| Cards | 10 |
| Topics | Adding & Subtracting Fractions, Adding & Subtracting Radicals, Integers, Least Common Multiple, PEMDAS, Percentages, Probability, Proportions, Rational Numbers, Ratios |
Fractions must share a common denominator in order to be added or subtracted. The common denominator is the least common multiple of all the denominators.
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 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.
Percentages are ratios of an amount compared to 100. The percent change of an old to new value is equal to 100% x \({ new - old \over old }\).
Probability is the numerical likelihood that a specific outcome will occur. Probability = \({ \text{outcomes of interest} \over \text{possible outcomes}}\). To find the probability that two events will occur, find the probability of each and multiply them together.
A proportion is a statement that two ratios are equal: a:b = c:d, \({a \over b} = {c \over d}\). To solve proportions with a variable term, cross-multiply: \({a \over 8} = {3 \over 6} \), 6a = 24, a = 4.
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.
Ratios relate one quantity to another and are presented using a colon or as a fraction. For example, 2:3 or \({2 \over 3}\) would be the ratio of red to green marbles if a jar contained two red marbles for every three green marbles.