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Reference Page Math Symbols+ add - subtract x multiply divide = equal % percent $ dollar cent # number/pound @ 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. Measurements- Measurement Abbreviations- Time: 60 seconds = 1 minute 60 minutes = 1 hour 24 hours = 1 day 7 days = 1 week 52 weeks = 1 year 365 days = 1 year 12 months = 1 year sec - seconds min - minutes hr - hours wk - week yr - year mo- months Weight: (how heavy an object is) 1 pound = 16 ounces 1 ton = 2000 pounds lb or # - pound 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 1 yard= 3 feet=36 inches 1 mile = 5280 feet ft- foot in-inches 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 1 pint = 2 cups 1 quart = 2 pints = 4 cups 1 gallon = 4 quarts c – cup pt – pint qt – quart 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 mi - mile Key Words in Math Addition sum all together total in all all together increased by more than combined together total of added to plus Subtraction Division difference left less than How many more? fewer than greater than more than How many less? reduced by decreased by difference of remainder less than minus quotient per average each divide equally out of ratio of percent goes into Multiplication product in all times all of total multiplied by twice addend + addend = sum sum – addend = addend factor X factor = product product factor = factor quotient divisor dividend 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. 4 + 2 = 6 just like 2+4=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+0=3 1X5=5 Order of Operations Please – Parenthesis ( ) or Brackets [ ] Excuse – Exponents 32 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 (2 X 3) X 4 = 24 just like just like 5 + (2 + 3) =10 2 X (3 X 4) = 24 MULTIPLICATIONAny 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 20. 5. 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 DIVISION- Divide & Conquer Dragon (Divide) Mouthwash (Multiply) Sweetens (Subtract) Charboiled (Check) Breath (Bring Down) How many times will 3 go into 4? 1 5 r2 3 47 1 X 3 =3 4–3=1 Is 1 equal to or larger than 3? No. Bring down the 7. - 3__ 1 7 -1 5 2 Repeat steps for each number “in the house”. Division HintsDivide by: 2 5 10 If: the last digit is even the last digit is a 5 or a 0 the number ends in 0 Decimals 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. Fraction TerminologyFraction- part of a whole part _____ whole numerator line represents division 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 1st Flip 2nd Change sign to multiplication % Percents What What % What ) __(1)___% of __(2)___ is __(3)___ X = Percent number (1) & (2) X (2) & (3) ÷ * (1) & (3) ÷ (1) or (2) ) (3) % to decimal Move decimal to the left 2 places Ex. 20% = .20 3% = .03 175% = 1.75 15 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 Ratio & ProportionRatio- 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” 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. 5 + -2 = 3 o (+ smaller number) + (-larger number) = (-) ex. 2 + -5 = -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 = -9 - -3= -9 + -3= -12 Follow subtracting integer rules when larger number is on the right 3 - 9 = 3 - -9 = 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 = 0 0 + or – any number = that number 0 is NOT positive or negative 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 Angles Acute angle measure less than 90O (skinny angle) Right angle measure 90O (the “perfect” angle; corner of a paper) Obtuse angle measures between 90O and 180O (the obese/fat angle) Straight angle measures 180O Complementary angles have measurements with a sum of 90O Supplementary angels have measurements with a sum of 180O Reflex angle measures more than 180O but less than 360O Straight line = 180O Circle = 360O Triangle = 180O 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)