| Cards | 10 |
| Topics | Adding & Subtracting Radicals, Defining Exponents, Distributive Property - Multiplication, Exponent to a Power, PEMDAS, Percentages, Prime Number, Rational Numbers, Simplifying Fractions |
To add or subtract radicals, the degree and radicand must be the same. For example, \(2\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}\) but \(2\sqrt{2} + 2\sqrt{3}\) cannot be added because they have different radicands.
An exponent (cbe) consists of coefficient (c) and a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
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.
To raise a term with an exponent to another exponent, retain the base and multiply the exponents: (x2)3 = x(2x3) = x6
Arithmetic operations must be performed in the following specific order:
The acronym PEMDAS can help remind you of the order.
Percentages are ratios of an amount compared to 100. The percent change of an old to new value is equal to 100% x \({ new - old \over old }\).
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.
Fractions are generally presented with the numerator and denominator as small as is possible meaning there is no number, except one, that can be divided evenly into both the numerator and the denominator. To reduce a fraction to lowest terms, divide the numerator and denominator by their greatest common factor (GCF).