Mathematics Fundamentals: Divisibility Rules, LCM, GCF, and Powers

This flashcard set covers math concepts from the lecture notes, including divisibility rules for 2 through 12, Least Common Multiple (LCM), Greatest Common Factor (GCF), powers, place value notation (Standard, Expanded, and Exponential forms), and decimal operations including order of operations.

What is the definition of a Divisibility Rule?

A rule to determine if a number goes evenly into another number.

What is Divisibility Rule 2?

The last digit should be an even number (e.g., $1254$, $2368$, $180$).

What is Divisibility Rule 3?

The sum of the digits should be a multiple of $3$ (e.g., $3612$ because $3+6+1+2 = 12$).

What is Divisibility Rule 4?

The last two digits should be a multiple of $4$ (e.g., $3512$, $4032$).

What is Divisibility Rule 5?

The last digit should be $5$ or $0$ (e.g., $1050$, $9065$).

What is Divisibility Rule 6?

The number should satisfy both Rule 2 and Rule 3 (e.g., $354$ because $3+5+4=12$; $114$ because $1+1+4=6$).

What are the three steps for Divisibility Rule 7?

1st - Multiply last digit by $2$. 2nd - Subtract remaining digits from product. 3rd - Repeat if unsure.

What is Divisibility Rule 8?

The last three digits should be a multiple of $8$ (e.g., $109,816$, $24,096$).

What is Divisibility Rule 9?

The sum of the digits should be a multiple of $9$ (e.g., $1026$ because $1+0+2+6=9$).

What is Divisibility Rule 10?

The last digit should be $0$ (e.g., $5890$, $1860$, $2690$).

What are the steps for Divisibility Rule 11?

1st - subtract last digit from remaining digits. 2nd - If difference is multiple of $11$ then it's divisible. 3rd - Repeat if needed.

What is Divisibility Rule 12?

The number must follow the divisibility rules of both $3$ and $4$ (e.g., $1224$ because $1+2+2+4=9$).

What does LCM stand for, and what are the examples provided?

Lowest Common Multiple. Examples include finding the LCM of $(24, 8)$ as $32$, $(48, 312, 24)$ as $96$, and $(310, 312)$ as $480$.

What does GCF stand for, and what were the calculation results for the provided examples?

Greatest Common Factor. Examples: for $(24, 30)$, $GCF = 6$; for $(40, 28)$, $GCF = 2$; for $(100, 105)$, $GCF = 5$.

How are Powers defined in the lecture notes?

A short way of showing repeated multiplication with the same number.

In the example of the power $8^3$, what are the terms for the numbers $8$ and $3$?

$8$ is the base and $3$ is the exponent.

What are the place value categories identified for numbers reaching up to one hundred billion?

One, Thousand, Million, and Billion.

What is the standard form of the large number example used in the places value chart?

$$638,005,021,003$$

What is the exponential form of the number $638,005,021,003$?

$$6 \times 10^{11} + 3 \times 10^{10} + 8 \times 10^9 + 5 \times 10^6 + 2 \times 10^4 + 1 \times 10^3 + 3$$

What are the results of the decimal division examples: $1.5 \div 0.3$ and $2.5 \div 0.5$?

$1.5 \div 0.3 = 5$ and $2.5 \div 0.5 = 5$.

According to the Order of Operation notes, how is the expression $(2.5 \times 2.0) - 4.3$ simplified?

$$5.00 - 4.3$$

According to the Order of Operation notes, how is $27.12 - (4.8^2 - 2 \times 2)$ simplified in steps?

$$27.12 - (23.04 - 2 \times 2) \rightarrow 27.12 - (23.04 - 4) \rightarrow 27.12 - 19.04$$