FLVS Algebra 1 Module 1 Foundations

Questions and Answers

What are natural numbers?

All positive whole numbers, not including zero (correct)

All negative whole numbers

All positive whole numbers, including zero

All numbers, including fractions

Which of the following is included in whole numbers?

Zero (correct)

All integers

Negative numbers

Fractions

What are integers?

Fractions and decimals only

Only negative whole numbers

Positive and negative whole numbers, including zero (correct)

Only positive whole numbers

Which of the following is a rational number?

√4 Signup and view all the answers

What are real numbers?

All non-imaginary numbers Signup and view all the answers

What do you do when adding integers with the same sign?

Find the sum and keep the sign. Signup and view all the answers

When adding integers with different signs, what do you keep?

Keep the sign of the larger number. Signup and view all the answers

What is PEMDAS?

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Signup and view all the answers

What are coefficients?

Numbers that come before the variable telling how many times the variable is added. Signup and view all the answers

What is the definition of factors?

Values that can be multiplied together to get a product. Signup and view all the answers

What does it mean to simplify an expression?

To substitute values into the variable and follow the order of operations. Signup and view all the answers

What property states that the order of operation does not affect the outcome?

Commutative Property Signup and view all the answers

When checking the solution of an equation, what should be done?

Substitute the solution back into the original equation. Signup and view all the answers

The term _____ refers to the ratio of two quantities.

rate Signup and view all the answers

What is the purpose of a conversion table?

To assist in converting between measurement units Signup and view all the answers

How do you determine significant figures?

By checking the accuracy in measurements. Signup and view all the answers

Match the following algebraic properties with their definitions:

Commutative Property = Order does not affect outcome Associative Property = Grouping does not affect outcome Distributive Property = Multiplying a sum by a number gives the same result as multiplying each addend individually Properties of Equality = Rules that maintain equality in algebraic expressions Signup and view all the answers

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).
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.