Subsets of Real Numbers
Natural numbers, whole numbers, integers, rational number and irrational numbers are all part of
Identify the property illustrated by the equation: 12 + 7 = 7 + 12
Commutative Property
Convert the decimal 0.65 into a fraction and a percentage.
Fraction = 65/100 = 13/20, Percentage = 65%
Write an integer representing a loss of 250 points in a game.
-250
Evaluate: 7 - (-12)
19
Which of the following is an irrational number?
A. √64 B. -5/8 C. √17 D. 0.125
C
Identify the property illustrated by the equation:
(4 + 9) + 6 = 4 + (9 + 6)
Associative Property
Express 7/20 as a decimal.
0.35
Which integer is greater: -13 or -7?
-7
(-8)(-6) ÷ 4
12
Is 0.363636... rational or irrational? Explain your answer.
Rational because it is a repeating decimal which can be converted as 36/99 or 4/11
Complete the equation using the Distributive Property: 5(2x + 3) =
10x + 15
Convert 75% into a decimal and a simplified fraction.
Decimal = 0.75, Fraction = 75/100, 3/4
Which has a greater absolute value -15 or -12?
-15
Simplify using GEMDAS: 20 - 3(4) + 18 ÷ (-6)
5
A number is rational but not an integer. Give one example and explain why it is rational.
Can be 5/8 since it is a rational number, expressed as a ratio of two integers but not an integer since it's between 0 and 1.
What is the multiplicative inverse of -5?
-1/5
Which value is greater 2/5 or 32%? Justify your reasoning.
2/5 is greater.
Reasoning: 2/5 = 0.40 = 40% > 32%
Arrange the integers from least to greatest: 8, -5, 0, -12, 3
-12, -5, 0, 3, 8
Evaluate the expression. Show the order of operations and all intermediate steps.
24 ÷ [2(5 - 3)] + (-2)3
-2
A student claims that √121 is irrational because it is written with a radical sign. Is the student correct? Explain your answer and identify the smallest applicable subset.
No. √121 =11, which belongs to the natural numbers.
A student claims that multiplication is distributive over subtraction. Verify the claim by expanding and simplifying: 6(10 - 4).
Show whether the student's claim is true or false.
Both sides equal 36.
Arrange the following rational numbers in ascending order (smallest to largest): 1/2, 0.53, 47%, 2/5, 56%.
2/5, 47%, 1/2, 0.53, 56%
At sunrise, the temperature was -8°C. By noon, it increased by 13°C, then dropped by 6°C in the evening. What was the final temperature in the evening?
-1°C
Evaluate 4 + {18 ÷ [3 × (−2 + 5)]}².
8