Quantitative Basics Flashcards
Reciprocal Rule
The product of a number and its reciprocal always equals 1
What effect will multiplying or dividing the numerator AND denominator of a fraction do to the value of said fraction?
No change
How do you multiply two numbers in scientific notation?
Multiply the numbers together to get the first number, add the exponents in order to get second number –> (2x10^2)(3x10^4) = (6x10^6)
How do you divide two numbers written in scientific notation?
Divide the numbers to get the first number, and then subtract the powers of ten to get second number. –> (8x10^5)(2x10^2) = (4x10^3)
Describe Smart Numbers?
When fraction problems include unspecified numerical amounts described by variables, choose real numbers to stand in for the variables based upon the common multiple (LCD) of the denominators of the fractions in the problem. –> if a problem includes 1/2 and 4/5, choose a number such as 10 to fill in for the variable –> DO NOT USE if amounts (or info to calculate amounts) is given
How to calculate successive percents?
Rephrase the percents to percents of the original and operate as necessary
Ex: Cost of ticket increases 25%, and then a week later goes on sale for 20%. What is the overall chance in price of the ticket?
–> (125/100)(80/100)p, where p is inital price of ticket
The rule of Terminating Decimals
Terminating decimals can be written as parts per 100 (ex: 0.47 = 47/100). As a result, positive powers of 10 are composed of only 2s and 5s as prime factors (after reduction). Every terminating decimal shares this characteristic. If after being fully reduced the denominator has any prime factors besides 2 and 5, the decimal will not terminate.
Fractions, Decimals, Percents…when is it best to use each?
Prefer FRACTIONS for doing multiplication or division, but prefer DECIMALS and PERCENTS for doing addition and subtraction, for estimating numbers, or for comparing numbers.
What is the best approach for dealing with problems with unspecified amounts percentages?
Pick 100 as the Smart Number
What is unique about the answer to a problem involving Absolute Values?
Problems asking you to solve for a variable when the variable is involved with Absolute Values cause the variable to have 2 answers. This is due to the reason that |5| = |-5| = 5. Make sure to plug both answers into original equation in order to see which one (or both) satisfies equation. –> if |w-4| = 18, solve for w-4=18 and w-4=-18
What happens to the value of a positive fraction if raised to consecutively increasing exponents? (ex: 1/2^2 versus 1/2^3)
Increasing powers cause positive fractions to decrease –> Just like proper fractions, decimals btw 0 and 1 decrease as their exponent increases
When working with inequalities, what happens when you multiply or divide by a negative number?
The inequality sign flips
**NOTE = you cannot multiply or divide an inequality by a variable unless you KNOW the sign of the number that the variable stands for
What is the definition of an integer?
All positive and negative whole numbers, and zero.
When can you add square roots?
Squre roots can only be summed together when the base of the roots (i.e. the number within the check) is the same
–> 2(3^1/2) + 2(3^1/2) = 4(3^1/2)
2(3^1/2) + 2(5^1/2) cannot be comined/summed
What is Standard Deviation?
How is it related to Variance?
What happens if each value in a data set is increased by the same amount?
Standard Deviation is a measure of how far values in a data set vary from the mean/average
–> The square root of the variance is equal to the Standard Deviation
–> If each value in a set is increased by the same amount, the range/variance/standard deviation would all remain the same however the mean/median/mode would change. This applies only for adding/substracting, not multiplying or dividing.
