Arithmetic and Pre-Algebra Flashcards

Flashcards for Arithmetic and Pre-Algebra review.

What are whole numbers?

0, 1, 2, 3, 4, 5… (No fractions)

What are integers?

Whole numbers that can be positive or negative.

What are even numbers?

Integers divisible by 2, ending in 0, 2, 4, 6, or 8.

What are odd numbers?

Integers not divisible by 2, ending in 1, 3, 5, 7, or 9.

What are prime numbers?

Whole numbers with only 1 and itself as factors.

What are composite numbers?

Whole numbers with more than two factors.

What is the rule for adding numbers with the same sign?

Add the numbers and copy the sign.

What is the rule for adding numbers with different signs?

Subtract smaller from bigger, retain the sign of the bigger number.

What is the rule for subtracting numbers with the same sign?

Subtract the numbers; copy the sign.

What is the rule for subtracting numbers with different signs?

Change the sign of the subtrahend, then follow addition rules.

What is the rule for multiplying numbers with the same sign?

Multiply the numbers; the product is positive.

What is the rule for multiplying numbers with different signs?

Multiply the numbers; the product is negative.

What is the rule for dividing numbers with the same sign?

Divide the numbers; the quotient is positive.

What is the rule for dividing numbers with different signs?

Divide the numbers; the quotient is negative.

What are factors?

Numbers multiplied to form a product.

What are common factors?

Factors common to two or more numbers.

What is the Greatest Common Factor (GCF)?

The common factor with the highest value.

What is prime factorization?

Factoring a composite number into a product of prime numbers.

What are multiples?

A given number multiplied by integers.

What are common multiples?

Multiples that are common for two or more given numbers.

What is the Least Common Multiple (LCM)?

The common multiple with the smallest value.

What is the first step in order of operations?

Perform operations inside parentheses.

What is the second step in order of operations?

Perform operations inside brackets.

What is the third step in order of operations?

Perform operations inside braces.

What is the fourth step in order of operations?

Perform operations with exponents.

What is the fifth step in order of operations?

Perform multiplication and division from left to right.

What is the sixth step in order of operations?

Perform addition and subtraction from left to right.

What is a useful mnemonic for remembering the order of operations?

PEMDAS

What is the divisibility rule for 2?

The number is even.

What is the divisibility rule for 3?

The sum of its digits is divisible by 3.

What is the divisibility rule for 4?

It is even and the number represented by its tens and ones digits is divisible by 4.

What is the divisibility rule for 5?

Its ones digit is either 0 or 5.

What is the divisibility rule for 6?

It is even and divisible by 3.

What is the divisibility rule for 8?

It is even and the number represented by its hundreds, tens, and ones digits is divisible by 8.

What is the divisibility rule for 9?

The sum of all its digits is divisible by 9.

What is the divisibility rule for 10?

Its ones digit is 0.

What do exponents determine?

It determines the number of times a number is multiplied by itself.

What is the base in an exponent?

The number being multiplied by itself in an exponent.

What is the power in an exponent?

The number of times the base is multiplied by itself.

What is any number (except 0) with an exponent of 0 equal to?

1

What is any number with an exponent of 1 equal to?

That number.

What is a^-x (a number having a negative exponent) equal to?

1/a^x

To multiply numbers having the same base, what do you do with their exponents?

Add their exponents.

To divide numbers having the same base, what do you do with their exponents?

Subtract their exponents.

To multiply numbers having the same exponent, what do you do with their bases?

Multiply their bases.

To divide numbers having the same exponent, what do you do with their bases?

Divide their bases.

What do you do with exponents inside and outside the parentheses?

Multiply exponents inside and outside the parentheses.

What do you do with the exponent outside the parentheses, to the factors inside it?

Distribute the exponent outside the parentheses to the factors inside it.

If a base has an exponent of 1/2, what do you do?

Get its square root.

If a base has an exponent of 1/3, what do you do?

Get its cube root.