MAKE A T-CHART
-- this is my favorite!!
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 at least 3 lines of numbers and look for the relationship between the 2 columns.
Ask yourself what do you do to the left side to get to the right?

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 l number of hours

1 ------l------24

2 ------l------48

3 ------l------72

Now look at the relationship between the left column and the right column. What do I do to 1 to get 24? What do I do to 2 to get 48? What do I do to 3 to get 72? For each 
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

d days l number of hours

1 ------l------24

2 ------l------48

3 ------l------72

d ------l-----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 l number of days

24------l------- 1

48------l------- 2

72 ------l-------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. or ask yourself "What do I do to 24 to get 1? What do I do to 48 to get 2? What do I do to 72 to get 3?" 
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

h hours l number of days

24------l------- 1

48------l------- 2

72 ------l-------3
h -------l-------h/24



Some interesting translations used all the time in Algebra:

The next consecutive number after n: n + 1

Does it work? Try it with any number: if you have 5, then 5 + 1 will give you 6


The next EVEN consecutive number after n: n + 2

Does it work? Try it with any EVEN number: if you have 12, then 12 + 2 will give you 14


The next ODD consecutive number after n: n + 2

Does it work? Try it with any number: if you have 9, then 9 + 2 will give you 11