Chapter 3 Notes

  • The Order Of Operations is this: Simplify grouping symbols, simplify exponents, multiply and divide left to right, add and subtract left to right

  • The order of operations provides the correct order to simplify expressions

  • The communitive property states that the order of addition and multiplication can be reversed without affecting the result ex. 5+2=2+5+7 5×2=2×5=10

  • Subtraction and division cannot be communitive

  • The associative property states that regrouping can be done within expressions containing more than 2 addition or multiplication steps without affecting the result ex. 8+(2+5)=(8+2)=5=15

  • The associative property cannot be applied to subtraction and division

  • The distributive property states that when a number is multiplied by a sum or difference, it can be distributed to each number of the sum or difference without affecting the answer ex. 4(5+8)=4(5)+4(8)= 52

  • Estimation is the process used to find an approximate answer ( an estimate) to an arithmetic problem

  • Subtraction can be defined as adding the opposite

  • To subtract signed numbers, express the subtraction problem as an addition problem by changing both the operation and the sign of the subtrahend ex. 4-8= 4+-8= -4

  • When signed addends have the same sign, add the absolute values of the numbers and keep the sign

  • When signed addends have different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the larger number

  • Two numbers whose sum is zero are called additive inverses ex. -4+4=0

  • When multiplying two positive numbers, the product is positive

  • When multiplying two factors with opposite signs, the product is positive

  • A sequence is a ordered list of numbers that follow a pattern

  • An arithmetic sequence is when a specific number is added to each term

  • A geometric sequence is when a specific number is multiplied to each term

  • To find the following term in a arithmetic sequence, you can subtract the second term from the first term

  • To find the following term in a geometric sequence, you can divide the second term from the first term

  • Algebra is a branch of mathematics that used letters and symbols to represent unknown numbers

  • Variables are the letters used to represent these unknown numbers

  • Constants are numbers that are known and fixed

  • Algebraic expressions contain numbers and letters

  • Factors are numbers, letters, or symbols that are being multiplied

  • When a variable is being multiplied by a constant, the constant is a numerical coefficient

  • A term is a group of one or more factors

  • A constant term contains no variables

  • A variable term contains constant and variable factors

  • A polynomial is a algebraic expression that contains single or multiple terms separated by addition or subtraction signs

  • A polynomial with one term is a monomial

  • A polynomial with two terms is a binomial

  • A polynomial with three terms is a trinomial

  • Like terms are terms that have the same exact variables with the same exact exponents

  • Evaluation is the process of substituting a variable’s numerical value for that variable and simplifying