Number Families (N, W, Z, Q, I, R)
These are ALL of the number families that 6 is classified under:
(Use the letter symbols to categorize the number)
What are: N, W, Z, Q, R
(Natural, Whole, Integer, Rational, Real)
The full name of the property for: 5 + 0 = 5
What is the Identity Property of Addition?
Are integers closed under addition? Give a counterexample if not.
Yes
The distributed form of 5(x + 4).
(Simplify the expression)
What is 5x + 20?
These are (solve both):
1. |-18|
2. -|9|
What is:
1. 18
2. -9
These are ALL of the number families that the square root of 20 (sq. rt. 20) is classified under:
(Use the letter symbols to categorize the number)
What are: I, R
(Irrational, Real)
The full name of the property for: 3 * (1/3) = 1
What is the Inverse Property of Multiplication?
Are whole numbers closed under subtraction? Give a counterexample if not.
No, ex. 3 - 5 = -2 which is not a whole number.
The distributed form of -3(2x - 6).
(Simplify the expression)
What is -6x + 18?
These are (solve both):
1. |6 - 13|
2. -|2 + 5 * -4|
What is:
1. 7
2. -18
These are ALL of the number families that 0 (zero) is classified under:
(Use the letter symbols to categorize the number)
What are: W, Z, Q, R
(Whole, Integer, Rational, Real)
The full name of the property for: (4 + 7) + 2 = 4 + (7 + 2)
What is the Associative Property of Addition?
Are natural numbers closed under division? Give a counterexample if not.
No, ex. 3 / 5 =0.6 which is not a natural number.
Simplify: 6x + 5 - 2x + 9
What is 4x + 14?
These are (solve both):
1. 2 + |-2|
2. The distance between -8 and 3 (write as absolute value)
What is:
1. 4
2. 11
These are ALL of the number families that the negative square root of 25 (-1 * sq. rt. 25) is classified under:
(Use the letter symbols to categorize the number)
What are: Z, Q, R
(Integer, Rational, Real- It simplifies to -5)
The full name of the property for: If x = 9, then 9 = x.
What is the Symmetric Property of Equality?
Are rational numbers closed under multiplication? Give a counterexample if not.
Yes
Simplify: 5(3x - 2) + 4x
What is 19x - 10?
Evaluate the absolute value, for x = 5 and y = -6:
|2x - y - 16|
What is 0 (zero)?
Name a number that is rational but NOT an integer.
Any fraction or decimal that does not simplify to a whole positive or negative number (on the number line), like 1/2 or 0.87. Use a calculator to verify!
A student says that 12/5 = 5/12 by the Commutative Property. What is wrong with this assumption?
Subtraction and division are not commutative (order matters), the left and right sides of the equals sign are not equal.
CHALLENGE: The example sqrt(2) - sqrt(2) = 0 shows that ___ numbers __are/are not__ closed under subtraction.
Irrationals (sqrt 2)
Not Closed (0 is not irrational)
Simplify: -6(x + 3) - 2x + 3
What is -8x - 15?
A box should weigh 40 grams but actually weighs an unknown x grams. These are the TWO equivalent distance expressions using absolute value that find how far away the box is from its target.
1. |a - 40|
2. |40 - a|