Download 1) When we talk about the inverse of a number, what do we mean

1) When we talk about the inverse of a number, what do we mean? Please list examples of a number and
its inverse.
Inverse of a given number (under addition) is that number which when added to the given number makes it 0.
Inverse of a given number (under multiplication) is that number which when multiplied with the given number makes
it 1.
Examples:
-3 is the additive inverse of 3; 6 is the additive inverse of -6
1/4 is the multiplicative inverse of 4; 5 is the multiplicative inverse of 1/5
2) What is a rational number? Please list a couple of examples of rational numbers, and a couple of
examples of numbers that are not rational numbers and explain why they are not rational numbers.
A number of the form p/q where p and q are integers and q ≠ 0 is called a Rational number.
Examples of rational numbers are 3, 1/7, -1/9 etc
Examples of numbers which are not rational are sqrt 2, sqrt 3, etc
(Sqrt 2, sqrt 3 etc are not irrational because when we calculate them, we get non-recurring and non-terminating
results.)
3) 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? How did the number game use the skill of simplifying rational
expressions? Create your own number game using the rules of algebra. Be sure to think about values that
may not work. State whether your number game uses the skill of simplifying rational expressions.
(a) Steps of the given game:
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 (This does not use rational expressions)
(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 eat
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.
4) Post a response to the following: How is doing operations (adding, subtracting, multiplying, and
dividing) with rational expressions similar to or different from doing operations with fractions? Can
understanding how to work with one kind of problem help understand how to work another type? When
might you use this skill in real life?
Doing addition and subtraction with rational expressions is similar to doing them with fractions. We work out the LCD
for all the denominators and rewrite each numerator with the LCD in the denominator. Then the numerators are added
or subtracted as required.
Example:
x/3 ± 7/x = [x(x) ± 3(7)]/3x = (x^2 ± 21)/3x
Multiplication and division are done exactly as with fractions.
Example:
(x/3) * (7/x) = 7/3 and (x/3) ¸ (7/x) = x^2 /21.