Take any number (except for 1). Square that number and then subtract one. Divide by one less than your original number. Now subtract your original number. Did you reached 1 for an answer? You should have. How does this number game work? (Hint: Redo the number game using a variable instead of an actual number and rewrite the problem as one rational expression). How did the number game use the skill of simplifying rational expressions? Create your own number game using the rules of algebra and post it for your classmates to solve. Be sure to think about values that may not work. State whether your number game uses the skill of simplifying rational expressions.
(a) x
x^2 – 1
(x^2 – 1)/(x – 1) = x + 1
x + 1 – x = 1, which is the desired result.
The game works because you are dividing an expression by one of its factors and then subtracting the original number.
(b) Number game:
(1) choose a number from 1 to 7, which represents the number of times you would like to eat dinner out each week (one per day)
(2) Multiply this number by two
(3) Then add 5
(4) Multiply this result by 50
(5) Now, if you have had your birthday this year already, add 1757 to the result in step 4. If not, add 1756.
(6) Then subtract your birth year.
The resulting number is a three-digit number. The first (leftmost) digit gives the number of times you would like to each out each week. The other two give your current age.
Example:
(1) 3
(2) 3 x 2 = 6
(3) 6 + 5 = 11
(4) 11 x 50 = 550
(5) 550 + 2306 = 2306
(6) 2306 – 1984 = 322
(This one does not use rational expressions.)