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Prime numbers vs. composite numbers - Correct Answers ✅primes: are the numbers that can only be divided by 1 and by them selves: ex:1, 2, 3 composite numbers: are all the mubbers that are not prime. EX: 2,4, Rational vs. irrational numbers - Correct Answers ✅rational - can be expressed as fraction (repeating decimal) (ex. 1/3) irrational - can't be expressed as fraction (non repeating decimal) (ex. square root of 2, pi) (in other words, rational numbers make sense while irrational do not) real numbers - Correct Answers ✅All rational and irrational numbers (basically all numbers that are real) how to write quantities in word form - Correct Answers ✅avoid using AND and use high fin between the tens and the ones. Ex: 9435 = nine thousand four hundred thirty-five
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how to write decimals in words - Correct Answers ✅do not state the zeros before the decimal, basically only the numbers that have value ex: 0.901= nine hundred one thousandths 0.06 = six hundredths 0.6= six tenths
- 0 = six can a fraction have a denominator of zero - Correct Answers ✅no, when a fraction has a zero as denominator, this is called undefined (whereas a fraction can have a zero on the numerator) how to know if a fraction is equivalent: - Correct Answers ✅just use a proportion, (cross multiply and then divide by the numerator and if the answer is the same then the fraction is the same/equivalent. every time you answer with a fraction, the fraction must be - Correct Answers ✅at is minimum terms (simplified) -does not matter if you are converting percent or decimal to fraction, you must simplify your answer
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- Add the total number of Decimal places to product, counting left to right (Ex: 22*233 = 5126 --> 5.126 final answer) Dividing Decimals - Correct Answers ✅Move the decimal to the right on both numbers until there is nothing to the right of the decimal, then move the decimal inside of the house, the same amount of spaces. add zeros if needed. then move the decimal up and divide normally. what is common factor - Correct Answers ✅A common factor is a number that can be divided into two different numbers, without leaving a remainder. The gcf of 18 and 30 can be obtained like this: The factors of 18 are 18, 9, 6, 3, 2, 1. The factors of 30 are 30, 15, 10, 6, 5, 3, 2, 1. The common factors of 18 and 30 are 6, 3, 2, 1, intersecting the two sets above. greatest common factor - Correct Answers ✅The largest factor that two or more numbers have in common. lowest common factor - Correct Answers ✅The smallest multiple shared by 2 or more numbers
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The prime factors of a number - Correct Answers ✅Prime factors are factors of a number that are, themselves, prime numbers. Ex: The only way to write 42 as the product of primes (except to change the order of the factors) is 2 × 3 × 7. We call 2 × 3 × 7 the prime factorization of 42. It turns out that every counting number (natural number) has a unique prime factorization, different from any other counting number. NOTE THE NUMBER 2 IS PART OF THE PRIME FACTORS; (remember in order to be a prime number, a number must be able to be divided by two numbers which are 1 and its self; and for number 2, this is true) least common multiple - Correct Answers ✅is the smaller number that is multiple of 2 or more numbers. Ex: the multiples of 3 include; 3,6,9,12,15.... and the multiples of 5 include; 5.10,15,20.... therefore, the least common multiple of 3 and 5 is 15. linear equation - Correct Answers ✅ax+b= (this is written in this way so that when it have numbers and variables, you can start by moving numbers to one side and the variable isolate it in the other side, when you finish, you must replace the variable in the equation, with the answer
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dividing gives you the 24 we are looking for, then divide both numbers by the same number and that should be the answer. another way is to divide the the reciprocal: 40/8 x24/ 40 x 24 = 96 8x 1= 8 then your new fraction is 960/8. then just divide the 960 by 8 and will get 120 (when finished, if you have calculator, prove your answer in a couple of ways and if the answer is the same, then its probably right.) proportion - Correct Answers ✅ Subtracting Decimals - Correct Answers ✅Line up the decimal points and subtract normally (ex. 20.02-1.36=18.66) how to get the percent off of a price? - Correct Answers ✅Ex: how much is the 20% of 18.74? convert the 20% to decimal and multiply be the quantity: (.20) x (18.74)= 3.
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another way is (if you have calculator, since dealing with decimals is a bit more complicated) just do a proportion: x/18.74 =20/ do 18x20 then the result divide it by 100 and the answer is 3.75. (then after calculating the amount, if the question say " this amount plus the 20% or minus the 20%" then just add or substract the 3.75 to the original quantity.) how to get the percentage of something plus the price of that something? - Correct Answers ✅Ex. a shirt cost 18.74 plus 20%. how much is the total? you can do 18.74 x .20 = 3.75 then just add the 3.75 to the 18.74 and is equal to 22. another way, just do 18.74 x 1.20 =22. 3 equations to work with percentages - Correct Answers ✅
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this formulas make sense because when you read them you notice that you are substracting from the big quantity, whether this is the original or the new amount. estimating a solution using money - Correct Answers ✅when you are asked to estimate, using money, in big amounts; what you have to do is just to round all quantities to the the point where all quantities have only one number and the rest of the numbers are zeros EX: estimate the solution to 345,932 + 96,369 = first turn 345,932 into 300, then turn 96,369 into 100, lastly add them both up to make up 400, Although this is not the specific answer, it will be fair enough because you are following a pattern. estimating a solution using things other than money - Correct Answers ✅if a patient's heart beats 422 in six beats, about how many beats does per minute? round 422 to 420
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then divide 420 into 6 and get an answer of about 70 beats per minute. what is direct proportion vs inverse proportion? - Correct Answers ✅-Direct proportion; is a relationship in which the ratio of two variables is constant; both variables are increasing or both variables are decreasing. EX: driving a car at specific speed, as the distance increases, the time it will take to get to the destination also increases. -inverse proportion: is a relation between two quantities such that one increases in proportion as the other decreases. EX: driving a car at specific destination. as the driving speed increases, the time to get to the specific destination will decrease. Ratios - Correct Answers ✅a comparison of two quantities in a particular order. EX: if there are 14 computers in a lab and the class has 20 students, there is a computer to student ratio of 20 to 14, commonly written as 20:14. ratios are normally reduce to their smallest whole number representation, so 20:14 will be reduced to 10:7 (in this case we divided both numbers by 2)
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- Correct Answers ✅ unit rate - Correct Answers ✅unit price etc (how much is a single thing from from the bunch) ex: 30 miles per 2 hours. the unit rate is 15 miles per 1 hour 5 lemons per dollar. the unit rate is 1 lemon per 20 cents. one dozen of eggs per 12 dollar. unit rate is 1 egg per 1 dollar. Inequalities signals - Correct Answers ✅(this signals tell how is one quantity in comparation to another = equal, was equal, is equal, same amount
greater than or is more than < less than or is less than grater or equal to, is at least, no less than < less than or equal to, is almost, is no more than How to translate word problems into equations using fractions and inequalities - Correct Answers ✅EX:
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A farm sells vegetables and dairy products. on e third of the sales from dairy products plus half of the sales from vegetables should be grater than the monthly payment (P) for the farm. write it in an inequality: Let D to stand for dairy and V for vegetables and P for payment. answer: D/3 +V/2 > P rational expression - Correct Answers ✅when you have an expression that has fraction with polynomials (variable plus number), remember that you can always multiply to get the expression into a linear equation. Ex: John and Luke play basketball. John can make 5 more shoots per minute than Loke. one day John made 30 shoots in the same time that it took to Luke to make 20. How fast are Luke and John making shoots? the rational expression: 30/X+5 = 20/x here you can cross multiply to end up with 30X = 20X + 100 then just solve the linear equation
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, < (open circle) ≥ , ≤, = (closed circle) simplifying fractions - Correct Answers ✅know that 4 is equal to 4/ know that 4/4 is equal to 1 what is data? - Correct Answers ✅is the name given to " pieces of information" (basically the name of whatever you are collecting, as information) Quantitative data - Correct Answers ✅numerical data (data that has to do with numbers. basically any type of data that
can be counted using numbers) this data is about quantities in numbers Qualitative data - Correct Answers ✅descriptive data -Information describing color, odor, shape, or some other physical characteristic -This data cannot be measured using numbers
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discrete data - Correct Answers ✅Information that can only be expressed by a specific value (people can only be counted in whole numbers) continuous data - Correct Answers ✅Information that can be expressed by any value within a given range (temperature) primary data - Correct Answers ✅information that is collected for the first time; used for solving the particular problem under investigation (the same as primary source in reading) secondary data - Correct Answers ✅information that has already been collected, sorted, and processed by a researcher. (the same as secondary source in reading) ordinal data - Correct Answers ✅information that can be placed in numerical order, such as age and weight nominal data - Correct Answers ✅is information that can not be placed in numerical order, such as names and places
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meaning that in the bunch of numbers there is one fifteen and one sixteen. Scatterplot - Correct Answers ✅a graphed cluster of dots, each of which represents the values of two variables (X and Y) -is the same thing as regression plot. both scatter and regression are charts that are used to predict future events. -Linear scatter plots can be positive or negative: meaning that they will continue going in that direction. -nonlinear scatter plots are exponential meaning that they will continue going in that direction (going up or down exponentially. dependent vs independent variable in mathematics - Correct Answers ✅Dependent variable is altered by the independent variable (and also by other variables within the equation). the independent variable can take any value(given by the mathematician), whereas the dependent variable change as a consequence of other variable in the equation (this includes the independent variable).
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ex: if you work and get 10$ per hour, you can write it as 10X. where X is the independent variable(hours). this because you can certainly change the variable X (number of hours) In an equation you will write 10X =Y this because Y(money) is the dependent variable that will change as consequence of changing X. if you increase the value of X(hours) of course the variable Y(amount of money) will change as a consequence of changing the value of X. independent variable vs independent variable (in a hypothesis) - Correct Answers ✅-Independent variable: is a variable that does not depend in any other variable -Dependent variable depends in the independent variable. Ex: a person runs 3 mules. After running one our starts feeling pain, after the second hour, more pain, after the third hour the person can no longer walk because of too much pain. -the independent variable is the distance -the dependent variable is the pain which changes as the distance increases. ( so it depends on the independent variable which is the distance running)
