1. Brackets Exponents Roots Addition Subtraction Division Multipl ication Factors Squares

2.  To translate sentences from English to math, I would use my Math-English dictionary.  Examples: ◦ Kelly swam twice as much as Bob  K=2xB ◦ Sam baked two more cookies than Alex  S=A+2 ◦ Ashley and Tom together ran as much as Dave  A+T=D +-x: Addition Plus More Subtraction Minus Less Multiplication Times Double Division Fraction Quotient

3.  The order of operations is the step by step process that helps you know in which order you should complete your math problems.  It is very important, because without it people would most likely get different answers for every question. Since we don’t want that to happen, we follow the rules of the order of operations, and that way get the same answers.  Here is a good way to remember the order: ◦ BEDMAS: Brackets, exponents, division, multiplication, addition, subtraction ◦ PEMDAS: Parentheses, exponents, multiplication, division, addition, subtraction  Examples: ◦ 2+3(7-5)+9*2  2+3*2+9*2  2+6+18= 26 ◦ 7-3*2*5+(3+2)= 7-3*2*5+5  7-6*5+5  7-30+5  -23+5= -18

4.  Squaring is the fuction that we use when we multiply a number by itslef.  Perfect squares are all the square numbers.  Here is the start of the list of all the square numbers: ◦ 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100,...  These numbers are perfect square numbers, because they have been formed by a number that has been multiplyed by itself.  Example: ◦ 0 = 0 x 0 ◦ 1 = 1 x 1 ◦ 4 = 2 x 2 ◦ 9 = 3 x 3 Etc.

5.  Factors are two or more numbers that divide a given number without a reminder.  Example: ◦ 2 and 3 are factors of 6 ◦ x and y are factors of xy  The GCF is short for the greatest common factor. The greatest common factor is the largest factor that two numbers have in common.  Example: ◦ 20: 1, 2, 4, 5, 10, 20 ◦ 15: 1, 3, 5, 15 The GCF of 20 and 15 is 5, since it is the largest factor they have in common.

6.  The set of real numbers is the set of numbers that include all the integers, rational numbers, whole numbers, and natural numbers.  Integers are all the negative and positive counting numbers.  Example: ◦ { -3, -2, -1, 0, 1, 2, 3 }  Rational numbers are all the numbers that can be written as a fraction.  Example: ◦ 3  3/1 ◦ ½  2/4, 3/6, 4/8, 6/12...  Whole numbers are all the counting numbers.  Example: ◦ { 1, 2, 3, 4, 5,... }  Natural numbers are all the counting numbers with zero added on.  Example: ◦ { 0, 1, 2, 3, 4, 5,... }

7.  Integers are all the positive and negative counting numbers.  To add and subtract integers, it is good to use a number line.  Adding and subtracting integers is basicly just like normal addition and subtraction.  Examples: ◦ 4 + 5 = 9 ◦ 7 – 2 = 5  Sometimes when you subtract, you will go to the negative side.  Example: ◦ 5 – 7 = -2  Sometimes the signs in front of the numbers aren’t the same. When this happens in addition, just subtract the two numbers, and keep the sign of the bigger number.  Example: ◦ -2 + 5 = 3 (5 – 2 = 3) The answer is positive, because the larger number is positive. ◦ 3 + -7 = -4 (7 – 3 = 4) The answer is negative, because the larger number is negative.  If the signs are different when you are subtracting, just add the opposite sign, and follow the rules of addition.  Example: ◦ -2 - -8 = 6 (-2 - -8  -2 + 8 = 6)

8.  Multiplying and dividing integers is just normal multiplication and division.  Example: ◦ 4 x 5 = 20 ◦ 8 : 4 = 2  When you are multiplying integers, if the signs are the same on both numbers, the answer is always going to be positive.  Example: ◦ 7 x 6 = 42 ◦ -7 x -6 = 42  If the signs are opposites, the answer is always going to be negative.  Example: ◦ 2 x -5 = -10 ◦ -2 x 5 = -10  If there are 3 or more numbers being multiplied together, these are the rules: ◦ Odd # of negatives, answer will be negative ◦ Even # of negatives, answer will be positive  All these same rules apply when you are dividing integers.

9.  A root number is a base number.  A square root is the base of the square number.  Example: ◦ The square root of 9 is 3, since 3 x 3 = 9 ◦ The square root of 64 is 8, since 8 x 8 = 64  A cube root is the base of a cube number. A cube number is a number that is fromed when you multiply a sertain number by itself 3 times.  Example: ◦ The cube root of 27 is 3, since 3 x 3 x 3 = 27 ◦ The cube root of 125 is 5, since 5 x 5 x 5 = 125