Khan Academy Pre-Algebra Flashcards

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What does prime factorization help with?

Finding GCF using distributive property

Making distributive property easier

Solving multiplication problems

All of the above (correct)

What is the value of a digit based on its position within a number called?

place value

What is the condensed form of expanded form?

standard form

How can numbers be represented to show the place value of each digit?

expanded form Signup and view all the answers

What is the method of writing or displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10 called?

scientific notation Signup and view all the answers

What acronym is used for the order of operations?

PEMDAS Signup and view all the answers

What is an arrangement of objects in equal rows called?

array Signup and view all the answers

What law states that any finite sum is unaltered by reordering its terms?

commutative law of addition Signup and view all the answers

What law states that any finite product is unaltered by reordering its terms?

commutative law of multiplication Signup and view all the answers

What is the identity property of 1?

any number multiplied by one is itself Signup and view all the answers

What is the identity property of 0?

any number added to 0 is itself Signup and view all the answers

What is the inverse property of addition?

the inverse of a number = 0 Signup and view all the answers

What does multiplying a number by its multiplicative inverse equal?

1 Signup and view all the answers

What is the inverse of multiplication?

division Signup and view all the answers

What is the inverse operation of addition?

subtraction Signup and view all the answers

What is the inverse operation of division?

multiplication Signup and view all the answers

What is the associative property of multiplication?

changing the grouping doesn't change the product Signup and view all the answers

What is the associative property of addition?

changing groupings doesn't change the sum Signup and view all the answers

What is the distributive law of multiplication over addition?

the product of a sum equals the sum of the products Signup and view all the answers

What is the Greatest Common Factor (GCF)?

the largest factor shared by two or more numbers Signup and view all the answers

What is a prime factor?

a factor that is a prime number Signup and view all the answers

What is a prime number?

a whole number greater than 0 that has exactly two different factors, 1 and itself Signup and view all the answers

What are factors?

numbers that are multiplied together to get a product Signup and view all the answers

What is the result of multiplying two or more factors?

product Signup and view all the answers

Study Notes

Prime Factorization and Distributive Property

Use prime factorization to simplify expressions using the distributive property.
Steps involve identifying prime factors, multiplying common factors, and simplifying the expression.

Place Value

Place value indicates the value of a digit based on its position in a number.
Example: In 356, the digits represent 3 hundreds, 5 tens, and 6 ones.

Number Forms

Standard Form: The condensed version of a number. Example: 536.
Expanded Form: A representation that shows individual place values. Example: 536 = 500 + 30 + 6.

Scientific Notation

A way to express numbers as a decimal between 1 and 10 multiplied by a power of 10.
Example: 34 can be written as 3.4 × 10^1.

Order of Operations (PEMDAS)

Follow the sequence: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction; evaluate from left to right.

Arrays

An arrangement of objects in equal rows, useful for visualizing multiplication.

Commutative Laws

Addition: The sum remains the same when addends are reordered. Example: a + b = b + a.
Multiplication: The product is unchanged when factors are reordered. Example: a × b = b × a.

Identity Properties

Identity Property of 1: Multiplying any number by one yields the original number. Example: 7 × 1 = 7.
Identity Property of 0: Adding zero to any number leaves it unchanged. Example: 20 + 0 = 20.

Inverse Properties

Addition: The inverse of a number is found by adding its negative. Example: 5 + (-5) = 0.
Multiplication: A number multiplied by its inverse equals one. Example: 5 × (1/5) = 1.
Reciprocal of Multiplication: Two numbers with a product of one are reciprocals.

Inverse Operations

Multiplication: The inverse operation is division; for example, the inverse of 5 is (1/5).
Division: The inverse operation is multiplication; e.g., the inverse of (1/5) is × 5.
Addition: The inverse operation is subtraction; e.g., the inverse of 5 is -5.
Subtraction: The inverse operation is addition; e.g., the inverse of -5 is 5.

Associative Properties

Multiplication: Changing the grouping of factors does not affect the product. Example: (2 × 3)4 = (2 × 4)3.
Addition: Reorganizing groupings of addends does not alter the sum. Example: (2 + 3) + 4 = 2 + (3 + 4).

Distributive Laws

Distributive Law of Multiplication over Addition: Distributes multiplication across addition. Example: 3(2 + 6) = 3(2) + 3(6).
Distributive Law of Multiplication over Subtraction: Distributes multiplication across subtraction. Example: 3(2 - 6) = 3(2) - 3(6).

Greatest Common Factor (GCF)

The largest shared factor of two or more numbers. Example: GCF of 8 and 4 is 4.
Finding GCF involves identifying prime factors, multiplying common factors, and writing the final result.

Factor Definitions

Prime Factor: A factor that is a prime number.
Prime Number: A whole number greater than 1 with exactly two distinct factors: 1 and itself.
Factors: Numbers multiplied together to yield a product.

Key Arithmetic Components

Product: The result from multiplying two or more factors.
Addend: A number that contributes to a sum.
Sum: The result of adding two or more addends.
Division Components: Dividend (the number being divided), Divisor (the number that divides) leading to a Quotient (the result of division).
Subtraction Components: Minuend (the number from which another is subtracted), Subtrahend (the number that is to be subtracted), leading to a Difference (the result of the subtraction).

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Explore essential pre-algebra concepts with these flashcards from Khan Academy. Each card presents a key term along with its definition to help reinforce your understanding of foundational topics in mathematics. Perfect for quick revision or study sessions.