Chapter 1

Whole Numbers

Read chapter 1 in the book

Summary

All digits to the left of that place value do not change unless the given place value is a 9, in which case it may. Underline the digit to the right of the given place value If yes—add 1 to the digit in the given place value. Use commas in the number to separate the periods

Key terms

whole numbers

The whole numbers are the numbers 0, 1, 2, 3, …

given place value

a 9, in which case it may

number line

A number line is used to visualize numbers. The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left

place value system

Our number system is called a place value system because the value of a digit depends on its position, or place, in a number

coordinate

A number paired with a point on a number line is called the coordinate of the point

divisor

When dividing two numbers, the divisor is the number dividing the dividend

dividend

When dividing two numbers, the dividend is the number being divided

difference

The difference is the result of subtracting two or more numbers

Chapter 2

The Language of Algebra

Read chapter 2 in the book

Summary

The expression of a n is read a to the n th power Order of Operations When simplifying mathematical expressions perform the operations in the following order Equality Symbol a = b is read as a is equal to b

Key terms

expressions

An expression is a number, a variable, or a combination of numbers and variables and operation symbols

expression of a n

read a to the n th power

solution of an equation

A solution to an equation is a value of a variable that makes a true statement when substituted into the equation. The process of finding the solution to an equation is called…

like terms

Terms that are either constants or have the same variables with the same exponents are like terms

least common multiple

The smallest number that is a multiple of two numbers is called the least common multiple (LCM)

prime factorization

The prime factorization of a number is the product of prime numbers that equals the number

Chapter 3

Integers

Read chapter 3 in the book

Summary

Addition of Positive and Negative Integers 5 + 3 -5 + ( -3 ) both positive, sum positive both negative, sum negative When the signs are the same, the counters would be all the same color, so add them. Opposite Notation - a means the opposite of the number a The notation - a is read the opposite of a Absolute Value Notation The absolute value of a number n is written as | n |

Key terms

integers

Integers are counting numbers, their opposites, and zero ... -3, -2, -1, 0, 1, 2, 3

absolute value

The absolute value of a number is its distance from 0 on the number line

signs

the same, the counters would be all the same color, so add them

opposites

The opposite of a number is the number that is the same distance from zero on the number line, but on the opposite side of zero

negative number

A negative number is less than zero

Chapter 4

Fractions

Read chapter 4 in the book

Summary

Proper and Improper Fractions The fraction a b is a proper fraction if a < b and an improper fraction if a ≥ b Mixed Numbers A mixed number consists of a whole number a and a fraction b c where c ≠ 0 Equivalent Fractions Property If a, b, and c are numbers where b ≠ 0 , c ≠ 0 , then a b = a ⋅ c b ⋅ c Write the mixed number as quotient remainder divisor

Key terms

fraction

A fraction is written a b . In a fraction, a is the numerator and b is the denominator. A fraction represents parts of a whole. The denominator b is the number of equal parts the…

mixed number

A mixed number consists of a whole number a and a fraction b c where c ≠ 0 . It is written as a b c , where c ≠ 0

equivalent fractions

Equivalent fractions are two or more fractions that have the same value

proper and improper fractions

The fraction a b is proper if a < b and improper if a ≥ b

fraction a b

a proper fraction if a < b and an improper fraction if a ≥ b

least common denominator (LCD)

The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators

simplified fraction

A fraction is considered simplified if there are no common factors in the numerator and denominator

complex fraction

A complex fraction is a fraction in which the numerator or the denominator contains a fraction

Chapter 5

Decimals

Read chapter 5 in the book

Summary

Name the “number” part to the right of the decimal point as if it were a whole number Name the decimal place of the last digit Look for the word “and”—it locates the decimal point.

Key terms

mean

The mean of a set of n numbers is the arithmetic average of the numbers. The formula is mean = sum of values in data set n

median

The median of a set of data values is the middle value. Half the data values are less than or equal to the median. Half the data values are greater than or equal to the median

ratio

A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of a to b is written a to b , a b , or a : b

diameter of a circle

A diameter of a circle is a line segment that passes through a circle’s center connecting two points on the circle

repeating decimal

A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly

rate

A rate compares two quantities of different units. A rate is usually written as a fraction

radius of a circle

A radius of a circle is a line segment from the center to any point on the circle

equivalent decimals

Two decimals are equivalent decimals if they convert to equivalent fractions

Chapter 6

Percents

Read chapter 6 in the book

Summary

Find the percent increase as a percent of the original amount If the denominator of the fraction is not 100, rewrite it as an equivalent fraction with denominator 100 Convert the fraction to a decimal by dividing the numerator by the denominator Write a sentence that gives the information to find it

Key terms

percent

A perfecnt is a ratio whose denominator is 100

percent increase

The percent increase is the percent the amount of increase is of the original amount

proportion

A proportion is an equation of the form a b = c d , where b ≠ 0 , d ≠ 0 .The proportion states two ratios or rates are equal. The proportion is read “ a is to b , as c is to d ”

simple interest

If an amount of money, P , the principal, is invested for a period of t years at an annual interest rate r , the amount of interest, I , earned is I = P r t . Interest earned…

discount

An amount of discount is a percent off the original price, determined by the discount rate

mark-up

The mark-up is the amount added to the wholesale price, determined by the mark-up rate

percent decrease

The percent decrease is the percent the amount of decrease is of the original amount

Chapter 7

The Properties of Real Numbers

Read chapter 7 in the book

Summary

Identity Properties Identity Property of Addition: For any real number a : a + 0 = a 0 + a = a 0 is the additive identity Identity Property of Multiplication: For any real number a : a ⋅ 1 = a 1 ⋅ a = a 1 is the multiplicative identity Inverse Properties Inverse Property of Addition: For any real number a : a + ( - a ) = 0 - a is the additive inverse of a Commutative Properties Commutative Property of Addition: If a , b are real numbers, then a + b = b + a

Key terms

Real number

a real number is a number that is either rational or irrational

Multiplicative Identity

The multiplicative identity is 1. When one multiplies any number, it does not change the value

Additive Identity

The additive identity is 0. When zero is added to any number, it does not change the value

Additive Inverse

The opposite of a number is its additive inverse . The additive inverse of a is - a

Irrational number

An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat

Rational number

A rational number is a number that can be written in the form p q , where p and q are integers and q ≠ 0 . Its decimal form stops or repeats

Multiplicative Inverse

The reciprocal of a number is its multiplicative inverse . The multiplicative inverse of a is 1 a

Chapter 8

Solving Linear Equations

Read chapter 8 in the book

Summary

Simplify the expressions on both sides of the equation Determine whether the resulting equation is true Subtraction and Addition Properties of Equality Subtraction Property of Equality For all real numbers a, b, and c , if a = b then a - c = b - c Addition Property of Equality For all real numbers a, b, and c , if a = b then a + c = b + c

Key terms

solution of an equation

A solution of an equation is a value of a variable that makes a true statement when substituted into the equation

Chapter 9

Math Models and Geometry

Read chapter 9 in the book

Summary

Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don't understand, look them up in a dictionary or on the internet Choose a variable to represent that quantity

Key terms

irregular figure

An irregular figure is a figure that is not a standard geometric shape. Its area cannot be calculated using any of the standard area formulas

trapezoid

A trapezoid is four-sided figure, a quadrilateral, with two sides that are parallel and two sides that are not

similar figures

In geometry, if two figures have exactly the same shape but different sizes, we say they are similar figures

angle

An angle is formed by two rays that share a common endpoint. Each ray is called a side of the angle

cylinder

A cylinder is a solid figure with two parallel circles of the same size at the top and bottom

supplementary angles

If the sum of the measures of two angles is 180° , then they are called supplementary angles

complementary angles

If the sum of the measures of two angles is 90° , then they are called complementary angles

vertex of an angle

When two rays meet to form an angle, the common endpoint is called the vertex of the angle

Chapter 10

Polynomials

Read chapter 10 in the book

Summary

Multiplying a Trinomial by a Binomial: To multiply a trinomial by a binomial, use the: Distributive Property Use the FOIL method for multiplying two binomials. Multiplying Two Binomials: To multiply binomials, use the: Distributive Property Exponential Notation This is read a to the m th power

Key terms

polynomial

A polynomial is a monomial, or two or more monomials, combined by addition or subtraction

trinomial

A trinomial is a polynomial with exactly three terms

binomial

A binomial is a polynomial with exactly two terms

greatest common factor

The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions

scientific notation

A number expressed in scientific notation when it is of the form a × 10 n , where a ≥ 1 and a < 10 , and n is an integer

monomial

A term of the form a x m , where a is a constant and m is a whole number, is called a monomial

zero exponent

If a is a non-zero number, then a 0 = 1 . Any nonzero number raised to the zero power is 1

degree of a term

The degree of a term of a polynomial is the exponent of its variable

Chapter 11

Graphs

Read chapter 11 in the book

Summary

Sign Patterns of the Quadrants Quadrant I Quadrant II Quadrant III Quadrant IV ( x , y ) (+,+) (-,+) (-,-) (+,-) Coordinates of Zero Points with a y- coordinate equal to 0 are on the x- axis, and have coordinates ( a , 0) Points with a x- coordinate equal to 0 are on the y- axis, and have coordinates ( 0, b )

Key terms

origin

The point ( 0 , 0 ) is called the origin. It is the point where the x -axis and y -axis intersect

quadrants

The x -axis and y -axis divide a rectangular coordinate system into four areas, called quadrants

y- coordinate equal to 0

on the x- axis, and have coordinates ( a , 0)

x- coordinate equal to 0

on the y- axis, and have coordinates ( 0, b )

horizontal line

A horizontal line is the graph of an equation that can be written in the form y = b . The line passes through the y- axis at ( 0 , b )

ordered pair

An ordered pair ( x , y ) gives the coordinates of a point in a rectangular coordinate system. The first number is the x -coordinate. The second number is the y -coordinate. ( x…

vertical line

A vertical line is the graph of an equation that can be written in the form x = a . The line passes through the x- axis at ( a , 0 )