CHAPTER 1B: : Foundations for Algebra

Transcription

1 CHAPTER B: : Foundations for Algebra 0-: Rounding and Estimating Objective: Round numbers. Rounding: To round to a given place value, do the following Rounding Numbers Round each number to the given place value. Example A: 857,2 to the nearest hundred Example B: 0.79 to the nearest tenth Assignment: 0- (Pg Z) - all Ch B Pg.

2 0-0: Equivalent Fractions Objectives: Write equivalent fractions Write fractions in simplest form. Equivalent fractions: For any fraction, an equivalent fraction can be found by either multiplying or dividing both the numerator and denominator by the same whole number. Finding Equivalent Fractions For each fraction, write two equivalent fractions. Example A: 8 a: 00 B: b: 0 Simplest form of a fraction: You can use the GCF of the numerator and the denominator to write a fraction in simplest form. Writing Fractions in Simplest Form Write each fraction in simplest form. 8 Example 2A: 56 2a: B: 0 2 2b: 6 Assignment: 0-0 (Pg Z2) 2-2 even Ch B Pg. 2

3 0-: Decimals, Fractions, and Percents Objectives: Write fractions as decimals and percents. Write decimals and percents as fractions. Many numbers can be written as decimals, fractions, or percents. The table below show three common fraction and their equivalent decimals and percents. Fraction Decimal Percent Picture % % % Terminating Decimal: Repeating Decimal: Writing Fractions as Decimals Write each fraction as a decimal. Example A: 8 Method : a: 2 7 Method : Method 2: Method 2: B: 6 5 Method : Method 2: Tenths Hundredths Thousandths 0. = = = 000 How do we get 0 0. =? Ch B Pg.

4 Writing Terminating Decimals as Fractions Write each decimal as a fraction in simplest form. Example 2A: 0.2 2a: 0.7 2B: 0.8 2b: C: c: Writing Repeating Decimals as Fractions Write each repeating decimal as a fraction in simplest form. Example A: Identify how many digits repeat 2. Divide by 9 s. Write in simplest form a: 0. 8 b: 0. 2 B: 0. 5 c: 0. 5 C: 0. 8 To write a decimal as a percent, move the decimal point two places to the right To write a percent as a decimal, move the decimal point two places to the left. Changing Between Decimals and Percents Example A: Write 0. as a percent B: Write 9% as a decimal Assignment: 0- (Pg Z27) 2-28 even Ch B Pg. a: Write 0.28 as a percent b: Write 75% as a decimal

5 Sec -5: Square Roots and Real Numbers Objectives: Evaluate expressions containing square roots. Classify numbers within the real number system. Square root: The operations of squaring and finding a are inverse operations. The radical symbol, is used to represent square roots. Positive real numbers have two square roots. = 2 = 6 6 = ( )( ) = 6-6 = The nonnegative square root is represented by. The negative square root is represented by. A Perfect square: Finding Square Roots of Perfect Squares Find each square root. Example A: 6 a: B: 9 b: 25 C: 25 8 The square roots of many numbers like 5, are not whole numbers. A calculator can approximate the value of 5 as Without a calculator, you can use square roots of perfect squares to help estimate the square roots of other numbers. Ch. B Pg.5

6 Problem Solving Application Example 2: As part of her art project, Shonda will need to make a square covered in glitter. Her tube of glitter covers square inches. What is the greatest side length Shonda s square can have? Understand the problem The answer will be List the important information: 2 Make a Plan Solve Look Back Natural numbers: Whole numbers: Integers: Rational numbers: Terminating decimals: Repeating decimals: Irrational numbers: Real Numbers: Ch. B Pg.6

7 Start Here Look at the decimal representation of the # Neither? Irrational Term Dec? Rep Dec? Rational Yes Yes Rational Integer? Whole? Natural? No No No Classifying Real Numbers Write all classifications that apply to each real number. Example A: -2 a: 7 9 b: -2 B: 5 c: 0 Assignment: Sec -5 (Pg 5),,, all, 56, 59 Ch. B Pg.7

8 Sec -6: Order of Operations Objectives: Use the order of operations to simplify expressions. When a numerical or algebraic expression contains more than one operation symbol, the Order of Operations: First: Second: Third: Fourth: Order of Operations Perform operations inside grouping symbols. Evaluate powers. Perform multiplication and division from left to right. Perform addition and subtraction from left to right. Grouping symbols include parentheses ( ), brackets [ ], and braces { }. If an expression contains more than one set of grouping symbols, evaluate the expression from the innermost set first. Helpful Hint: P E M D A S P E M D A S Translating from Algebra to Words Simplify each expression Example A: a: 8 2 B: b: c: -20 [-2( + )] Ch. B Pg.8

9 Evaluating Algebraic Expressions Evaluate the expression for the given value of x. Example 2A: 0 x 6 for x = 2a: + x 2 for x = 2 2B: 2 (x + ) for x = 2 2b: (x 22) (2 + 6) for x = 6 Fraction bars, radical symbols, and absolute-value symbols can also be used as grouping symbols. Remember that a fraction bar indicates division. Simplifying Expressions with Other Grouping symbols Simplify. Example A: 2( ) ( 8) a: ( 2 ) 2 b: 7 B: c: 50 Remember: Look for words that imply mathematical operations Difference Subtract Sum Add Product Multiply Quotient Divide Assignment: Sec -6 (Pg ), 2, 5, 8,,,, 7, 2-8,, 2-6, 6, 66, 8, 8, 85, 87, 88 Ch. B Pg.9

10 Sec -7: Simplifying Expressions Objectives: Use the Commutative, Associative, and Distributive Properties to simplify expressions. Combine like terms. The Commutative and Associative Properties of Addition and Multiplication allow you to rearrange an expression to simplify it. Using the Commutative and Associative Properties Simplify Example A: ( 5)( ) 2 a: b: B: c: Example 2: skip Terms: Like terms: Ch. B Pg.0

11 Label like terms and constants x x + 2 Coefficient: Label the coefficients x 2 + x ***Combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same. *** Combining Like Terms Simplify the expression by combing like terms. Example A: 72p 25p a: 6p + 8p B: x + x b: -20t 8.5t 2 C: 0.5m + 2.5n c: m 2 + m Simplifying Algebraic Expressions Simplify. Justify each step. Example : x +(2 + x) Procedure. x + (2 + x) 2. x + (2) + (x). x x. x + x (x + x) x + 8 Justification a: 6(x ) + 9 Procedure. 6(x ) b: 2x 5x + a + x Procedure. 2x 5x + a + x 2.. Justification Justification Assignment: Sec -7 (Pg 9), 2, 5,, 7, 20, 2,, 26, 27, -,, Ch. B Pg.