Summary: Review Topics
Key Concepts
- Phrases such as sum, increased by, difference, decreased by, of, and, etc. can be translated into mathematical operations and notation to help solve a problem.
- To add or subtract fractions, make sure they each have the same denominator first.
- When dividing fractions, use the phrase keep-change-flip to remind you to multiply the first fraction by the reciprocal of the second one.
- Just like the digits of a whole number increase to the left by powers of 10, the digits after the decimal on the right decrease by fractions of powers of ten.
- When using inequality symbols, the smaller side of the symbol faces the smaller number and the larger side faces the larger number.
- The product or quotient of two negative numbers or two positive numbers is always positive; the product or quotient of two differently signed numbers is always negative.
Key Expressions, Equations, and Inequalities
- is read as " is equal to ."
- is read as " is not equal to ."
- can be read " is greater than " or " is less than ."
- A fraction is written where and are integers and . In a fraction, is called the numerator and is called the denominator.
- The distributive property, , represents the distribution of multiplication over addition or subtraction.
- The property of one states that any number, except zero, divided by itself is one. That is , where .
- if are numbers such that then .
- To multiply fractions,
Glossary
- absolute value
- a number's distance from zero on the number line, which is always positive
- constant
- a number whose value always stays the same
- distributive property
- a number multiplying an expression inside of parentheses distributes to each term in the contained expression
- equation
- two expressions connected by an equal sign
- equivalent fractions
- fractions that have the same value
- exponent
- a number in a superscript position that tells how many times to multiply the base by itself
- expression
- a number, a variable, or a combination of numbers and variables and operation symbols
- improper fraction
- a fraction is proper if , and is improper if
- inequality
- two expressions connected by an inequality sign
- integers
- counting numbers like 1, 2, 3, ... including their opposites (negatives) and zero
- like terms
- terms where the variables match exactly (exponents included)
- operators
- symbols that represent arithmetic operations such as addition, subtraction, multiplication, and division
- order of operations
- the universally accepted order to perform operations when more than one is present in an expression, often represented by the acronym PEMDAS
- real numbers
- fractions, negative numbers, decimals, integers, square roots, and zero
- reciprocal
- two fractions are reciprocals if their product is
- simplified fraction
- also called a reduced fraction, or a fraction in lowest terms, a fraction having no common factors in the numerator and denominator
- term
- a single number, variable, or a product or quotient of numbers and/or variables
- variable
- a letter that represents a number or quantity whose value may change