Rational vs. Irrational
Variable Sub. & Properties
Graphing
Translating Algebra
Solving Equations
100
1
Rational- Natural Number
100
x + 1 for x = 8
x + 1 = 8 + 1 = 9
100
True or False?
The x-axis is horizontal (left and right)
True!
100
Translate: Two more than a number, n
n + 2 or 2 + n
100
Solve for x if: x + 2 = 7
x = 5
200
√4
Rational- Perfect Square
200
xy for x = 2 and y = 7
xy = 2 x 7 = 14
200
True or False?
The ordered pair for the origin is (0, 0)
True!
200
Translate: Three times a number, n
3n
200
9 more than x is 12. Create and solve the equation for x.
x + 9 = 12
x = 3
300
π (pi)
Irrational- The most famous example!
300
a + b + c for a = 9, b = -12, and c = 20
a + b + c = 9 + -12 + 20 = 17
300
What is the ordered pair for point A?
(1, 1)
300
Translate: 8 less than a number, n
n - 8
300
2x + 1 = 9
x = 4
400
-3 x 0.222222222...
Rational- The product of two rational numbers is rational.
400
ef / g for e = 5, f = 4, and g = 2
ef / g = 5 x 4 / 2 = 10
400
What is the ordered pair for Point B?
(-3, -1)
400
Translate: 6 more than twice a number, n is 12
2n + 6 = 12
400
3 less than one-half of x is 4. Create and solve an equation for x.
x/2 - 3 = 4
x = 14
500
√3 x √4
Irrational- The product of an irrational number and a rational number is always irrational.
500
If f(x) = 2x - 7 + x, then f(9) = ?
f(9) = 2(9) - 7 + 9 = 20
500
What is the ordered pair for Point C?
(0, 4)
500
Mary is 1 year less than three times the age of her son, a. Write an expression that represents Mary's age
3a - 1
500
Leo's age is two more than seven times his brother's age, n. If Leo is 16, how old is his brother? Create and solve an equation for n.
7n + 2 = 16
n = 2 years old