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Questions and Answers
What is a common property of whole numbers and rational numbers?
What is a common property of whole numbers and rational numbers?
- Distributive property
- Commutative property
- Closure property
- All of the above (correct)
The result of adding two whole numbers is always a rational number.
The result of adding two whole numbers is always a rational number.
False (B)
What is the formula to calculate the percentage increase of a value?
What is the formula to calculate the percentage increase of a value?
Original value × (Percentage increase / 100)
A fraction can be expressed as a ______________ number.
A fraction can be expressed as a ______________ number.
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Match the following types of numbers with their definitions:
Match the following types of numbers with their definitions:
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What is the result of multiplying two whole numbers?
What is the result of multiplying two whole numbers?
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The order of rational numbers changes the result of addition.
The order of rational numbers changes the result of addition.
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What is the formula to calculate the percentage decrease of a value?
What is the formula to calculate the percentage decrease of a value?
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A decimal number can be converted to a ______________ by dividing the numerator by the denominator.
A decimal number can be converted to a ______________ by dividing the numerator by the denominator.
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What is the result of dividing two rational numbers?
What is the result of dividing two rational numbers?
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Study Notes
Whole Numbers
- A set of positive integers, including 0, without fractions or decimals
- Examples: 0, 1, 2, 3, ...
- Properties:
- Closure: The result of adding or multiplying whole numbers is always a whole number
- Commutative: The order of whole numbers does not change the result of addition or multiplication
- Associative: The order in which whole numbers are added or multiplied does not change the result
- Distributive: Multiplication distributes over addition
Rational Numbers
- A set of numbers that can be expressed as the ratio of two integers (fractions)
- Examples: 3/4, 22/7, 1/2
- Properties:
- Closure: The result of adding, subtracting, multiplying, or dividing rational numbers is always a rational number
- Commutative: The order of rational numbers does not change the result of addition or multiplication
- Associative: The order in which rational numbers are added or multiplied does not change the result
- Distributive: Multiplication distributes over addition
Percentages
- A way to express a value as a fraction of 100
- Examples: 25%, 50%, 75%
- Calculating percentages:
- Increase: Original value × (Percentage increase / 100)
- Decrease: Original value × (100 - Percentage decrease) / 100
- Percentage change: ((New value - Original value) / Original value) × 100
Fractions
- A way to express a part of a whole as a ratio of two integers
- Examples: 1/2, 3/4, 2/3
- Operations with fractions:
- Addition: Add numerators, keep denominators the same
- Subtraction: Subtract numerators, keep denominators the same
- Multiplication: Multiply numerators and denominators separately
- Division: Invert and multiply
Decimals
- A way to express a fraction as a base-10 number
- Examples: 0.5, 0.25, 1.75
- Converting between decimals and fractions:
- Decimal to fraction: Divide numerator by denominator
- Fraction to decimal: Divide numerator by denominator and simplify
Whole Numbers
- A set of positive integers including 0, without fractions or decimals
- Examples: 0, 1, 2, 3, ...
- Properties:
- Closure: Addition and multiplication of whole numbers always result in whole numbers
- Commutative: Order of whole numbers does not affect addition and multiplication results
- Associative: Order of whole numbers in addition and multiplication does not affect results
- Distributive: Multiplication distributes over addition
Rational Numbers
- A set of numbers that can be expressed as the ratio of two integers (fractions)
- Examples: 3/4, 22/7, 1/2
- Properties:
- Closure: Operations on rational numbers result in rational numbers
- Commutative: Order of rational numbers does not affect addition and multiplication results
- Associative: Order of rational numbers in addition and multiplication does not affect results
- Distributive: Multiplication distributes over addition
Percentages
- A way to express a value as a fraction of 100
- Examples: 25%, 50%, 75%
- Calculating percentages:
- Increase: Original value × (Percentage increase / 100)
- Decrease: Original value × (100 - Percentage decrease) / 100
- Percentage change: ((New value - Original value) / Original value) × 100
Fractions
- A way to express a part of a whole as a ratio of two integers
- Examples: 1/2, 3/4, 2/3
- Operations with fractions:
- Addition: Add numerators, keep denominators the same
- Subtraction: Subtract numerators, keep denominators the same
- Multiplication: Multiply numerators and denominators separately
- Division: Invert and multiply
Decimals
- A way to express a fraction as a base-10 number
- Examples: 0.5, 0.25, 1.75
- Converting between decimals and fractions:
- Decimal to fraction: Divide numerator by denominator
- Fraction to decimal: Divide numerator by denominator and simplify
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