Using a Commutative Property You are going on a 400 mile bike trip. You plan to cycle at an average speed of 12 miles per hour for 7 hours per day. Can.

Slides:

Advertisements

Similar presentations

EXAMPLE 1 Standardized Test Practice SOLUTION Substitute several values of h into the equation C = h and solve for C.Then identify the table that.

Advertisements

Example 1 Multiplying Integers a. 3 () 4 – Different signs, so product is negative. = 12 – b. () 3 – 6 – Same sign, so product is positive. = 18 c. ()

Divide. Evaluate power – 3 = – 3 EXAMPLE – 3 = 3 2 – – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.

Evaluate expressions with grouping symbols

Evaluate the expression for the given value(s) of the variable(s).

Using a Power EXAMPLE 3 Cliff Height A stone falls over the edge of a cliff next to a waterfall. The stone hits the water 5 seconds later. How tall is.

EXAMPLE 1 Multiplying Integers

EXAMPLE 5 Write and solve an equation

Solving Multiplication and Division Equations. EXAMPLE 1 Solving a Multiplication Equation Solve the equation 3x = x = 15 Check 3x = 45 3 (15)

EXAMPLE 1 Using a Variable Expression Hot Air Balloons You are riding in a hot air balloon. After traveling 5 miles, the balloon speed changes to 6 miles.

EXAMPLE 4 Writing and Evaluating an Expression Heart Rate a. Use n to write an expression for heart rate in beats per minute. b. After exercising, you.

Tell which property is being illustrated.

EXAMPLE 1 a. –5(–7) = 35 b. –8(2) = –16 c. –12(0) = 0

EXAMPLE 3 Using the Associative Property = = Associative property of addition Add fractions. Write as one. 5 5 Add. 4=

Standardized Test Practice

Standardized Test Practice

EXAMPLE 2 Evaluate exponential expressions a. 6 – Product of a power property = 6 0 Add exponents. = 1 Definition of zero exponent = 6 –

EXAMPLE 1 Evaluate powers a. (–5) 4 b. –5 4 = (–5) (–5) (–5) (–5)= 625 = –( )= –625.

Using Grouping Symbols

Operations: Add, Subtract, Multiply, Divide

Algebra Part 4 Of Math Survival Guide.

Students will make Connections to Algebra  Variable:  A letter used to represent a range of numbers.

EXAMPLE 1 Use a formula High-speed Train The Acela train travels between Boston and Washington, a distance of 457 miles. The trip takes 6.5 hours. What.

EXAMPLE 1 Use a formula High-speed Train The Acela train travels between Boston and Washington, a distance of 457 miles. The trip takes 6.5 hours. What.

Evaluate numerical expressions

Order of Operations Also known to as PEMDAS. EXAMPLE 1 Following Order of Operations Music You buy a used guitar for $50. You then pay $10 for each of.

EXAMPLE 1 Following Order of Operations Music You buy a used guitar for $50. You then pay $10 for each of five guitar lessons. The total cost can be found.

3-2 HW: Pg #4-34e, 38, 40, ) B 47.) C.

EXAMPLE 2 Rationalize denominators of fractions Simplify

3.1 Solving Equations Algebra I.

Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations What are the steps for solving multi-step equations? What are the steps for solving multi-step.

Divide. Evaluate power – 3 = – 3 EXAMPLE – 3 = 3 2 – – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.

Read a problem and make a plan EXAMPLE 1 Running You run in a city where the short blocks on north-south streets are 0.1 mile long. The long blocks on.

Evaluating a Variable Expression To evaluate a variable expression:

Find the sum or difference. Then simplify if possible.

Divide. Evaluate power – 3 = – 3 EXAMPLE – 3 = 3 2 – – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.

Do Now 9/13/10 Take out HW from Wednesday. Take out HW from Wednesday. Text p , #2-32 evenText p , #2-32 even Copy HW in your planner. Copy.

EXAMPLE 1 Using the Commutative Property SOLUTION Write a verbal model to find the total distance you can cycle in 5 days. Tour Biking You are going on.

Solving Linear Systems Using Linear Combinations There are two methods of solving a system of equations algebraically: Elimination (Linear Combinations)

Evaluating Algebraic Expressions 3-3Solving Multi-Step Equations Extension of AF4.1 Solve two-step linear equations in one variable over the rational numbers.

Using Properties of Addition Tell whether the commutative or associative property of addition allows you to rewrite the problem as shown. EXAMPLE 4 Explain.

KAYAKING EXAMPLE 4 Write and solve a linear system During a kayaking trip, a kayaker travels 12 miles upstream (against the current) and 12 miles downstream.

EXAMPLE 4 Multiplying Numbers in Scientific Notation Find the product ( ) ( ). = ( ) ( ) = =

1. x = x = x = x = x = x = x = x = x = x = x = x = 4 Story Problems.

Identify properties of multiplication

= 31 = – 31 Find the difference. EXAMPLE 1 Subtract real numbers a. – 12 – 19 b. 18 – (–7) = – 12 + ( – 19) =

EXAMPLE 1 Subtracting Integers –56 – (–9) = – = –47 –14 – 21 = –14 + (–21) = –35 Add the opposite of –9. Add. Add the opposite of 21. Add. a. –56.

Example 1 Multiplying Fractions a. 5 2 – 3 2 – Use rule for multiplying fractions. = 2 – () 2 – 5 3 Use rule for multiplying fractions. = – 5 Evaluate.

Multiply one equation, then add

EXAMPLE 1 Using a Variable Expression Hot Air Balloons You are riding in a hot air balloon. After traveling 5 miles, the balloon speed changes to 6 miles.

Example 2 Writing an Algebraic Expression You are riding in a hot air balloon. After traveling 5 miles, the balloon speed changes to 6 miles per hour.

Order of Operations and the Distributive Property COURSE 2 LESSON 1-9 Use the Distributive Property to find 7(52). What you think 52 is Finding.

Find the product (3  10 3 ) (7  10 5 ). Write the result in scientific notation. Exponents and Multiplication COURSE 3 LESSON 7-2 (3  10 3 ) (7  10.

Integers: One of the positive or negative numbers I,2,3 Ex: 2+(-6)=-4.

Add and Subtract Rational Expressions

EXAMPLE 1 Using the Commutative Property

EXAMPLE 2 Rationalize denominators of fractions Simplify

Algebra 1 Notes: Lesson 1-6: Commutative and Associative Properties

Add and subtract complex numbers

EXAMPLE 1 Evaluate powers (–5)4 = (–5) (–5) (–5) (–5) = 625 –54 = –( )

Multiplication Properties of Exponents 7-3

Warm Up Write each expression using an exponent • 2 • 2

Equivalent Linear Expressions

Properties of Numbers Use mental math to simplify –2 • 13 • 5.

Properties in Math.

Divide the number in C by 10.

Warm Up Solve. 1. 3x = 102 = z – 100 = 21 w = 98.6 x = 34 y 15

Warm Up Write each expression using an exponent • 2 • 2

Multiplying Decimals.

Presentation transcript:

Using a Commutative Property You are going on a 400 mile bike trip. You plan to cycle at an average speed of 12 miles per hour for 7 hours per day. Can you complete the trip in 5 days? TOUR BIKING Example 1 SOLUTION Write a verbal model to find the total distance you can cycle in 5 days.

Using a Commutative Property Example = Substitute known values = Commutative property of multiplication 607 = Multiply 12 and = Multiply 60 and 7. ANSWER Because 400 miles is less than the 420 miles you can cycle in 5 days, you can complete the trip in 5 days.

Using a Commutative Property Example – 5416– Change subtraction to addition. = () – 54– Commutative property of addition = – () – Add 54 and 16. = – –– Add 70 and 45. = – 25 –

Guided Practice 1. for Examples 1 and 2 ANSWER yes Use a commutative property to evaluate the expression () –9 ANSWER – 900 WHAT IF? In Example 1, suppose you only want to bike for 6 hours a day at an average speed of 14 miles per hour. Can you complete the trip in 6 days?

Guided Practice for Examples 1 and 2 ANSWER 14 Use a commutative property to evaluate the expression – 137 – – ANSWER 54