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April 10 ORDER of OPERATIONS Example: 24

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April 10 ORDER of OPERATIONS Example: 24 ALGEBRA 2 ASSIGNMENTS Name __________________________________ April 6 – April 10 Teacher_________________________________ Monday: Read the following description of Order of Operations. You can also search online for “Order of operations in math” and read an explanation or watch a video describing how to apply the order of operations. ORDER OF OPERATIONS The steps we use to solve any mathematical expression are: 1. Simplify all of the parentheses. 2. Simplify all exponents. 3. Simplify all multiplication and division working from left to right. 4. Simplify all addition and subtraction working from left to right. By following this order, you can solve the problem and get the correct solution. A shortcut to help remember these steps is called PEMDAS. It stands for: P - Parentheses E – Exponents (powers) M - Multiplication D - Division A – Addition S - Subtract Example: 24 - (4 + 2)2 ÷ 4 × 2 24 – 62 ÷ 4 × 2 24 – 36 ÷ 4 × 2 24 – 9 × 2 24 – 18 = 6 Tuesday: List 3 vocabulary words from this section. 1. 2. 3. Wednesday: Give a definition, example or description for each of the words that you listed on Tuesday. 1. 2. 3. Thursday: Simplify the following using the order of operations. 1. 8 × 3 + 70 ÷ 7 - 7 2. 36 ÷ 9 + 48 - 10 ÷ 2 3. 18 ÷ 6 × (4 - 3) + 6 4. 8 × 3 + 40 ÷ 5 – 8 5. 12 ÷ (3 + 1) - 10 ÷ 5 6. 52 - (4 + 1)2 ÷ 5 × 1 7. 8 + 6 - (4)2 ÷ 4 × 2 8. 12 + 8 × 2 - (10 ÷ 2)2 9. (4)2 + (2)2 ÷ 4 × 2 10. (8 + 10) - (2 + 2)2 ÷ 4 × 2 Friday: Create a problem like those above and simplify it using the order of operations. April 13 – April 17 Name________________________________________ Teacher_______________________________________ Monday: Read the following description of Evaluating Algebraic Expressions. You can also search online for “How to evaluate an algebraic expression” and read an explanation or watch a video describing how it is done. Evaluating Algebraic Expressions A variable is a letter, for example x, y or z, that represents a number. To evaluate an algebraic expression, you have to substitute a number for each variable and perform the operations. The number in front of a variable is called a coefficient and it is multiplied by the variable. If we know the value of our variables, we can replace the variables (plug in or substitute) with their values and then simplify the expression. Example: Evaluate the expression below for x = 2, y = -3, and z = 5 2 4x – 2y + z plug in the numbers… 4(2) – 2(-3) + 52 8 + 6 + 25 = 39 Tuesday: List 3 vocabulary words from this section. It’s ok to repeat words that you used in previous lessons. 1. 2. 3. Wednesday: Give a definition, example or description for each of the words that you listed on Tuesday. 1. 2. 3. Thursday: Evaluate the expressions for x = -2, y = 5, and z = -1 1. 3x + 2y + z 2. xy ÷ z 3. x ÷ z ∙ (2 + y) 4. y ∙ z + 4 ÷ x 5. 12 ÷ (y + z) 6. y2 - (x + z)2 7. x + z + (y - 1)2 8. 10 + x ∙ 2 - z2 9. (x)2 + (y)2 ÷ z 10. (z + y) - (x + 1)2 Friday: Create a problem like those above and then work it out by evaluating the expression. April 20 – April 24 Name________________________________________ Teacher_______________________________________ Monday: Read the following description of Simplifying Algebraic Expressions. You can also search online for “How to simplify an algebraic expression” and read an explanation or watch a video describing how it is done. Simplifying Algebraic Expressions An algebraic expression is a set of math terms, variables, numbers and operations, listed without an equal sign. The operations are add, subtract, multiply, divide, exponents, etc. To simplify an algebraic expression, distribute the number in front of parentheses. If there is no number, just drop the parentheses ( ). If there is a negative in front of a ( ), distribute -1 and then drop ( ). Now, combine (ADD) like terms. Variables with variables, plain numbers (these are called CONSTANTS) with other plain numbers (CONSTANTS). Like terms are terms with the same variable and exponent, or no variable at all, just numbers. Example: Simplify… (3x + 2) – (4 – 3x) + 5(2x + 5) 3x + 2 – 4 + 3x + 10x + 25 16x + 23 Tuesday: List 3 vocabulary words from this section. It’s ok to repeat words that you used in previous lessons. 1. 2. 3. Wednesday: Give a definition, example or description for each of the words that you listed on Tuesday. 1. 2. 3. Thursday: Simplify the Algebraic Expressions. 1. 3x + 2x - x 2. x + 4 – 5x - 3 3. (x + 7) + (2 + 3x) 4. (3x + 1) + (2x – 7) 5. (4x + 5) - (2x - 3) 6. (x – 7) – (3x – 1) 7. 5(4x - 1) 8. -3(2 – 6x) -(6x - 2) Friday: Create a problem like those above and then work it out by simplifying and combining like terms. April 27 – May 1 Name________________________________________ Teacher_______________________________________ Monday: Read the following description of One and Two-Step Equations. You can also search online for “How to solve a one or two-step equation” and read an explanation or watch a video describing how they are solved. One and Two-Step Equations An algebraic equation is a math problem where two expressions are set equal to each other and there is at least one variable. To solve an algebraic equation, first combine like terms. Next move all terms with variables to one side of the =, and regular numbers to the other side (this is the leave it or move it step). Don’t forget, “if it changes sides, it changes signs.” Combine like terms again on each side, then divide by the number in front of the variable, also known as the coefficient. Example: Solve… 3x + 5 – 7 = -2x + 12 – 2x Combine like terms 3x – 2 = -4x + 12 Leave it or move it 3x + 4x = 2 + 12 Combine like terms 7x = 14 Divide by 7 7x/7 = 14/7 x = 2 Tuesday: List 3 vocabulary words from this section. It’s ok to repeat words that you used in previous lessons. 1. 2. 3. Wednesday: Give a definition, example or description for each of the words that you listed above. 1. 2. 3. Thursday: Solve the following equations. 1. 3x + 1 = 2x – 7 2. 3x + 2x = -8 + 18 3. -3x + 4 = – 5x - 10 4. x + 7 + 5 = 2x - 4 + 3x 5. -2 + 4x + 5 = -2x – 3 6. -x – 7 + 4x = –3x – 1 + 12 Friday: Create an equation like those above and then solve it. It’s ok to get a decimal answer. May 4 – May 8 Name________________________________________ Teacher_______________________________________ Monday: Read the following description of Multi-Step Equations. You can also search online for “How to solve multi-step equations” and read an explanation or watch a video describing how they are solved. Multi-Step Equations A multi-step algebraic equation is a math problem where two expressions are set equal to each other, there is at least one variable, and there are parentheses. To solve a multi-step equation, first clear parentheses by distributing. Next combine like terms on each side. Then move all terms with variables to one side of the =, and regular numbers to the other side. This is the leave it or move it step, and remember if it changes sides, it changes signs. Combine like terms on each side again, then divide by the number in front of the variable, also known as a coefficient. Example: Solve… 14x – 2(x + 5) = 14 + 3(5x – 7) Distribute to clear parentheses 14x – 2x – 10 = 14 + 15x - 21 Combine like terms 12x - 10 = -7 + 15x Leave it or move it 12x - 15x = 10 – 7 Combine like terms -3x = 3 Divide by 7 -3x/-3 = 3/-3 x = -1 Tuesday: List 3 vocabulary words from this section. It’s ok to repeat words that you used in previous lessons. 1. 2. 3. Wednesday: Give a definition, example or description for each of the words that you listed above. 1. 2. 3. Thursday: Solve the following equations. 1. 3(x + 1) = 2(x – 3) 2. 3x + 2(x + 5) = -8 + x - 2 3. -3(x + 4) = – 5(x – 2) 4. x + 3(7 – x) = 2 – (-x – 4) 5. -2(1 + 4x) + 5 = 2x – 3(4 + 3x) 6. – (x – 3) + 4x = –3(x – 1) + 12 Friday: Create an equation like those above and then solve it. It’s ok to get a decimal answer. May 11 – May 15 Name________________________________________ Teacher_____________________________________ Monday: Read the following description of Proportion Equations. You can also search online for “How to solve a proportion equation” and read an explanation or watch a video describing how they are solved. Proportion Equations A proportion is an equation where two fractions are set equal. In algebra, a proportion equation has a variable in one or more parts of the problem. To solve a proportion equation, cross multiply setting the products equal. Distribute to clear parentheses if needed. Move all terms with variables to one side of the =, and regular numbers to the other side. This is the leave it or move it step, and remember if it changes sides, it changes signs. Combine like terms on each side, then divide by the number in front of the variable, also known as a coefficient. 2 x + 10 Example: Solve… = 3 5 + 4x Cross Multiply 2(5 + 4x) = 3(x + 10) clear parentheses 10 + 8x = 3x + 30 Leave it or move it 8x - 3x = -10 + 30 Combine like terms 5x = 20 Divide by 7 5x/5 = 20/5 x = 4 Tuesday: List 3 vocabulary words from this section. It’s ok to repeat words that you used in previous lessons.
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