to make Math really make sense Math Resource Helpful hints to make Math really make sense

Decimals (parts) Whole Numbers Place Value

Types of Numbers Real Numbers: numbers found on a number line Integers: numbers (positive and negative) that don’t have decimals Whole Numbers: positive integers, including O, Odd Numbers: any number that ends in 1,3,5,7,9 Even Numbers: any number that ends in 0,2,4,6,8 Consecutive Numbers: in a natural row (3,4,5)

More Numbers Rational numbers: any number that can be expressed as a fraction (3 = 3/1, 2/3, 0.25) Irrational numbers: numbers that dont make sense - repeating decimals, go on forever (∞, π) Prime numbers: only factors of 1 and itself (2,3,5,7,11, . . ) Composite numbers: three or more factors (4,6,8,9,10, . . )

Sieve of Erasthosenes Composite Numbers - Prime Numbers - in yellow/gold Composite Numbers - crossed out First five Prime Numbers 2, 3, 5, 7, 11

Written Numbers Standard form: written with digits (individual numbers) 23 456 Expanded form: broken into place values * 20 000 + 3 000 + 400 + 50 + 6 *(2x10 000)+(3x1 000)+(4x100)+(5x10)+6 Scientific Notation: making very large or very small numbers easier to deal with 234 000 = 2.34 X 10 5th power 0.0000234 - 2.34 x 10 -5th power

Adding Positive and Negative Numbers 1.) Same signs - just add and keep same sign (-3 + -2 = -5) 2.) Different signs - subtract smaller from larger and keep sign of larger digit (-3 + 2 = -1) Subtraction: “add the opposite” then follow addition rules -3 -(-2) = -3 + (+2) = -1

Multiplying and Dividing Positive and Negative Numbers Same signs = positive answers Different signs = negative answers (+)(+) = + (-)(-) = + (+)(-) = - (-)(+) = - (-5)(-6) = +30 (+4)(-5) = -20

Multiplication Term to Know Multiples - like skip counting, groups of numbers with common number - can go on forever (4,8,12,16, 20 . . .) Factor: numbers when multiplied make a product (when finding factors start on outside and work in (1, 18) Product - the answer to a multiplication problem factor X factor = product Least (or lowest) Common Multiple (LCM) - comparison of two numbers 4,8,12,16,20 5,10,15,20 LCM =20 Greatest Common Factor (GCF) - comparison of two numbers factors 6: (1,2,3,6) 9: (1,3,9) GCF = 3

LCM =20 LCM =20 How to Multiply Traditional Method Alternate Method

Divisibility Rules 2 - any even number 3 - digits add up to a multiple of 3 4 - last two digits divisible by 4 5 - ends in 5 or 0 6 - divisible by both 2 and 3 8 - last 3 digits divisible by 8 9 - digits add up to a multiple of 9 10 - end in 0

Dividend / divisor = Quotient How to Divide Dividend / divisor = Quotient Traditional Method Alternate Method

division or multiplication Order of Operations 3 + (2+1) x 4 = 3² + 3 x 4 = 9 + 3 x 4 = 9 + 12 = = 21 BEDMAS = brackets exponents division or multiplication addition or start at Left side then move to right

Exponents Exponent is the small number that tells how many times the base multiplies itself Base: large number that is multiplying itself Together the base and exponent are know as Power 3 to the power of 4 = 3 x 3 x 3 x 3 = 81 Positive exponents = positive whole numbers Negative exponents = fractions or decimals Power of 10 - positive exponents tell how many zeros behind the 1 Negative exponents tell how many zeros in front of the 1 including the 0 before the decimal.

Squared Numbers Squared numbers are numbers that have both factors the same (6 x 6 = 36) Perfect squared numbers have an ODD number of factors (1,2,3,4,6,9,12,18,36) = 9 factors Radical sign : answers can be positive or negative 6² = (6)(6) = 36 -6² (-6)(-6) = 36 Know the common squared numbers!! 2 x 2 = 4 3 x 3 = 9 4 x 4 = 16 5 x 5 = 25 6 x 6 = 36 7 x 7 = 49 8 x 8 = 64 9 x 9 = 81 10 x 10 = 100 11 x 11 = 121 12 x 12 = 144 13 x 13 = 169 14 x 14 = 196 15 x 15 = 225

Finding Squared numbers Guess and Check 1) find the nearest square numbers that it lies between 2) Find the square roots 3) Guess which root is it closer to 4) Check with multiplication if your guess is correct 5) Guess and try again if not close Formula Based Method 1) Find the nearest square number without going over 2) Subtract the closest square number from the square number you are dealing with 3) Divide that answer by 2 times the square root of the closest square number 4) Add that answer to the nearest square root to get the final answer)

Fractions - Terminology Numerator = top part of the fraction Denominator = bottom part of the fraction 2 3 Improper Fraction = numerator larger than denominator 3 2 1 Mixed Number = whole number with fraction 2 3 Reciprocal = “flipping the fraction” Inverse operation = opposite operation

Improper Fraction to Mixed number 1.) Denominator goes into numerator = whole number 2.) Remainder = new numerator 3.) Denominator stays the same

Mixed number to improper number 1.) Denominator x whole number 2.) Add the numerator to find the new numerator 3.) Denominator stays the same

Adding and Subtracting Fractions 1.) Fractions must have COMMON DENOMINATORS 2.) Add numerators together 3.) common denominator stays the same 4.) Change to lowest terms

Formulas to know and love! Area of a rectangle/square/parallelogram A = b x h or A = l x w Area of a triangle A = (b x h)/2 Area of a Circle A = πr²

Pythagorean Theorem

Pythagorean Theorem Hypotenuse - side opposite the right angle Legs - sides of the triangle that make up the right angle used only on Right angle triangles