| Cards | 10 |
| Topics | Commutative Property, Distributive Property - Multiplication, Factors & Multiples, Integers, Least Common Multiple, PEMDAS, Prime Number, Rational Numbers, Sequence, Simplifying Radicals |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.
A factor is a positive integer that divides evenly into a given number. The factors of 8 are 1, 2, 4, and 8. A multiple is a number that is the product of that number and an integer. The multiples of 8 are 0, 8, 16, 24, ...
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
Arithmetic operations must be performed in the following specific order:
The acronym PEMDAS can help remind you of the order.
A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
A sequence is a group of ordered numbers. An arithmetic sequence is a sequence in which each successive number is equal to the number before it plus some constant number.
The radicand of a simplified radical has no perfect square factors. A perfect square is the product of a number multiplied by itself (squared). To simplify a radical, factor out the perfect squares by recognizing that \(\sqrt{a^2} = a\). For example, \(\sqrt{64} = \sqrt{16 \times 4} = \sqrt{4^2 \times 2^2} = 4 \times 2 = 8\).