40 Questions
What is a characteristic of a real number?
It can belong to more than one set of numbers.
Which property of real numbers states that a + b = b + a?
Commutative property
What is the result of a + (-a) for any real number a?
0
Which property of real numbers states that a + 0 = a?
Identity property
What is the result of a · 1 for any real number a?
a
Which property of real numbers states that (a + b) + c = a + (b + c)?
Associative property
What is the closure property of real numbers?
The result of adding two real numbers is always a real number.
What is the purpose of the inverse property of real numbers?
To find the additive inverse of a number.
What type of numbers consist of several different kinds of numbers?
Real numbers
What property can be used to calculate the total cost when multiple items are purchased?
Distributive Property
What is the purpose of using the properties of real numbers in the context of the Central High School Boosters?
To make determining the total cost easy
What is an example of a scenario where the properties of real numbers are used?
Buying snacks and beverages at school
What is the term for the numbers that can be expressed as a ratio of two integers?
Rational numbers
What is the main benefit of using the properties of real numbers in calculations?
To make calculations easier
What is the term for the numbers that include rational numbers, irrational numbers, and more?
Real numbers
What is the purpose of evaluating expressions using the properties of real numbers?
To make determining the total cost easy
What is the value of the expression $\frac{7}{22} \cdot \frac{22}{7}$?
1
What is the additive inverse of 12.1?
-12.1
How many pounds of dry cement will Jorge need for the quick-drying concrete?
30
What is the multiplicative inverse of -0.25?
4
What is the value of the expression 8b - 3c + 4b + 9c?
12b + 6c
What is the additive inverse of -8?
8
Jorge needs 5 times more quick-drying concrete and 3 times more slow-drying concrete. How many times more dry cement will he need in total?
20
What is the value of the expression √15?
√5
What is the simplified form of 6q + 20q + 3r - 35r?
26q - 32r
Which property is illustrated by the equation (6 · 8) · 5 = 6 · (8 · 5)?
Associative Property
What is the additive inverse of -7?
7
What is the multiplicative inverse of 3/8?
8/3
What is the simplified form of 3(4x - 2y) - 2(3x + y)?
12x - 6y - 6x - 2y
Which of the following numbers is a rational number?
-12
What is the value of x in the equation 5x + 16 = 84?
14
How much money will Melba have after mowing 25 lawns?
$450
What is the total cost of the computer package?
907.44
What is the sales tax rate in the given example?
0.06
How much money did Kayla earn in one day if she worked 3 hours?
24
What is the total number of hours Kayla worked in one week?
11.5
What is the result of applying the Distributive Property to 3(2q + r)?
6q + 3r
What is the simplified form of the expression 3(2q + r) + 5(4q - 7r)?
6q + 3r + 20q - 35r
What is the educational requirement for a store manager?
Either a high school diploma or a 4-year degree
What is the total amount of money Kayla earned in one week?
72
Study Notes
Real Numbers
- Real numbers consist of different kinds of numbers, including natural, whole, integer, rational, and real numbers.
- A number can belong to more than one set of numbers.
Properties of Real Numbers
- Commutative Property of Addition:
a + b = b + a - Commutative Property of Multiplication:
a · b = b · a - Associative Property of Addition:
(a + b) + c = a + (b + c) - Associative Property of Multiplication:
(a · b) · c = a · (b · c) - Identity Property of Addition:
a + 0 = a = 0 + a - Identity Property of Multiplication:
a · 1 = a = 1 · a - Inverse Property of Addition:
a + (-a) = 0 = (-a) + a - Inverse Property of Multiplication:
a · 1/a = 1 = 1/a · a, wherea ≠ 0 - Closure Property:
a + bis a real number.
Applying Properties of Real Numbers
- Using the Distributive Property to evaluate expressions:
a(b + c) = ab + ac - Simplifying algebraic expressions using the properties of real numbers.
- Examples of applying properties to simplify expressions:
3(2q + r) + 5(4q - 7r),3(4x - 2y) - 2(3x + y)
Examples and Applications
- Finding the total cost of items using the properties of real numbers.
- Calculating the sales tax charged using the properties of real numbers.
- Earning money and calculating total earnings using the properties of real numbers.
- Simplifying expressions and finding the additive and multiplicative inverses of numbers.
- Applying the properties of real numbers to real-world problems, such as construction and lawn care.
This quiz is about identifying and using the arithmetic properties of real numbers, such as the Central High School Boosters selling snacks and beverages at school. Test your knowledge of real numbers!
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