Math
Integer
All whole numbers (both positive and negative), including zero.
Prime Factor
Also a prime number. - The prime factors of 12 are 2, and 3. - The prime factors of 15 are 3 and 5.
Composite Number
Any whole number greater than 1 that has more than two different factors AKA any whole number that is not a prime number. Example: The composite number 8 has the factors of 1, 2, 4, and 8.
Prime Number
Any whole number greater than 1 that has only two factors, itself and 1; that is, a number that can be divided evenly only by 1 and itself.
Real Numbers
Are the set of all rational and irrational numbers.
Median Formula
Arrange numbers in ascending order, and it is the number right in the middle. OR n(quantity of numbers on list)+1 / 2 *If there are an even amount of numbers, you add the two middle numbers and divide by 2.
How do you calculate percentage change?
Calculate percentage change using this formula:% change=𝑛𝑒𝑤−𝑜𝑙𝑑𝑜𝑙𝑑×100Ex. A house is originally priced at $350,000. After 6 months of not selling, the price is lowered to $315,000. What is the percent change from the original to the new price?% change= 315,000−350,000350,000×100=−10%
Controlled Variable
Factor in an experiment that a scientist purposely keeps the same.
How do you convert a decimal into a fraction?
Figure out the number of decimal places in your number. The number of decimal places equals the numbers of zero after a 1. Sometimes you can reduce the fraction by finding the lowest common denominator
How do you find the percentage of a number?
Find the percentage of a number by turning the percentage into a decimal and multiplying by the number. Ex. What is 75% of 152? 0.75 × 152 = 114
How do I turn fractions into decimals?
Fractions can be converted into decimals by using long division. For example, the fraction 4/25 is expressing "4 divided by 25". This can be set up as 25⟌4. Place a decimal and zeros after the 4 so that it becomes 4.00. Now we have 25⟌4.00. 25 does not go into 4, but it does go into 40, one time. From here, the standard rules of long division apply. The result will be 0.16. The important thing to remember is that the fraction bar represents division, so fractions can be calculated as decimals by dividing the numerator by the denominator.
Rational Numbers
Include all integers, decimals, and fractions. Any terminating or repeating decimal number is a rational number.
Range Formula
Largest Value - Smallest Value
How do you calculate a percentage increase?
Let I stand for increase, N for new number, and O for original number. I=[[(N-O)/O](100%)]
How do you divide a decimal by a whole number?
Long divide as you would with two whole numbers, but put the decimal point in the answer at the same place it is at in the dividend. If it does not divide evenly, add a 0 to the end of the dividend and continue dividing until there is no remainder.
Are all rational numbers whole numbers?
No, not all rational numbers are whole numbers. Rational numbers include all numbers that end or repeat. A whole number is any number without a fractional part that is greater than or equal to zero. Ex. 2.7 is a rational number but not a whole number.
Probability Formula
Number of favorable outcomes/Number of possible outcomes
Factors
Numbers that are multiplied together to get a product. Example: 2 X 3 = 6; the numbers 2 and 3 are factors.
How do you change a fraction into a percent?
Step 1: Divide the numerator by the denominator. Step 2: Multiply this decimal by 100.
How do you subtract decimals from whole numbers?
Subtract decimal numbers from whole numbers by turning the whole number into a decimal by adding a decimal point and as many zeroes as needed. Then, subtract as normal.
How do you subtract repeating decimals?
Subtract repeating decimals by turning them into fractions and subtracting the fractions, or by rounding the repeating decimals and subtracting. Ex.: 0.6⎯⎯⎯−0.3⎯⎯⎯0.6⎯⎯⎯=23 and 0.3⎯⎯⎯= 1323−13 =13 OR 0.6⎯⎯⎯ ≈0.67 and 0.3⎯⎯⎯≈0.330.67−0.33=0.34
How do you subtract negative decimals?
Subtracting a negative number is like adding that number. So, subtracting a negative decimal is adding that negative decimal. Ex.: -2.3 - (-7.4) = -2.3 + 7.4 = 5.1
Mean Formula
Sum of all data values/Quantity of data values
Are negative numbers rational?
Yes, most negative numbers are rational. A rational number is any number that can be written as a fraction. These include whole numbers, fractions, decimals that end, and decimals that repeat. Positive and negative do not affect rationality.
How do you divide decimals?
You move the divisor as many times to right to make it into a whole number (must treat both numbers the same regarding this). To divide 6.54 by 3.2, for example, move the decimal place in 6.54 two places to the right to make it a whole number (654). Move the decimal in 3.2 the same number of places to the right to make it 320. Divide 654 by 320 and get the result of 2.04.
Diameter of a Circle Formula
d=2r
High Positive Correlation
increase performance on one task, and you see a similar increase of performance on other task, what correlation is that?
Are all integers rational numbers?
Yes, a rational number is any number that can be expressed as a fraction. All integers fit this definition.
Point Slope Form
Y - Y1 = m (X - X1), where m is the slope and (X1 ,Y1) is a point on the line.
Slope
Y2-Y1 over (/) X2-X1
How do you divide fractions?
1. Keep 2. Change 3. Flip *Then multiply the fractions! Simplify as needed.
How do you multiply a mixed number by a decimal?
1. Mixed number/mixed fraction = Convert it to an improper fraction first. 2. Decimal = Convert it to a fraction first.
How to multiply decimals?
1. Multiply as usual. 2. Count the number of digits above the line and to the right of all decimal points. 3. Place the decimal point in your answer.
How do you multiply mixed fractions?
1. Turn mixed fraction into an improper fraction. 2. Multiply across as normal. *If there are common factors in the numerator and denominator, cancel those out first to simplify multiplying across. To convert the fraction back to a mixed number, divide the numerator by the denominator. The number of full divisions becomes the whole number and the remainder becomes the numerator of the fractional part over the original denominator. Ex. 3 and 1/5 × 2 and 7/9 = 16/5 × 25/9 = 16/1 × 5/9 = 80/9 = 8 and 8/9 Ex. 3 and 1/5 × 2 and 7/9 = 16/5 × 25/9 = 16/5 × 5×5/9 = 16/1 × 5/9 = 80/9 = 8 and 8/9
Volume Formula of a Cone
1/3πr²h
Write place value of each digit: 14,059.826.
1: Ten thousands 4: Thousands 0: Hundreds 5: Tens 9: Ones 8: Tenths 2: Hundredths 6: Thousandths
What is 3 and 6/100 in decimal form?
3.06
Positively Skewed
A distribution that trails off to the right.
Quadrilateral
A four-sided polygon.
Line Graph
A graph that uses line segments to show changes that occur over time
Scatter Plot
A graph with points plotted to show a possible relationship between two sets of data.
Line Plot
A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.
Binary
A number system that uses something other than 10 digits.
Common Factor
A number that divides exactly into two or more other numbers. Example: The factors of 12 are 1, 2, 3, 4, 6 and 12. The factors of 15 are 1, 3, 5 and 15. The COMMON FACTOR of 12 and 15 are 3 and 5.
Rhombus
A parallelogram with four congruent sides.
Parallelogram
A quadrilateral with two pairs of parallel sides.
Write each of the following numbers: A. Nine thousand four hundred thirty-five B. Three hundred two thousand eight hundred seventy-six C. Nine hundred one thousandths D. Nineteen thousandths E. Seven thousand one hundred forty-two and eighty-five hundredths
A. 9,435 B. 302,876 C. 0.901 D. 0.019 E. 7,142.85
Write out each of the following in words: A. 29 B. 478 C. 98,542 D. 0.06 E. 13.113
A. Twenty-nine B. Four hundred seventy-eight C. Ninety-eight thousand five hundred forty-two D. Six hundredths E. Thirteen and one hundred thirteen thousandths
Area of a Triangle Formula
A= 1/2bh
Area of a Parallelogram Formula
A= bh
Area of a Circle Formula
A=πr²
Linear Equation
AX +BY = C A, B, C = Constants X, Y = Variables
How do you calculate percentage difference?
Calculate percentage difference using this formula:% difference=|Value 1−Value 2Value 1+Value 22|×100%Ex. If chocolate ice cream costs $4.25 and cookie dough ice cream costs $6.35, what is the percentage difference between the two ice creams?% difference=|4.25−6.35(4.25+6.35)2|×100%=|−2.15.3|×100%=39.62%
How do you calculate percentage increase?
Calculate percentage increase using this formula:% increase=𝑛𝑒𝑤−𝑜𝑙𝑑𝑜𝑙𝑑×100Ex. A student scored a 73 on his first test and a 92 on his second test. What is the percentage increase from his first test score to his second test score?% increase=92−7373×100=1973×100=26%
Irrational Numbers
Cannot be written as fractions or decimals because the number of decimal places is infinite and there is no recurring pattern of digits within the number. Example: Pi (π)
How do you change a percent to a fraction and decimal?
Change a percent into a fraction by taking the percent and placing it over 100. Then, simplify the fraction if needed. Change a percent to a decimal by turning the percent sign into a decimal point and moving it two places to the left. Ex. Change 16% into a fraction and a decimal. Fraction: 16%=16100=16÷4100÷4=425 Decimal: 16%→16.→0.16
How do I convert decimals to percentages?
Convert a decimal to a percentage by moving the decimal point two places to the right and then placing a percent sign at the end. Ex. Convert 0.713 to a percentage. 0.713→71.3→71.3%
How do you convert percentages to decimals?
Convert a percentage to a decimal by turning the percent sign into a decimal point and moving it two places to the left. Ex. Convert 49% to a decimal. 49%→49.→0.49
How do I convert percentages to fractions?
Convert percentages to fractions by dropping the percent sign and placing the number over 100. Then, simplify if necessary. Ex. Convert 45% to a fraction. 45%=45/100= 45÷5 over 100÷5 =9/20
Continuous Data
Data that can take on any value. There is no space between data values for a given domain. Graphs are represented by solid lines.
Discrete Data
Data with space between possible data values. Graphs are represented by dots.
How do you divide mixed fractions?
Divide mixed fractions by first converting them to improper fractions and then dividing the fractions as normal. Example: 4 and 3/5 ÷ 2 and 1/2 --> 23/5 ÷ 5/2 --> 23/5 × 2/5 --> 46/25 --> 1 and 21/25
Converting Improper Fractions to Mixed Numbers
Divide the numerator by the denominator. 7/2, ask, "How many times can 7 go into 2 evenly?" The answer is 3. "How much is left over?" One. The remainder of the numerator of the fractional portion of the mixed number and the denominator stays the same. *Go "clockwise" for answer.
How do you multiply fractions with whole numbers?
Multiply fractions by whole numbers by turning the whole number into a fraction by placing it over 1. Any number divided by itself is itself, so this does not change the value of the whole number. Then, multiply across as with normal fractions. Example: 2/3 × 4 = 2/3 × 4/1 = 8/3 = 2 and 2/3
How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator. Simplify as needed.
How do you multiply percentages?
Multiply percentages by first converting them to decimals. Then, multiply the decimals. Finally, convert back to a percentage, if necessary. Ex. 13%×21%=.13×.21=.0273=2.73%
How do you calculate a percentage decrease?
Multiply the original number by the percent decrease and then move the decimal two places to the right.
Converting a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator, then add the numerator. Keep the same denominator at the end.
Constant of proportionality.
The constant ratio in a proportional linear relationship.
Adding and Subtracting Fractions
The denomination has to be the same. If it is different find the lowest common multiple of the denominators AKA the least common denominator (LCD). 5/6 - 3/4 = 5/6 x 2/2 - 3/4 x 3/3 = 10/12 - 9/12 = 1/12.
What is the difference between rational and irrational numbers?
The difference between rational and irrational numbers is that a rational number can be represented as an exact fraction and an irrational number cannot. A rational number includes any whole number, fraction, or decimal that ends or repeats. An irrational number is any number that cannot be turned into a fraction, so any number that does not fit the definition of a rational number.
Independent Variable
The experimental factor that is manipulated; the variable whose effect is being studied.
Greatest Common Factor
The largest number that is a factor of two or more numbers. Example: The factors of 15 are 1, 3, 5 and 15. The factors of 35 are 1, 5, 7 an d 35. The greatest common factor of 15 and 35 is 5.
Dependent Variable
The outcome factor; the variable that may change in response to manipulations of the independent variable.
A city's population grows from 96,200 to 99,400 in ten years. How much did the city's population grow, in percent, over the ten-year period?
The percent increase formula takes the difference between the new and old values, divides it by the old value, and then multiplies it by 100 to get the percent increase. The difference between the new and old city population is 3,200, divided by 96,200 then multiplied by 100 is 3.32640...Therefore, the city's population grew by 3.3% in ten years.
Decimal Place
The position of a number to the RIGHT of the decimal point.
Multiplication Rule of Probability
The probability of independent events occurring in a particular sequence is equal to the product of their separate probabilities.
Conditional Probability
The probability that one event happens given that another event is already known to have happened.
Place Value
The value of a digit based on its position within a number.
What are the steps for adding and subtracting decimals?
To add or subtract decimal numbers, set up the numbers as usual for vertical addition or subtraction, aligning the numbers at the decimal points. Add extra zeroes after the decimal if necessary. Add or subtract as normal, keeping the decimal in the same position.
How do you calculate a grade percentage?
To calculate a grade percentage, add each grade from one category and then divide by the number of grades in that category (take the average). Next, multiply by the weight (percentage) that category holds. Repeat for as many categories as there are and then add them together.Ex. At my school, major grades are worth 60% of my final grade, daily grades are worth 30% of my final grade, and my final exam is worth 10% of my final grade. If my grades are as follows, what is my final grade?Daily Grades: 95, 87, 73, 92, 98Major Grades: 93, 88, 95Final Exam: 94Daily Grade Average=95+87+73+92+985=4455=89Daily Grade Portion=89×30%=89×.3=26.7%Major Grade Average=93+88+953=2763=92Major Grade Portion=92×60%=92×.6=55.2%Final Exam Portion=94×10%=94×.1=9.4%Final Grade=26.7+55.2+9.4=91.3%
How do you calculate percentage with a calculator?
To calculate percentage with a calculator, divide the part by the whole and multiply by 100. Ex. What percentage of 20 is 5? 5/20 = .25 × 100 = 25%
Kaya wants to buy a pair of jeans that are $28 and have been marked down 20%. How much money will Kaya save on the jeans? (PERCENTAGE DECREASE).
To find the amount Kaya will save, we will multiply the price of the jeans by the marked down percentage (20) and then move the decimal two places to the left to reflect the percent. Therefore, the discount amount, or the amount that will get subtracted from the price of the jeans, is $5.60.
Mode Formula
To find the mode, or modal value, it is best to put the numbers in order. Then count how many of each number. A number that appears most often is the mode.
How do you turn a normal number into a percentage?
Turn a normal number into a percentage by adding a decimal point followed by 2 zeroes. Remember, adding a decimal point and 0s to the end of a number does not change its value. Then, move the decimal point two places to the right, and add a percent sign. It's the same process as converting a decimal to a percentage. Ex. What is 14 as a percentage? 14→14.00→1400→1,400%
Volume of a Prism Formula
V=Bh
Volume of a Cylinder Formula
V=πr²h
Radius Formula
r=d/2
Quadratic Formula
x = -b ± √(b² - 4ac)/2a
Slope Intercept Form
y = mx + b
Circumference of a Circle
πd OR 2𝜋𝑟
Trapezoid Area Formula
𝐴=ℎ(𝑏1+𝑏2)/2
Standard Form
𝐴𝑥 + 𝐵𝑦 = 𝐶