Subsets of Real Numbers
Which subset of real numbers includes all the counting numbers?
Natural Numbers
What property is illustrated by (4 + 5) + 6 = 4 + (5 + 6)?
Associative Property
Is the set of whole numbers closed under subtraction? Justify your answer with a counterexample if false.
False. Counterexample: 4 - 9 = -5, which is a negative integer and not a whole number.
Convert the fraction 2/3 into a decimal and a percentage.
Decimal = 0.67, Percentage = 67%
A student converted 79% to a decimal and wrote 0.079. What error did they make and what is the correct decimal?
The student moved 3 decimal places to the left instead of 2 decimal places only. The correct decimal is 0.79.
What is the most specific subset within the Real Number System for the number -67?
Integer
What property is illustrated by 1 + (-1) = 0?
Inverse Property
Use the Commutative and Associative Properties of Addition to rearrange and group the numbers below so they are much easier to add. Show your groupings using parentheses and solve the total.
36 + 98 + 24
(36 +24) + 98 = 60 + 98 = 158
Convert 0.55 into a fraction in simplest form and a percentage.
Fraction = 55/100 = 11/20, Percentage = 55%
How would you shade a 100-square grid to represent the value of 0.6?
Shade 60 individual squares out of the 100-square grid (or 6 complete rows/columns out of 10).
True or False. The number 0 is a natural number. If false, state the correct subset.
False, 0 is a whole number.
Complete the equation using the Identity property of Addition:
32 + __ = 32
0
Apply the Distributive Property by filling in the blanks:
15(100 + 4) = (15 × ___ ) + (15 × ___ ) = _______
100, 4, 1560
Convert 75% into a decimal and a simplified fraction.
Decimal = 0.75, Fraction = 75/100, 3/4
Bonus: Multiply the number of thumbs that everyone in the world has. What is the result?
0, because at least one person in the world doesn't have thumbs.
Is 0.387 a rational or an irrational number? Explain
Rational because it is a terminating decimal that can be written as a ratio of integers 387/1000
Complete the following using the Associative Property of Addition:
12 + (28 + 45) = ?
(12 + 28) + 45
Two students evaluated 7 + (8 + 9):
Student A: (7 + 8) + 9
Student B: 7 + (9 + 8)
Which student demonstrated the Associative Property of Addition? Explain.
Student A, because they changed the grouping of the addends using parentheses without altering their order.
Which value is greater 2/5 or 35%? Justify your reasoning.
2/5 is greater.
Reasoning: 2/5 = 0.40 = 40% > 35%
A student scored 21 out of 25 on a test and claimed they scored 80%. Evaluate their claim
Why is √10 classified as an irrational number?
Because 10 is not a perfect square, making its decimal representation non-terminating and non-repeating.
True or False: The set of non-zero integers is closed under division. If false, provide a counterexample.
False. Counterexample: 5 ÷ 2 = 2.5 or 5.2, which is a rational number/fraction, not an integer.
Formulate a numerical expression using parentheses that correctly models the distributed sum (8 × 50) + (8 × 3)
8(50 + 3)
Arrange the following rational numbers in ascending order (smallest to largest): 1/2, 0.58, 48%, 0.52.
48%, 1/2, 0.52, 0.58
What does a weather forecast of a 55% chance of rain mean based on the definition of percentages?
Out of 100 days with these exact same weather conditions, it is expected to rain on 35 of them.