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Questions and Answers
What is the value of a in the equation a + (b + c) = a + b + a + c?
What is the value of a in the equation a + (b + c) = a + b + a + c?
- a is an even number
- a is an odd number
- a is a prime number
- a is any integer (correct)
On a number line, where would you find the negative integers?
On a number line, where would you find the negative integers?
- To the right of 0
- At the origin
- Not on the number line
- To the left of 0 (correct)
What is a characteristic of prime numbers?
What is a characteristic of prime numbers?
- They are never negative
- They are always even
- They are always odd
- They have exactly two distinct positive divisors (correct)
What is an example of an even number?
What is an example of an even number?
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What determines the value of a digit in a number?
What determines the value of a digit in a number?
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Which property of multiplication states that a × b = b × a?
Which property of multiplication states that a × b = b × a?
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Study Notes
Integer Operations
- Addition:
- Commutative property:
a + b = b + a - Associative property:
(a + b) + c = a + (b + c) - Distributive property:
a + (b + c) = a + b + a + c
- Commutative property:
- Subtraction:
- Not commutative:
a - b ≠b - a - Not associative:
(a - b) - c ≠a - (b - c)
- Not commutative:
- Multiplication:
- Commutative property:
a × b = b × a - Associative property:
(a × b) × c = a × (b × c) - Distributive property:
a × (b + c) = a × b + a × c
- Commutative property:
- Division:
- Not commutative:
a ÷ b ≠b ÷ a - Not associative:
(a ÷ b) ÷ c ≠a ÷ (b ÷ c)
- Not commutative:
Number Lines
- A visual representation of integers on a straight line
- Positive integers to the right of 0, negative integers to the left
- Used to visualize integer operations, such as addition and subtraction
Prime Numbers
- A prime number is an integer greater than 1 that has exactly two distinct positive divisors: 1 and itself
- Examples: 2, 3, 5, 7, 11,...
- Prime numbers are used in many mathematical concepts, such as cryptography and number theory
Odd and Even Numbers
- Even numbers:
- Can be divided by 2 without a remainder
- Examples:..., -4, -2, 0, 2, 4,...
- Odd numbers:
- Cannot be divided by 2 without a remainder
- Examples:..., -3, -1, 1, 3,...
Place Value
- The value of a digit in a number depends on its position or place
- Places: units, tens, hundreds, thousands,...
- Each place has a value 10 times the value of the place to its right
- Used to understand the value of integers and perform arithmetic operations
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Description
Test your knowledge of integer operations, including addition, subtraction, multiplication, and division, as well as number lines, prime numbers, odd and even numbers, and place value. Assess your understanding of mathematical concepts and properties.
