MrE's Algebra Blog

Algebra 1: Chapter 1 Benchmark

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Algebra 1a: Chapter 1, Lesson 6, page 29.

Writing Expressions

“Many problems can be solved by translating data given with words into algebraic expressions. To do this, you must know which phrases suggest each of the operations (addition, subtraction, multiplication and division).”

There are key words in this lesson and my note card looks like:

• Add – More than; sum of; greater than; added to
• Subtract – Less than;, fewer than; subtracted from; minus; difference of
• Multiplication – Times; product of; multiplied by; “double” means 2 times; half of
• Division – Divided by; quotient of

Whenever you see these type of key words, you can figure out what order operation is being requested!

Two of tonight’s homework problems solved by MrE are here! Just click it!!

Algebra 1: Chapter 1 Review

Thursday, EVEN problems for classwork and ODD problems for homework. Make sure your notes are ready for tomorrow’s Chapter 1 BENCHMARK TEST! Bring your calculator!!

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Algebra 1a: Chapter 1, Lesson 6, page 29.

Writing Expressions

“Many problems can be solved by translating data given with words into algebraic expressions. To do this, you must know which phrases suggest each of the operations (addition, subtraction, multiplication and division).”

There are key words in this lesson and my note card looks like:

• Add – More than; sum of; greater than; added to
• Subtract – Less than;, fewer than; subtracted from; minus; difference of
• Multiplication – Times; product of; multiplied by; “double” means 2 times; half of
• Division – Divided by; quotient of

Whenever you see these type of key words, you can figure out what order operation is being requested!

Two of tonight’s homework problems solved by MrE are here! Just click it!!

Algebra: Chapter 1, Lesson 10, page 44

Reasoning Strategies – or Try, Test and Revise

1. UNDERSTAND the Problem
2. Develop and carry out a PLAN
3. Find the ANSWER and CHECK

Strategies look like:

• Draw a diagram
• Make an Organized list
• Look for a Pattern
• Try, Test and Revise
• Use Logical Reasoning
• Simplify the Problem
• Write an Equation
• Make a Table
• Work Backwards

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Algebra 1a: Chapter 1, Lesson 5, page 24 (DAY 3).

Distributive Property of Mutiplication over Addition

The distributive property of mulitplication over addition is written as `a(b+c)=ab+ac`. For example:

`3(x+2)=3x+6`
The opposite of distribution is factoring where we go backward. For example:

`3x+3y=3(x+y)`

In an expression like `6s+6t+6w`, the `6s`, `6t` and `6w` are called terms. Like terms are terms with like variables THAT HAVE THE SAME EXPONENT!

You can collect like terms, for example:

`6y^2+2y^2` is the same as `8y^2`

and `4x^3+5x^3` is the same as `9x^3`

Try these 2 links from purplemath.com, this one for distribution and this one for factoring.

Two of tonight’s homework problems solved by MrE are here! Just click it!!

Algebra: Chapter 1, Lesson 9, page 40.

Using Formulas

A formula is an equation that shows a relationship between 2 or more variables. The formula for the area of a rectangle is `a = l⋅w`. Given the length and width of an object, you can easily find the area. Be careful, however, and make sure that you are using consistent UNITS in the formula. Do not mix up seconds with minutes or hours or inches with feet or miles. The units must ALWAYS be consistent.

Don’t forget too to add the units to the answer!

Two of tonight’s homework problems solved by MrE are here! Just click it!

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Algebra 1a: Chapter 1, Lesson 5, page 24.

Distributive Property of Mutiplication over Addition

The distributive property of mulitplication over addition is written as `a(b+c)=ab+ac`. For example:

`3(x+2)=3x+6`
The opposite of distribution is factoring where we go backward. For example:

`3x+3y=3(x+y)`

In an expression like `6s+6t+6w`, the `6s`, `6t` and `6w` are called terms. Like terms are terms with like variables THAT HAVE THE SAME EXPONENT!

You can collect like terms, for example:

`6y^2+2y^2` is the same as `8y^2`

and `4x^3+5x^3` is the same as `9x^3`

Try these 2 links from purplemath.com, this one for distribution and this one for factoring.

Two of tonight’s homework problems solved by MrE are here! Just click it!!

Algebra 1: Chapter 1, Lesson 9, page 40 (we did lesson 9 instead of 8).

Using Formulas

A formula is an equation that shows a relationship between 2 or more variables. The formula for the area of a rectangle is:

Area `a = l ⋅ w`

Given the length and width of an object, you can easily find the area.

Another formula as we talked about today:

`d=r ⋅ t` (DIRT problems) with d = distance, r = rate (or speed) and t = time.

Be careful, however, and make sure that you are using consistent UNITS in the formula. Do not mix up seconds with minutes or hours or inches with feet or miles. The units must ALWAYS be consistent.

Don’t forget too to add the units to the answer!

Two of tonight’s homework problems solved by MrE are here! Just click it!

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Algebra 1a: Chapter 1, Lesson 5, page 24.

Distributive Property of Mutiplication over Addition

The distributive property of mulitplication over addition is written as `a(b+c)=ab+ac`. For example:

`3(x+2)=3x+6`
The opposite of distribution is factoring where we go backward. For example:

`3x+3y=3(x+y)`

In an expression like `6s+6t+6w`, the `6s`, `6t` and `6w` are called terms. Like terms are terms with like variables THAT HAVE THE SAME EXPONENT!

You can collect like terms, for example:

`6y^2+2y^2` is the same as `8y^2`

and `4x^3+5x^3` is the same as `9x^3`

Try these 2 links from purplemath.com, this one for distribution and this one for factoring.

Two of tonight’s homework problems solved by MrE are here! Just click it!!

Algebra 1: Chapter 1, Lesson 7, page 33.

Solving Equations, An Introduction

An EQUATION is a mathematical sentence that uses the equal sign `=` to state that 2 expressions represent the same number or are equivalent. An equation that contains at least 1 variable is called an OPEN SENTENCE.

The set of numbers from which you can select replacements for the variable is called the REPLACEMENT SET, usually noted with squiggly brackets `{2, 5, 12}`. A replacement for a variable that makes an equation true is called the SOLUTION. To SOLVE and equation means to find all of its solutions. The collection of all the solutions is called the SOLUTION SET, usually contained in the { brackets}.

2 equations are EQUIVALENT if one can be obtained from the other by a sequence of the following steps. You can:

• add the same number to both sides of an equation
• subtract the same number from both sides of an equation
• multiply both sides of an equation by the same number
• divide both sides of an equation by the same number

Equivalent equations have the same solutions set.

Two of tonight’s homework problems solved by MrE are here! Just click it!!

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Algebra 1a: Chapter 1, Lesson 4, page 19.

The Associative Property

We discussed the use of the Associative property by re-grouping terms in paranthesis. We also used both commutative and associative properties together to help simplify expressions for evaluation.
We looked for patterns in expressions again to help speed up our mental math computation speed.

Remember, the associative property ONLY holds true for addition and multiplication. Just like the commutative property, it doesn’t work for subtraction or division.

For any numbers a, b, and c, we have in equation forms for adding and multiplication:
`a+(b+c)=(a+b)+c and a⋅(b⋅c)=(a⋅b)⋅c`

Two of tonight’s homework problems solved by MrE are here! Just click it!!

Algebra 1: Chapter 1, Lesson 6, page 29.

Writing Expressions

“Many problems can be solved by translating data given with words into algebraic expressions. To do this, you must know which phrases suggest each of the operations (addition, subtraction, multiplication and division).”

There are key words in this lesson and my note card looks like:

• Add – More than; sum of; greater than; added to
• Subtract – Less than;, fewer than; subtracted from; minus; difference of
• Multiplication – Times; product of; multiplied by; “double” means 2 times; half of
• Division – Divided by; quotient of

Whenever you see these type of key words, you can figure out what order operation is being requested!

Two of tonight’s homework problems solved by MrE are here! Just click it!!

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Algebra 1a: Chapter 1, Lesson 4, page 19.

The Associative Property

We discussed the use of the Associative property by re-grouping terms in paranthesis. We also used both commutative and associative properties together to help simplify expressions for evaluation.
We looked for patterns in expressions again to help speed up our mental math computation speed.

Remember, the associative property ONLY holds true for addition and multiplication. Just like the commutative property, it doesn’t work for subtraction or division.

For any numbers a, b, and c, we have in equation forms for adding and multiplication:
`a+(b+c)=(a+b)+c and a⋅(b⋅c)=(a⋅b)⋅c`

Two of tonight’s homework problems solved by MrE are here! Just click it!!

Algebra 1: Chapter 1, Lesson 5, page 24.

Distributive Property of Mutiplication over Addition

The distributive property of mulitplication over addition is written as `a(b+c)=ab+ac`. For example:

`3(x+2)=3x+6`
The opposite of distribution is factoring where we go backward. For example:

`3x+3y=3(x+y)`

In an expression like `6s+6t+6w`, the `6s`, `6t` and `6w` are called terms. Like terms are terms with like variables THAT HAVE THE SAME EXPONENT!

You can collect like terms, for example:

`6y^2+2y^2` is the same as `8y^2`

and `4x^3+5x^3` is the same as `9x^3`

Try these 2 links from purplemath.com, this one for distribution and this one for factoring.

Two of tonight’s homework problems solved by MrE are here! Just click it!!

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Algebra 1a: Chapter 1, Lesson 3, page 15.

Exponential Notation

A product in which the factors are the same is called a power. We can write `2⋅2⋅2⋅2` as `2^4`. The number 4 is called the exponent and the 2 is called the base. The exponent tells how many times the base is used as a factor. When an expression is written with exponents, we say the expression is written using exponential notation.

Remember, anything to the zero power is = 1, `z^0=1` or `4^0=1` as well. Anything raised to the 1 power is just the number, `y^1=y` and `101^1=101`.

Don’t forget PEMDAS too with the exponents being the second operation to be performed.

I like to use a site called purplemath.com. They have some great explanations about our lessons. See these explanations on exponents too!

Two of tonight’s homework problems solved by MrE are here! Just click it!!

Algebra 1: Chapter 1, Lesson 4, page 19.

The Associative Property

QUIZ #1 ON TUESDAY, MAKE SURE THAT YOUR NOTES AND CALCULATOR ARE WITH YOU! IT IS WORTH 100 POINTS!

We discussed the use of the Associative property by re-grouping terms in paranthesis. We also used both commutative and associative properties together to help simplify expressions for evaluation.
We looked for patterns in expressions again to help speed up our mental math computation speed.

Remember, the associative property ONLY holds true for addition and multiplication. Just like the commutative property, it doesn’t work for subtraction or division.

For any numbers a, b, and c, we have in equation forms for adding and multiplication:
`a+(b+c)=(a+b)+c and a⋅(b⋅c)=(a⋅b)⋅c`

Two of tonight’s homework problems solved by MrE are here! Just click it!!

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Algebra 1a: Chapter 1, Lesson 2, page 9.

The Commutative and Identity Properties

Commutative property is only for addition and multiplication.

`x+5=5+x`

`5*y=y*5`

Remember the identify properties of addition (0) and multiplication (1).

Anything to the 1st power is the number and anything to the 0 power is always = 1.

`z^1=z` and `z^0=1`

To form equivalent expressions, multiply the expression by `1/1` or variable/variable, like `y/y`. For example, convert `z/2` to an equivalent expression using `1/1` or `y/y`. To do this we have:

`z/2=z/2⋅y/y=zy/(2y)`

We can simplify algebraic expressions using the identity property for multiplication. For example, simplify `(xy)/(3y)`

`(xy)/(3y)=(x⋅y)/(3⋅y)=(x/3)⋅(y/y)=x/3`

Don’t forget, please put your first and last name on homework pages and make sure that I can read it. Show all work as well!!

Here is a link to tonight’s homework on Chapter 1, Lesson 2. There are 2 solutions provided. Remember, you need to have Quicktime for either the PC or Mac installed on your computer!

Algebra 1: Chapter 1, Lesson 3, page 15.

Exponential Notation

A product in which the factors are the same is called a power. We can write `2⋅2⋅2⋅2` as `2^4`. The number 4 is called the exponent and the 2 is called the base. The exponent tells how many times the base is used as a factor. When an expression is written with exponents, we say the expression is written using exponential notation.

Remember, anything to the zero power is = 1, `z^0=1` or `4^0=1` as well. Anything raised to the 1 power is just the number, `y^1=y` and `101^1=101`.

Don’t forget PEMDAS too with the exponents being the second operation to be performed.

I like to use a site called purplemath.com. They have some great explanations about our lessons. See these explanations on exponents too!

Two of tonight’s homework problems solved by MrE are here! Just click it!!

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Algebra 1a: Chapter 1, Lesson 2, page 9.

The Commutative and Identity Properties

Commutative property is only for addition and multiplication.

`x+5=5+x`

`5*y=y*5`

Remember the identify properties of addition (0) and multiplication (1).

Anything to the 1st power is the number and anything to the 0 power is always = 1.

`z^1=z` and `z^0=1`

To form equivalent expressions, multiply the expression by `1/1` or variable/variable, like `y/y`. For example, convert `z/2` to an equivalent expression using `1/1` or `y/y`. To do this we have:

`z/2=z/2⋅y/y=zy/(2y)`

We can simplify algebraic expressions using the identity property for multiplication. For example, simplify `(xy)/(3y)`

`(xy)/(3y)=(x⋅y)/(3⋅y)=(x/3)⋅(y/y)=x/3`

Don’t forget, please put your first and last name on homework pages and make sure that I can read it. Show all work as well!!

Here is a link to tonight’s homework on Chapter 1, Lesson 2. There are 2 solutions provided. Remember, you need to have Quicktime for either the PC or Mac installed on your computer!