Podcast
Questions and Answers
What are natural numbers?
What are natural numbers?
Which of the following is included in whole numbers?
Which of the following is included in whole numbers?
What are integers?
What are integers?
Which of the following is a rational number?
Which of the following is a rational number?
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What are real numbers?
What are real numbers?
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What do you do when adding integers with the same sign?
What do you do when adding integers with the same sign?
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When adding integers with different signs, what do you keep?
When adding integers with different signs, what do you keep?
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What is PEMDAS?
What is PEMDAS?
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What are coefficients?
What are coefficients?
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What is the definition of factors?
What is the definition of factors?
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What does it mean to simplify an expression?
What does it mean to simplify an expression?
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What property states that the order of operation does not affect the outcome?
What property states that the order of operation does not affect the outcome?
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When checking the solution of an equation, what should be done?
When checking the solution of an equation, what should be done?
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The term _____ refers to the ratio of two quantities.
The term _____ refers to the ratio of two quantities.
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What is the purpose of a conversion table?
What is the purpose of a conversion table?
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How do you determine significant figures?
How do you determine significant figures?
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Match the following algebraic properties with their definitions:
Match the following algebraic properties with their definitions:
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Study Notes
Number Types
- Natural Numbers: Positive whole numbers excluding zero. Examples include 4, 7, 9.
- Whole Numbers: All positive whole numbers including zero. Examples are 0, 3, 6.
- Integers: Positive and negative whole numbers, including zero. Excludes fractions or decimals. Examples: -2, 0, 4.
- Rational Numbers: Numbers expressible as a ratio of two integers. Includes terminating or repeating decimals. Examples: 4/5, -14, 2.1, √4.
- Real Numbers: All non-imaginary numbers. Includes integers, rational numbers, and irrational numbers. Examples: -4, 1/3, √5, 3.2.
Integer Operations
- Addition/Subtraction (Same Sign): Sum the numbers and keep the sign. Examples: 4 + 5 = 9, -4 + -5 = -9.
- Addition/Subtraction (Different Signs): Find the absolute difference and keep the sign of the larger number. Examples: -6 + 2 = -4, 6 - 2 = 4.
- Double Signs: Change minus a negative to addition. Example: 3 - (-4) = 3 + 4 = 7.
- Opposite Signs: Simplify by substituting with the appropriate operation. Example: 3 + (-5) = 3 - 5 = -2.
Multiplication and Division
- Same Sign: The product or quotient is positive. Examples: (3)(4) = 12, -12/-3 = 4.
- Different Signs: The product or quotient is negative. Example: (-3)(4) = -12.
Algebraic Concepts
- PEMDAS: Order of operations stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
- Combining Like Terms: Only variables with the same base can be combined. Example: 2x + 3x = 5x.
- Coefficients: Numbers before variables indicating multiplication. Example: In 3x, 3 is the coefficient.
- Factors: Values that multiply together to yield a product. Examples include factors of 6: 1, 2, 3, 6.
- Exponents: Indicate repeated multiplication of a number. Example: (7^2 = 7 \times 7).
- Simplifying Expressions: Substitute values for variables and apply order of operations.
Units and Measurement
- Selecting Units: Choose units appropriate to the context (e.g., miles for long distances).
- Units in Formulas: Use compatible units in calculations. Example: (1 \text{ ft} \times 1 \text{ ft} = 1 \text{ ft}^2).
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Conversion Tables:
- Distance: 1 inch = 2.54 cm, 1 mile = 1.609 km.
- Weight: 1 pound = 16 ounces, 1 kg = 2.2 pounds.
- Volume: 1 gallon = 3.785 liters, 1 cup = 8 fluid ounces.
Graphs and Data
- Graph Scales: Properly scale axes for clarity. The origin is (0, 0).
- Precision vs. Accuracy: Precision refers to data consistency; accuracy refers to how close data is to the true value.
- Rounding: Check significant figures for appropriate accuracy in answers.
Algebraic Properties
- Commutative Property: Order of numbers does not affect the result for addition/multiplication.
- Associative Property: Grouping of numbers does not affect the result for addition/multiplication.
- Distributive Property: Multiply a number by a sum or difference of terms. Example: (3(5 + 2) = 3 \cdot 5 + 3 \cdot 2).
Solving Equations
- Steps to Solve: Use distributive property, combine like terms, apply inverse operations to isolate the variable, and check solutions.
- Helpful Tips: Be cautious with signs when multiplying/dividing negatives, and take care of fractions with negatives.
Terms in Operations
- Addition Keywords: sum of, plus, total, more than, increased by.
- Subtraction Keywords: difference of, minus, less than, decreased by, subtracted from.
- Multiplication Keywords: product of, times, per.
- Division Keywords: quotient of, ratio of, half of, third of.
Translating Algebra
- Special Terms: Use keywords for clearly defining operations. "Twice the difference of n and 6" translates to 2(n - 6).
- Breaking Down Phrases: Highlight key words and translate gradually into algebraic expressions.
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Description
This quiz covers the foundational concepts of Algebra in Module 1 of FLVS Algebra 1. Learn about natural numbers, whole numbers, and integers through flashcards that define each term with examples. It’s an essential start to understanding algebraic principles.
