Reference Page Math Symbols- + add - subtract x multiply divide = equal % percent $ dollar cent # at degree.

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1 Reference Page Math Symbols- + add - subtract x multiply divide = equal % percent $ dollar cent # at degree. decimal point pi Roman Numerals Conversion I = 1 C = 100 V = 5 D = 500 X = 10 M = 1000 L = 50 Roman Numerals Conversion Rules: The letters should be arranged from the one with the largest value to the one with the smallest. Each letter's value is added to the previous ones. Only powers of ten (I, X, C, M) can be repeated. Do not repeat any letter more than three times in a row. Because of the preceding rule, certain numbers must be written using subtraction. In this case, a letter with a smaller value precedes one with a larger value and the value of the smaller is subtracted from the larger. The result is then added to the rest of the letters. The following rules apply to subtraction: Only powers of ten (I, X, C, M) can be subtracted. The smaller letter must be 1/5th (one-fifth) or 1/10th (one-tenth) the larger one. The smaller letter must be either the first letter or preceded by a letter at least ten times greater than it. If another letter follows the larger one, it must be smaller than the number preceding the larger one.

2 Measurements- Measurement Abbreviations- Time: 60 seconds = 1 minute sec - seconds 60 minutes = 1 hour min - minutes 24 hours = 1 day hr - hours 7 days = 1 week wk - week 52 weeks = 1 year yr - year 365 days = 1 year mo- months 12 months = 1 year Weight: (how heavy an object is) 1 pound = 16 ounces lb or # - pound 1 ton = 2000 pounds oz - ounces 1 oz is similar to the weight of an envelope 1 pound is similar to a box of powdered sugar Length: 1 foot = 12 inches ft- foot mi - mile 1 yard= 3 feet=36 inches in-inches 1 mile = 5280 feet yd- yard 1 inch is similar to the width of two fingers 1 foot is similar to the length of your foot 1 yard is similar to the length of your stride (a giant step) Volume: (how much an object holds) 1 cup = 8 fluid ounces c cup 1 pint = 2 cups pt pint 1 quart = 2 pints = 4 cups qt quart 1 gallon = 4 quarts gal gallon 1 fluid ounce is similar to the amount the tablespoon holds 1 cup is similar to a carton of yogurt 1 gallon is similar to a large plastic jug of milk

3 Key Words in Math Addition Division sum quotient all per together average total each in all divide equally all together out of increased by ratio of more than percent combined together goes into total of added to plus Subtraction Multiplication difference product left in all less than times How many more? all fewer than of greater than total more than multiplied by How many less? twice reduced by decreased by difference of remainder less than minus addend + addend = sum sum addend = addend factor X factor = product product factor = factor quotient divisor dividend

4 Properties of Numbers Commutative- when you add or multiply you can do it in any order or swap the numbers around and get the same answer = 6 just like = 6 5 X 3 = 15 just like 3 X 5 = 15 Identity- a number added to 0 is that number; a number multiplied by 1 is that number = 3 1 X 5 = 5 Order of Operations Please Parenthesis ( ) or Brackets [ ] Excuse Exponents 3 2 My Dear Multiplication & Division left to right Aunt Sally Addition & Subtraction left to right Associative Property- The order in which numbers are grouped does not affect the sum or product. (5 + 2) + 3 = 10 just like 5 + (2 + 3) =10 (2 X 3) X 4 = 24 just like 2 X (3 X 4) = 24

5 MULTIPLICATION- Any number multiplied by 0 = 0 5 X 0 = 0 Any number multiplied by 1 = that number 2 X 1 = 2 When multiplying an even number by 6, the ones column equals that number and the tens column equals ½ the number in the ones column. 6 X 2 = 12, 6 X 4 = 24 When multiplying by 9: (the finger trick) 1. Hold out your hands Each finger is a number. Starting with the pinky on the left hand as one. 2. Decide on the problem, for example 9 x 3 =. 3. Holding up your hands, bend down the "3" finger. 4. The fingers to the left of the "3" are the tens. How many tens are still straight- "2". That's right, 2 tens or The fingers to the right of the "3" finger are the "ones", include both hands. There are 2 fingers raised on the left hand and 5 on the right, making a total of 7 fingers. 6. Put them together, 2 tens and 7 ones or 27! That's the answer. 9 x 3 = 27

6 DIVISION- Divide & Conquer Dragon (Divide) How many times will 3 go into 4? Mouthwash (Multiply) 1 X 3 =3-3 Sweetens (Subtract) 4 3 = Charboiled (Check) Is 1 equal to or larger than 3? No Breath (Bring Down) Bring down the 7. 2 Repeat steps for each number in the house. Division Hints- Divide by: If: 2 the last digit is even 5 the last digit is a 5 or a 0 10 the number ends in 0 Decimals 1 5 r 2 Addition- When you add decimals be sure to line up the decimal points and keep the columns straight. Subtraction- When you subtract decimals, be sure to line up the decimal points and keep the columns straight. Multiplication- When you multiply decimals, the number of decimal places in the product should equal the total number of decimal places in the factors. Division- When you divide decimals, move the divisor s decimals point to the right to make it a whole number. Move the dividend s decimal point the same number of places to the right. Write the quotient decimal point directly above the dividend s decimal point.

7 Fraction Terminology- Fraction- part of a whole part numerator line represents division whole denominator proper fraction- numerator is smaller than denominator improper fraction- numerator is larger than denominator mixed number- whole number and fraction reduce/simplify/lowest terms- all fractions should be reduced determine if there is a (same) number that will go into the numerator and denominator both evenly improper fraction to a mixed number- divide your denominator into your numerator if there is a remainder make it into fraction form using the remainder as your numerator and keep the same denominator mixed number to an improper fraction- multiply the denominator times the whole number, then add the product and numerator, that sum becomes the numerator and the denominator stays the same Any time there is a whole number by itself, put it over the whole number 1 to make it into fraction form. fraction to a decimal- divide your numerator by your denominator Keep the 1 st Flip 2 nd Change sign to multiplication

8 % Percents % What What What Percent number ) (1) % of (2) is (3) X = (1) & (2) X (2) & (3) * (1) or (2) ) (3) (1) & (3) % to decimal Move decimal to the left 2 places Ex. 20% =.20 3% = % = ½% =15.50% =.155 decimal to % Move decimal to the right 2 places Ex..50 = 50%.110= 11.0% or 11% 125.5= 12,550% 2.25=225% Always change % to a decimal before performing the operation. * change decimal answer to % for final answer

9 Ratio & Proportion- Ratio- comparison of two numbers -can be written with the word to, a colon (:), or as a fraction -always write the numbers in the same order as the problem compares them -the number listed first is the numerator -reduce Proportion- two ratios written as equal ratios (4 terms) -in a proportion problem one of the four terms is missing use an x to represent the missing number -to find the missing number cross multiply 1. multiply the first numerator by the second denominator put the sum on the left of the equals sign 2. multiply the first denominator by the second numerator put the sum on the right of the equals sign 3. divide the number with the x by the sum 4. the quotient represents the missing x

10 Integers/Signed Numbers/Positive & Negative Numbers Positive Numbers greater than zero (doesn t have a sign) Negative Numbers are less than zero (always written with a negative sign - ) Zero has no sign and is always written as 0 Adding Integers Same signs-1. Add the numbers 2. Keep the sign o (+) + (+) = (+) o (-) + (-) = (-) Different/Opposite signs 1. Subtract the numbers 2. Take the sign of your larger number o (+ larger number) + (- smaller number) = (+) ex = 3 o (+ smaller number) + (-larger number) = (-) ex = -3 Subtracting Integers 1. Change the sign of the second number (if it s negative it becomes positive, if it s positive it becomes negative) 2. Change subtraction sign to addition 3. Follow adding integer rules o -9 3 = = = -12 Follow subtracting integer rules when larger number is on the right 3-9 = = = -6 Multiplying/Dividing Integers Same sign answer is positive multiply/divide numbers and make a positive o (+) X/ : (+) = (+) o (-) X/ : (-) = (+) Different sign answer is negative Multiply/divide numbers and make a negative o (+) X/ : (-) = (-) o (-) X/ : (+) = (-) Multiplying more than two signed numbers o If there is an even number of negative signs, give the product a positive sign. o If there are an odd number of negative signs, give the product a negative sign. 0 x or : by any number = or any number = that number 0 is NOT positive or negative

11 Lines and More Point- an exact location in space Line- extends indefinitely in both directions Line Segment- a portion of a line that has two endpoints Ray- begins at a fixed point and extends indefinitely in one direction Angle- two rays that share an endpoint Parallel Lines- two lines that will NEVER intersect Perpendicular Lines- tow lines that cross to form four right angles Intersecting Lines- lines that have exactly one point in common

12 Angles Acute angle measure less than 90 O (skinny angle) Right angle measure 90 O (the perfect angle; corner of a paper) Obtuse angle measures between 90 O and 180 O (the obese/fat angle) Straight angle measures 180 O Complementary angles have measurements with a sum of 90 O Supplementary angels have measurements with a sum of 180 O Reflex angle measures more than 180 O but less than 360 O Straight line = 180 O Circle = 360 O Triangle = 180 O

13 Triangles A triangle is a polygon with three sides. Triangles can be classified by the length of their sides or by the measure of their angles. Equilateral triangles have three equal sides. Equiangular triangles have three equal angles. Isosceles triangles have two equal sides. Acute triangles have three acute angles Scalene triangles have no equal sides. Right triangles have one right angle. Obtuse triangles have one obtuse angle. dr d-diameter (distance across the circle) r-radius (middle of the circle to the outside edge)