EXAMPLE 1 Using the Commutative Property

Slides:

Advertisements

Similar presentations

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

Advertisements

1.2 Apply order of operations

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 5 Write and solve an equation

Solve an equation with variables on both sides

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.

Tell which property is being illustrated.

EXAMPLE 3 Combining Like Terms a. 3x + 4x = (3 + 4)x = 7x b.

Solve a compound inequality with and

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

Taks Objective 2 Properties and attributes of function.

Operations: Add, Subtract, Multiply, Divide

Algebra Part 4 Of Math Survival Guide.

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.

EXAMPLE 2 Rationalize denominators of fractions Simplify

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.

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.

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.

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.

Properties are special qualities of something. Addition and multiplication have special qualities that help you solve problems mentally = MENTAL MATH!!

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.

The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra.

Identify properties of multiplication

The Order of Operations Chapter Evaluate inside grouping symbols ( ), { }, [ ], | |, √ (square root), ─ (fraction bar) 2.Evaluate exponents 3.Multiply.

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.

2-2 The Distributive Property Distributive Property of Multiplication over Addition : Ex. 3(2+6) Multiplication Addition You can distribute a factor to.

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.

1 Math I can create equivalent expressions. Using the Distributive Property.

Sec Math II 1.3.

Music You buy a used guitar for $50. You then pay $10 for each of 5 guitar lessons. The total cost can be found by evaluating the expression 

1.5 Translating Words into Mathematical Symbols

Add and Subtract Rational Expressions

Math 1B Exponent Rules.

EXAMPLE 2 Rationalize denominators of fractions Simplify

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

Knowing your math operation terms

Warm Up Lesson Presentation Lesson Quiz

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

Equivalent Linear Expressions

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

Objectives Use the Commutative, Associative, and Distributive Properties to simplify expressions.

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Solve an equation by combining like terms

Section 1.1 “Expressions and Variables”

Properties in Math.

Mr. Peter Richard, The most profound Math teacher in all of the worlds in this universe and the rest of them will teach you the multiple steps of stepping.

Integers & Absolute Value

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

Objectives Use the Commutative, Associative, and Distributive Properties to simplify expressions.

Presentation transcript:

EXAMPLE 1 Using the Commutative Property Tour Biking 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 a day. Can you complete the trip in 5 days? SOLUTION Write a verbal model to find the total distance you can cycle in 5 days.

Using the Commutative Property EXAMPLE 1 Using the Commutative Property 12 7 5 = Substitute known values. 12 5 7 = Commutative property of multiplication 60 7 = Multiply. 420 = Multiply.

EXAMPLE 1 Using the Commutative Property The unit for the result is miles. days = miles miles hour hours day Because 400 miles is less than the 420 miles you can cycle in 5 days, you can complete the trip in 5 days. Answer

Using the Commutative Property EXAMPLE 2 Using the Commutative Property –54 + 35 – 16 = –54 + 35 + (–16 ) Change subtraction to addition. = –54 + (–16) + 35 Commutative property of addition = –70 + 35 Add –54 and –16. = –35 Add –70 and 35.

GUIDED PRACTICE for Examples 1 and 2 1. What If? Suppose in Example 1 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? SOLUTION Write a verbal model to find the total distance you can cycle in 6 days.

GUIDED PRACTICE for Examples 1 and 2 14 6 6 = 14 6 6 = 84 6 = 504 = 14 6 6 = Substitute known values. 14 6 6 = Commutative property of multiplication 84 6 = Multiply. 504 = Multiply.

GUIDED PRACTICE for Examples 1 and 2 The unit for the result is miles. days = miles miles hour hours day Answer Yes , Because 400 miles is less than the 504 miles you can cycle in 6 days, you can complete the trip in 6 days.

Use the commutative property to evaluate the expression. GUIDED PRACTICE for Examples 1 and 2 Use the commutative property to evaluate the expression. 4 (–9) 25 2. 4 25 (–9) = Commutative property of multiplication 100 (–9) = Multiply 4 and 25. –900 = Multiply.

Use the commutative property to evaluate the expression. GUIDED PRACTICE for Examples 1 and 2 Use the commutative property to evaluate the expression. 3. –13 + 34 –7 = –13 + 34 + (–7) Change subtraction to addition. = –13 + (–7) + 34 Commutative property of addition = –20 + 34 Add –13 and –7. = 14 Add –20 and 34.

Use the commutative property to evaluate the expression. GUIDED PRACTICE for Examples 1 and 2 Use the commutative property to evaluate the expression. 4. 3 7 8 + 4 + 3 7 = + 8 + 4 Commutative property of addition 4 7 3 + + 8 = Associative property of addition 7 + 8 = Add inside grouping symbols. 1 + 8 = Add. = 9

Using the Associative Property EXAMPLE 3 Using the Associative Property 3 5 + 2 = 3 5 + 2 Associative property of addition 5 + 3 = Add fractions. Write as one. 5 1 + 3 = 4 = Add.

Using the Associative Property EXAMPLE 4 Using the Associative Property 5 (11 2) 5 (2 11) = Commutative property of multiplication (5 2) 11 = Associative property of multiplication 10 11 = Multiply inside grouping symbols. 110 = Multiply.

Use properties to evaluate the expression. GUIDED PRACTICE for Examples 3 and 4 Use properties to evaluate the expression. 5. 18 + (–34 + 12) = 18 + (12 + (–34)) Commutative property of addition = (18 + 12) + (–34) Associative property of addition = 30 + (–34) Add inside grouping symbols. = –4 Add.

Use properties to evaluate the expression. GUIDED PRACTICE for Examples 3 and 4 Use properties to evaluate the expression. 4 5 8 + 1 + 4 5 = + 8 + 1 Commutative property of addition 1 5 4 + = + 8 Associative property of addition 5 + 8 = Add inside grouping symbols. 1 + 8 = Add. 9 =

Use properties to evaluate the expression. GUIDED PRACTICE for Examples 3 and 4 Use properties to evaluate the expression. 12 (6 ) 1 12 = 12 6) ( 1 Commutative property of multiplication = 12 6 1 ( ) Associative property of multiplication = 1 6 Multiply inside grouping symbols. = 6 Multiply.

Use properties to evaluate the expression. GUIDED PRACTICE for Examples 3 and 4 Use properties to evaluate the expression. 6 5 (3 ) = 3) ( 5 6 Commutative property of multiplication = ( 5 6 ) 3 Associative property of multiplication = 1 3 Multiply inside grouping symbols. = 3 Multiply.

GUIDED PRACTICE for Examples 3 and 4 Evaluate the expression using mental math. 4 ( 23) 1 4 = 23 –4 ( 50 ) 46 = – 4600 –21 – (–29) = (–6 ) 10 1 ( ) = –6