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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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