Chapter 10 Lesson 10-1 SWBAT use the distributive property to simplify algebraic expression
Bellwork • Grab a textbook • Turn to page 467 • Do the EVEN PROBLEMS ONLY on the Getting Started quiz on this page. • This is to help you remember skills you will need for Chapter 10 • Turn this into Ms Swartz when you are finished
Today and Tomorrow: lesson 10-1 • What are we learning: How to simplify algebraic expressions (pop quiz: what’s the difference between an equation and an expression?) using the Distributive Property (Can you remember this from way back when?). • How will we learn the material: Listen and watch the powerpoint, do the your turn problems, ask questions, do the homework. USE THE HOMEWORK TONIGHT AND THE SGI workbook to help you learn the material. • How will we know we have learned the material: When we can correctly simplify algebraic exressions and use vocabulary words correctly • How will I use this information: In our high school algebra class next year. This is prerequisite knowledge for high school.
Lesson 1 Contents Example 1Write Equivalent Expressions Example 2Write Equivalent Expressions Example 3Write Expressions with Subtraction Example 4Write Expressions with Subtraction Example 5Identify Parts of an Expression Example 6Simplify Algebraic Expressions Example 7Simplify Algebraic Expressions Example 8Simplify Algebraic Expressions Example 9Translate Phrases into Expressions
Distributive Property • What does distribute mean? • Example is 2(2+1) = 2(2)+2(1) • Distributive property says that if you have a number multiplied by something in parentheses, you can multiply everything in that parentheses by that number. • a(b+c) = a(b)+a(c) • We can use the distributive property to rewrite expression, creating equivalent expressions. • Equivalent expressions look different, but are the same value
Use the Distributive Property to rewrite . Example 1-1a We want to write an equivalent expression for 3(x+5). Simplify. Answer: 3x+15 is an equivalent expression to 3(x+5)
Use the Distributive Property to rewrite Example 1-1b Answer:
Use the Distributive Property to rewrite Example 1-2a It doesn’t matter what side of the parentheses the number is on. Simplify. Answer:
Use the Distributive Property to rewrite Example 1-2b Answer:
IMPORTANT: Remember from chapter 1that when we are subtracting, we change it to addition, and add the additive inverse. Use the Distributive Property to rewrite Rewrite Example 1-3a Distributive Property We always want the number in front of the variable Simplify. Definition of subtraction Answer: 9q-27 and (q-3)9 are ___________ ______________.
Use the Distributive Property to rewrite Example 1-3b Answer:
Use the Distributive Property to rewrite Example 1-4a REMEMBER: Your rules for multiplying and dividing integers. Rewrite Distributive Property A neg times a neg = a pos, remember? Simplify. Answer:
Use the Distributive Property to rewrite Example 1-4b Answer:
Parts of an algebraic expression Example 2x+4 • Term: The parts of an expression separated by our operation signs. 2x and 4 our are terms • Coefficient: The number part of a term with a variable. 2 is our coefficient • Variable: x is our variable • Constant: A term without a variable. 4 is our constant. Its constant because it doesn’t have a variable that could change.
An algebraic expression labeled 2x is a term 2 is a coefficient X is a variable 3 is a term 3 is a constant 4y is a term 4 is a coefficient y is a variable
Identify the terms, like terms, coefficients, and constants in Answer: The like terms areThe coefficients areThe constant is –5. Example 1-5a Definition of subtraction Identity Property;
Identify the terms, like terms, coefficients, and constants in Answer: The terms are The like terms areThe coefficients areThe constant is –2. Example 1-5b
END OF DAY 1 • Homework: vocabulary sheet and SGI lesson 10-1, numbers 1- 4 only. Read the examples in the SGI.
Review • 2 expression written differently but with the same ultimate value are ____________ ___________________. • The parts of an expression divided by our operations signs are ___________. For example in 2x+3 these are 2x and 3. • The number in front of a variable is the _________________. For example in 2x+3, this is 2. • ___________ ____________ have the same variable. • A term without a variable is a _________________. • An algebraic expression is in _________________ __________________ if there are no terms in parentheses.
DAY 2! • Remember how we used the distributive property yesterday and distributived out what was outside of the parentheses. Today we will sorta do the opposite of that. • Today we will be simplifying expressions. This means we will be using the distributive property to combine like terms (terms with the same variable) to produce expressions in simplest form.
Example 1-6a Before we were distributing, now we are pulling out, much like when we were factoring out (jimmy neutroning), we are pulling out what is common for each term. Simplify 6n – n. 6n and n are like terms. Identity Property; Distributive Property Each term has a n in common Simplify. Answer:
Example 1-6b Simplify 7n n. Answer:
are like terms. Example 1-7a Simplify 5s 3 – 12s. Commutative Property Distributive Property Answer:
Example 1-7b Simplify 6s 2 – 10s. Answer:
are like terms. –5 and 2 are also like terms. Example 1-8a Simplify 8z z – 5 – 9z 2. Definition of subtraction One thing I like to do is change all my subtractions to plus a negative number. Commutative Property Distributive Property Simplify. Answer: –3
Example 1-8b Simplify 6z z – 2 – 8z 2. Answer: –z
Example 1-9a THEATER Tickets for the school play cost $5 for adults and $3 for children. A family has the same number of adults as children. Write an expression in simplest form that represents the total amount of money spent on tickets. If x represents the number of adult tickets, then x also represents the number of children tickets. To find the total amount spent, multiply the cost of each ticket by the number of tickets purchased. Then add the expressions.
Example 1-9a Distributive Property Simplify. Answer: The expression $8x represents the total amount of money spent on tickets, where x is the number of adults or children.
Example 1-9b MUSEUM Tickets for the museum cost $10 for adults and $7.50 for children. A group of people have the same number of adults as children. Write an expression in simplest form that represents the total amount of money spent on tickets to the museum. Answer: $17.50x
Classwork/homework • Page 472 in textbook 17-49 odd.