CHAPTER 9 GEOMETRY OF PLANE FIGURES LESSON 7 TRIANLES AND ANGLE SUMS
LESSON 8 SALES, TAX, AND DISCOUNTS
LESSON 7 SIMPLE INTEREST
LESSON 6 MENTAL MATH: ESTIMATE WITH PERCENTS
LESSON 4 PERCENT RELASHONSHIPS
LESSON 3 FIND A NUMBER WHEN A PERCEENT IS KNOWN
LESSON 2 FIND A PERCENT
CHAPTER 8 LESSON 1 FINDING A PERCENT OF A NUMBER
LESSON 9 FRACTIONS AND PERCENTS
LESSON 8 DECIMAL AND PERCENTS
LESSON 7 SCALE DRAWINGS
LESSON 6 DISTANCE, SPEED, AND TIME
LESSON 3 SOLVE PROPORTIONS
LESSON 2 EQUIVALENT RATIOS
CHAPTER 7 LESSON 1 RATIOS
LESSON 12 EQUATIONS WITH FRACTIONS
LESSON 11 WRITE EXPRESSIONS WITH FRACTIONS
LESSON 10 EQUATIONS WITH MULTIPLICATION AND DIVISION
LESSON 9 EQUATIONS WITH ADDITION & SUBTRACTION
LESSON 8 WRITE MULTIPLICATION AND DIVISON EXPRESSIONS Ex.
LESSON 7 WRITE ADDITION AND SUBTRACTION EXPRESSIONS Ex.
LESSON 5 EVALUATE EXPRESSIONS WITH FRACTIONS Ex.
LESSON 4 USE DISTRIUBUTIVE PROPERTY TO EVALUATE EXPRESSIONS Distributive Property - The property which states that when two addends are multiplied by a factor the product is the same as if each addended was multiplied by the factor and those products were added.
LESSON 3 ORDER OF OPERATIONS P . E . M . D . A . S P- Parenthesis E- Exponent M- Multiplication D- Division A- Addition S- Subtraction
LESSON 2 USE MULTIPLICATION PROPERTIES TO EVALUATE EXPRESSIONS
Associative Property - Changing the grouping of factors does not change their product Commutative Property - Changing the order of factors does not change their product Identity Property - The product of a number and 1 is that number Zero Property - The product of a number and 0 is 0
CHAPTER 6 LESSON 1 USEADDITIONPROPERTIES TO EVALUATE EXPRESSIONS
Commutative Property - The order in which numbers are added does not affect their sum. Associative Property - The way in which numbers are grouped does not affect their sum. Identity Property - The sum of any number and 0 is that number.
Expression: A mathematical sentence with an equal sign. Example: 3+1=4 and 2x + 5 =9 are equations Equation:A number, a variable, or any combination of numbers, variables, operation signs, and grouping symbols. Variables: A letter or symbol that represents a number in an algebraic expression.
LESSON 7 RATIONAL NUMBERS AND COMAPARING AND ORDERING RATIONAL NUMBERS
CHAPTER 5 LESSON 1 INTEGERS LESSON 2 COMPARING AND ORDERING INTEGERS Integers - The set of positive whole numbers and their opposites (negative numbers) and 0. Examples: -3, -2, -1, 0, +1, +2, +3, ...
LESSON 11 METRIC UNITS OF MEASUREMENT
LESSON 10 RECIPROCALS The product of a number and its reciprocal is 1. Examples: 2/3 x 3/2 = 1 7/9 x 9/7 = 1
LESSON 9 DIVIDE MIXED NUMBERS
LESSON 8 DIVIDE WHOLE NUMBERS AND FRACTIONS
LESSON 7 DIVIDING FRACTIONS To find how many times 1/5 goes into 9/10 or 3/5.
LESSON 6 MULTIPLY MIXED FRACTIONS
LESSON 5 MULTIPLY FRACTIONS
LESSON 4 SUBTRACT FRACTIONS AND MIXED NUMBERS WITH UNLIKE DENOMINATORS First, change 4 1/2 to an improper fraction and that will be 9/2. Then, find the common denominator for 9/2 and 3/4 by finding its least common denominator which is 4. Next, by multiplying 2 to 9/2's denominator and numerator you will get 18/4. Subtract those 2 fractions together get the answer, simplify it and then change into a mixed fraction.
LESSON 3 ADDING FRACTIONS AND MIXED NUMBERS WITH UNLIKE DENOMINATORS First, change 2 1/3 to an improper fraction and that will be 7/3. Then, find the common denominator for 7/3 and 1/6 by finding its least common denominator which is 6. Next, by multiplying 2 and 7/3 denominator you will get 6. Multiply 2 to its numerator as well and you will get 14 so, the fraction is now 14/6. Do this step to 1/6 but, multiply the numerator and denoinator by 1. Add those 2 fractions together get the answer, simplify it and then change into a mixed fraction.
LESSON 2 SUBTRACT FRACTIONS AND MIXED NUMBERS WITH LIKE DENOMINATORS Change 5 3/10 and 3 9/10 to an improper fraction. The improper fractions of 5 3/10 and 3 9/10 are 53/10 and 30/10. Subtract both fractions and you will get the answer.
CHAPTER 4 LESSON 1 ADD FRACTIONS AND MIXED NUMBERS WITH LIKE DENOMINATORS Change 4 2/5 and 7 3/5 to an imroper imroper fraction. The improper fractions of 4 2/5 and 7 3/5 are 22/5 and 38/5. Add them together and you will get the answer.
LESSON 11 TERMINATING AND REPEATING DECIMALS Terminating Decimal: A decimal quotient that terminates or stops because the repeating block of digits consists only zeros.
Repeating Decimal: A decimal quotient that comntains a repeating block of digits
LESSON 10 COMPARING DECIMALS, FRACTIONS, AND MIXED NUMBERS To compare decimals, fractions, and mixed numbers, express the numbers in the same form.
LESSON 9 COMPARE AND ORDER FRACTIONS Two fractions have a common denominator if their denominators are same. For example, the fractions 2/4 and 3/4 have a common denominator. The least common denominator (LCD) of 2 fractions is the least common multiple of their denominators
LESSON 8 SIMPLEST FORM A fraction whose numerator and denominator have the number 1 as the only common factor.
LESSON 7 EQUIVALENT FRACTIONS Fractions that show different numbers with the same value Example: 1/2 and 4/8 are equivalent fractions.
LESSON 6 LEAST COMMON MULTIPLE (LCM) The least number that is a multiple of two or more numbers. Example: 12 is the least common multiple of 3 and 4.
LESSON 5 GREATEST COMMON FACTOR (GCF) Definition: The greatest whole number that is a common factor of two or more numbers. It is also called the greatest common divisor. Ex.
LESSON 4 DIVISIBILITY RULES What are divisibility rules? 2. the number must be even 3. the sum of the digits must be a multiple of 3 4. the last two digits must form a number that is a multiple of 4 5 . the number must end with a 0 or 5 6. the number must be divisible by 2 and 3 8. the last 3 digits must form a number that is a multiple of 8 9. the sum of the digits must be a multiple of 9 10. the last digit must be 0 ---------------------------------------------------------------------------- Example: The 196 campers at camp Lake-way play games that require equal groups. For the groups to be equal, 196 must be divisible by the number of campers in each group. Knowing the divisibility rules can help the counselors decide the size of groups possible for the games. The counselors have different games that require 2,3,4,5,6,9 or 10 campers on each tea. Which games can they plan to play?
LESSON 3 PRIME FACTORIZATION A prime factorization expresses a composite number as a product of prime factors. Example: The prime factorization if 12 is 2 x 2 x 3. The factors in a prime factorization often are written in order from least to greatest. Example: Find the prime factorization of 45
Step 3: Rewrite the prime factorization using exponents. 3 x 3 x 5 = 3^2 x 5
LESSON 2 EXPONENTS Many numbers can be written as the product as repeated factors. For example, 16 = 2 x 2 x 2 x 2 When a factor is repeated, the product can be written using exponents. 16 = 24 2^4 is read as " two to the fourth". The exponent (4) tells how may time the base (2) is used as a factor. Example: Use exponents to write the expression 2 x 2 x 2 x3 x3 Step 1: Count the number of times each number (base) is used as a factor. 2 x 2 x 2 3 x 3 used 3 times used 2 times Step 2: Write the exponent for each base 2 x 2 x 2 x 3 x 3 = 2^3 x 3^2 Solution: Another way to write 2 x 2 x 2 x 3 x 3 is 2^3 x 3^2
CHAPTER 3 LESSON 1 FACTORS AND PRIME NUMBERS A prime number is a whole number with two factors 1 and the number itself. The first prime numbers are 2,3,5,7, and 11. A composite number has more than 2 factors. The number 1 is neither prime nor composite. Example: A museum has 100 coins from ancient greece. How many ways could the coins be displayed in equal rows? Knowing whether 100 is a prime or composite number can halp you answer the question. I can use division to find the factors of 100 with each number starting with 1.