Order of Operations: Mathematicians must follow a specific order when solving a multi step problem. For each operation work left to right. Absolute Value: The distance a number is from zero. - 5 = 5 13 = 13 – 7 = – 7 Mean, Median, Mode, Range, Outlier: 14, 30, 4, 10, 7, 4, 5, 12, 4, Mean (average): Add the numbers and divide by total number of terms ( ) ÷ 9 = Mean = 10 Median (middle number): First put all numbers in order, then find the middle Median = 7 Mode (Most frequent number): Mode = 4 Range (Difference between lowest and highest number): 30 – 4 = Range = 26 Outlier = 30 (Relatively too large or too small of number based on other numbers in series) Exponents: An exponent tells the base how many times to multiply by itself. 5 3 = 5 x 5 x = = = 1 Exponent Rules: When you multiply two numbers raised to an exponent, add the exponents. C 4 x C2 = C 6 Because C x C x C x C x C x C = C 6 When you raise an number with an exponent to another exponent, multiply the exponents. (x 4 ) 2 = X 8 Because x 4  x 4 = X  X  X  X  X  X  X  X = X 8 When you divide numbers with exponents, subtract the exponents. If there are whole numbers, simplify the fraction first. 6 X 2 Y 5 = 3 Y 3 Because X X Y Y Y Y Y 14 X 6 Y 2 7 X 4 X X X X X X Y Y Prime Factorization: Writing a number as a product of prime number (in exponential form) P.F. OF 18 = 2 x x x 3 3 Greatest Common Factor (GCF) or (GCD): List out all the factors of the numbers you are comparing. (numbers that it can be divided by) Find the largest number that divides into both Least Common Multiple (LCM): List several multiples of the numbers you are comparing. (create a multiplication table) Find the smallest multiple that they share. Rules: Place the decimal behind the 1 s on-zero Always multiply by 10 to an exponent Use positive exponents for BIG numbers Use negative exponents for small numbers The exponent corresponds to the number of places you moved the decimal 3.45 x 10 5 = x = = 6.75 x = 4.5 x Negative Numbers: As you move to the left on a number line, values get smaller. As you move to the right, values get larger. -17 is farther away (to the left) from zero than -5, Therefore -17 is smaller than is bigger than -6 because it is a positive value.

Inequalities: Solve the one-step equation using an inequality sign. Shade in the direction of the inequality sign. - Greater than > Shade to the Right - Less than < Shade to the left - Use a close circle for = ≥ ≤ - Use an open circle for 16 + n < 20 n < 4 Adding and Subtracting Decimals: Line up decimals Put zeros in for place holders where needed. Follow basic adding and subtracting rules. Multiplying Decimals: Do not line up decimals. Line up on right. Multiply following basic multiplication rules (don’t worry about the decimals until the end). Count how many numbers come after a decimal in the problem (in both numbers), then place the decimal in the answer so that it has the same amount of numbers after the decimal. Dividing Decimals: Use long division. Work out until you have a zero remainder or a series of repeating numbers. The first number you say goes under the division house. When dividing by a whole number, carry the decimal straight up and lock into position. When dividing by a decimal, move the decimal to the end of the number on the outside, then move the inside decimal to the right the same number of places, then straight up. Changing Between Decimals & Percents: Move the decimal 2 places D P Move 2 to the right D P Move 2 to the left 45% = = 3% 1.25 =125% Percents to Fractions: Place percent over 100, then simplify. 45% = 45/100 = 9/20 6/50 = 12/100 = 12%.60 = 60% = 60/100 = 6/10 = 3/5 Comparing fractions, decimals, and percents: Change all numbers to the same form to compare. Easier to compare all as decimals. Changing a Fraction to a Decimal or Percent Use long Division. ½ = 1  2 =.50 ½ = 50% How to find a percent of a number: Multiply the number by the percents as a decimal. 80 Your answer is a number, not a percent. Find 60% of 80 =.60 x 80 = 48 X

Distributive Property: Multiply the outside term by every term inside the parenthesis, one at a time. Keep the operation signs. Ordered Pairs: (X,Y) (Input, Output) X horizontal Y is Vertical Area Formulas: Memorized These! rize These! Angle Measurement: Complimentary Angles: Add up to 90 o Supplementary Angles: Add up to 180 o Vertical Angles: Are congruent angles. If <1 = 35 o, the <2 = 35 o Alternate Angles: All obtuse angles will be congruent. All acute angles will be congruent. Triangle: Internal angles add up to 180 o 4 Sided Figure: Internal angles add up to 360 o because it is made up of 2 triangles. 5 Sided Figure: Internal angles add up to 540 o because it is made up of 3 triangles. Finding area of irregular shapes: Break shape into knows figures. Find area of each shape and add together. Total Area= 300 in 2 kjh = 28ft Circumference: The perimeter of a circle. You must use the formula: Types of Triangles: Triangles all have two names. One based on the measurement of its angles and one based on the measurement of its sides. Adding/Subtracting Fractions: Make sure the bottom numbers (the denominators) are the same. Find a common denominator is needed. Add or subtract the top numbers (the numerators). Put the answer over the same denominator. Simplify the fraction (if needed). Multiplying Fractions: Multiply straight across and simplify Dividing Fractions: Flip the 2 nd fraction (find the reciprocal) change division sign into multiplication and follow multiplication rules (Flip and Multiply) Perimeter Formulas: Add all outside edges of a shape. P= P = 15 in 8 ft 2 Area of triangle 20 ft 2 Find area of the square

Probability: The likelihood an event will occur Theoretical probability: Mathematical likelihood (written as a fraction) P(a die will land on a 4) = 1/6 There is one 4 out of six possible outcomes. Sample Space: All possible outcomes The sample space for a penny is (Heads, Tails) Events (Independent or Dependent): Multiply the individual theoretical probabilities together. P(rolling a 4 on a die and getting a head on a penny) 1/6 x 1/2 = 1/12 = Roughly 8% If a bag contains 2 white marbles, 5 red marbles, and 3 green marbles, what is P(red, green) without replacement. 5/10 x 3/9 = 15/90 = 1/6 = Roughly 17% Combinations: Multiply the number of choices in each category. How many outfits can be made from 4 shirts, 3 shoes, and 5 pants. 4 x 3 x 5 = 60 outfits How many different ways can you line up five students? 5 x 4 x 3 x 2 x 1 = 120 different ways How many ways you pick a President and Vice President out of 20 people? 20 x 19 = 380 ways Making Predictions: Use ratios or percents to determine likelihood of future event. If I spun the spinner 78 times, how many times should I land on a triangle. set up a Ratio 6X = (2 * 78) I should expect to 2 = X 6X = 156 get the triangle about 6 78 X = times. If 5% of middle schoolers at centennial like snakes, then how many students can I expect to like snakes if I surveyed 2,000 students in wake county?.05 x 2000 = 100 students Transformations: Translations: To Slide Rotations: To Turn Reflections: To Flip Translations: Moving to the right – Add to X Moving to the left – Subtract from X Moving up – Add to Y Moving down – Subtract from Y Remember X goes left and right. Y goes up and down Rotations: Rotate 180 – All points go to their opposite signs Rotate 90 clockwise – Switch location of X and Y, then change all y points to their opposite signs. Rotate 90 counterclockwise – Switch location of X and Y, then change all the x points to their opposite signs. Reflections: Reflect over x-axis – All x points stay the same and all y points go to their opposites reflect over y-axis – All y points stay the same and all x points go to their opposites Converting an improper fraction to a mixed number: Divide the denominator into the numerator. This becomes the whole number Place the remainder as the numerator Keep the original denominator Change 33/4 into a mixed number. Change a mixed number into an improper fraction: You must turn mixed numbers into improper fractions before you perform multiplication or division. I recommend changing mixed number for addition and subtraction as well. Multiply the denominator by the whole number Then add that number to the numerator Place back over original denominator Measurement (Extra) 1 Yard = 3 Feet 1 Mile = 5280 Feet 1 Gallon = 4 Quarts 1 Quart = 2 pints 1 Pint = 2 Cups 1 Kilogram = 1000 Grams 1 Gram = 1000 Milligrams King Henry Doesn’t Usually Drink Chocolate Milk Kilo hecto deka [unit] deci centi milli