lesson 5 homework practice simplify algebraic expressions answer key

With this worksheet generator, you can make printable worksheets for simplifying variable expressions for pre-algebra and algebra 1 courses. The worksheets can be made either as PDF or html files (the latter are editable in a word processor).

The expressions include ones where you need to combine like terms (such as 2 − 9 − 6 + 2), use the distributive property (such as 9 − 2( + 7)), and to multiply and divide monomials, such as 2 · (−5 ) and −4 · / 3 .

Each worksheet is randomly generated and thus unique. The and is placed on the second page of the file.

You can generate the worksheets — both are easy to print. To get the PDF worksheet, simply push the button titled " " or " ". To get the worksheet in html format, push the button " " or " ". This has the advantage that you can save the worksheet directly from your browser (choose File → Save) and then in Word or other word processing program.

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Use these quick links to create some common types of worksheets for simplifying expressions. Below, with the actual generator, you can generate worksheets to your exact specifications.

Worksheets for evaluating expressions with variables

Worksheets for writing expressions with variables from verbal expressions

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Use the generator to customize the worksheets as you wish. You can make them as PDF or html files. The html files are editable: just save the worksheet from your browser and then open it in your favorite word processor.

To customize the worksheets, you can control the number of problems, difficulty level, range of numbers used as coefficients and constants, the usage of decimals, the amount of workspace, a border around the problems, and additional instructions.

With level 1 problems, you can additionally exclude the usage of negative integers (keep everything nonnegative).

Key to Algebra Workbooks

Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system.

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Simplifying expressions

Combining like terms.

Students simplify 1-variable expressions by combining like terms.

Rewrite & evaluate:

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Simplify Expressions Worksheets

How to Simplify Expressions - Simplification is one of the key skills that students need to learn in the early stage of learning algebra. It not only helps them in breaking down a complex equation, but it also helps them in mastering the advanced concepts of algebra quickly and easily. Here we have elaborated on a few tips that can help students learn the simplification skill. 1. For simplifying the algebraic expression, you need to separate the like terms. Like terms with the same variable and exponents are supposed to be written together. Like terms need to be with sane variables with the same power or no power at all. 2. Another step of simplifying expressions is by factoring. Factoring is the algebraic concept represents a given number in the form of the two factors multiplied together. Next, we can also use the order of operation to simplify an algebraic expression. PEMDAS allows us to solve the problem in a stepwise manner. It enables us to solve the problem according to the acronym. First, we solve parenthesis followed by exponents, multiplication, and division, and lastly, addition, and subtraction.

Basic Lesson

Demonstrates how to collect like terms to find an equivalent expression. Practice problems are provided. Combinations of constants and variables connected by basic operations of addition, subtraction, multiplication and division are called expressions. Terms having the same powers of variables are like terms; otherwise, they are unlike terms.

Intermediate Lesson

Explains how to use parenthesis while simplify expressions. Remove parenthesis to find equivalent expression. Practice problems are provided.

Independent Practice 1

The sum of several like terms is another like term whose coefficient is the sum of those like terms. To subtract an expression from another, we change the sign of each term of the expression to be subtracted and then add expressions. Contains 20 simplify expressions problems. The answers can be found below.

Independent Practice 2

Features another 20 simplify expressions problems.

Homework Worksheet

12 simplify expressions problems for students to work on at home. Example problems are provided and explained.

10 simplify expressions problems. A math scoring matrix is included.

Homework and Quiz Answer Key

Answers for the homework and quiz.

Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

Thoughts of Einstein

For those who are having trouble with algebra, take heart: "Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater." -- Albert Einstein

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Into Math Grade 6 Module 8 Lesson 5 Answer Key Identify and Generate Equivalent Algebraic Expressions

We included  HMH Into Math Grade 6 Answer Key  PDF   Module 8 Lesson 5 Identify and Generate Equivalent Algebraic Expressions to make students experts in learning maths.

HMH Into Math Grade 6 Module 8 Lesson 5 Answer Key Identify and Generate Equivalent Algebraic Expressions

I Can use the properties of operations to determine if two expressions are equivalent and to generate equivalent algebraic expressions.

Step It Out

Turn and Talk How could you compare the expressions in Part A using the Distributive Property? Answer:

Turn and Talk How can you show that 8(xy + xy) is equivalent to 16xy? Answer: 8(xy + xy) = 8(2xy) = 16xy So, the answer is yes, the expression 8(xy + xy) is equivalent to 16xy

Check Understanding

Rewrite the first expression to determine whether the expressions are equivalent.

Question 1. 8x + 4y = ____________ 8x + 4y is ____________ to 4(2x + 1). Answer: 8x + 4y Using the distributive property of addition 8x + 4y = 4(2x + y) 8x + 4y is not equivalent to 4(2x + 1).

Question 2. 3 (k + 3) = ____________ 3(k + 3) is ____________ to 3k + 9. Answer: 3(k + 3) = 3k + 9 3(k + 3) is equivalent to 3k + 9.

On Your Own

Question 4. Reason Marcus wrote an expression equivalent to 7(x + 8). Liz wrote a different expression that has the same value as Marcus’ expression when x = 2. What could Liz’s expression be? Answer: Given, Marcus wrote an expression equivalent to 7(x + 8). x = 2 7(2 + 8) = 7(10) = 70

Question 6. What property of operations is used to show that 12x + 6y is equivalent to 6(2x + y)? Answer: 12x + 6y By using the distributive property of addition we can write the equivalent expression of 12x + 6y 12x + 6y = 6(2x + y)

Question 7. Open-Ended Write an expression that is equivalent to 5(d + 2f) + 5d. Answer: 5(d + 2f) + 5d = 5d + 10f + 5d = 10d + 10f = 10(d + f)

For Problems 8-13, combine like terms.

Question 8. 8w 2 – 3w 2 = ______________ Answer: 8w 2 – 3w 2 = w 2 (8 – 3) = 5w 2

Question 9. x + 5 + 7x = ______________ Answer: x + 5 + 7x Combine the like terms x and 7x x + 5 + 7x =8x + 5

Question 10. 6p 3 + 2p 2 + p 3 = _____________ Answer: 6p 3 + 2p 2 + p 3 Combine the like terms. 7p 3 + 2p 2 Take p as common factor. p(7p 2 + 2p) 6p 3 + 2p 2 + p 3 = p(7p 2 + 2p)

Question 11. 2(x + 4) – 5 = _______________ Answer: 2(x + 4) – 5 2x + 8 – 5 2x + 3 2(x + 4) – 5 = 2x + 3

Question 12. g + 3 + 4(g + 2) = _____________ Answer: g + 3 + 4(g + 2) g + 3 + 4g + 8 5g + 11 g + 3 + 4(g + 2) = 5g + 11

Question 13. 3(x 2 + 2) + 8 = _______________ Answer: 3(x 2 + 2) + 8 Multiply the parentheses expression with 3. 3x 2 + 6 + 8 = 3x 2 + 14

Question 14. Construct Arguments Determine whether 6y + 18 + 3y is equivalent to 9(y + 2). Use properties of operations to justify your answer. Answer: 6y + 18 + 3y = 9y + 18 By using the distributive property of addition we can simplify the expression. 6y + 18 + 3y = 9y + 18 = 9(y + 2).

Question 15. 6(4x + 3y) and 3(8x + 6y) are equivalent expressions. Explain why this is true. Answer: 6(4x + 3y) = 24x + 18y 3(8x + 6y) = 24x + 18y Yes, both the expressions are equivalent.

Question 17. Reason If 2n is added to an expression, it will be equivalent to 6(2n + 3). For which expression is this true: 12n + 21, 10 + 9, 2(5n + 9), or 12n + 1? Show how you know. Answer: Given, If 2n is added to an expression, it will be equivalent to 6(2n + 3). We have to check whether the given expressions are equivalent to 6(2n + 3) 12n + 21 = 3(4n + 7) + 2n = 14n + 21 ≠ 6(2n + 3) 10 + 9 ≠ 6(2n + 3) 2(5n + 9) = 10n + 18 + 2n = 12n + 18 = 6(2n + 3) 12n + 1 + 2n = 14n + 1 ≠ 6(2n + 3) So, the expression 2(5n + 9) is true.

Question 19. Identify the property used in each step. 6x + (19 + 5x) = 6x + (5x + 19) ____________ Property of Addition = (6x + 5x) + 19 _____________ Property of Addition = 11x + 19 Answer: 6x + (19 + 5x) = 6x + (5x + 19) Associative Property of Addition The associative property of addition states that when adding more than two numbers, the grouping of the numbers doesn’t change the sum. = (6x + 5x) + 19 Associative Property of Addition 6x + (19 + 5x) = 11x + 19 6x + (5x + 19) = 11x + 19 (6x + 5x) + 19 = 11x + 19 6x + (19 + 5x) = 6x + (5x + 19) = (6x + 5x) + 19 = 11x + 19

For Problems 20-21, determine if the expressions are equivalent.

Question 20. 4m + 3m is ______________ to 7m. Answer: 4m + 3m The above expression is the like terms so we can combine the numbers. 4m + 3m = 7m So, 4m + 3m is equivalent to 7m.

Question 21. 3j + 3k is ______________ to \(\frac{1}{4}\)(8j + 12k) Answer: \(\frac{1}{4}\)(8j + 12k) = 2j + 3k So, 3j + 3k is not equivalent to \(\frac{1}{4}\)(8j + 12k).

Question 22. Which expression is NOT equivalent to the others? Explain. 12p + 8 6p + 8 + 6p 4(p + 2) + 3p 4(3p + 2) Answer: 12p + 8 We can write it as 6p + 6p + 8 = 12p + 8 12p + 8 = 4(3p + 2) = 12p + 8 4(p + 2) + 3p = 4p + 8 + 3p = 7p + 8 Therefore 12 + 8 is not equivalent to 4(p + 2) + 3p.

Question 23. A rectangle is 4 units wide and 6 + x units long. Write two expressions to represent the area of the rectangle. Answer: Given, A rectangle is 4 units wide and 6 + x units long. Width = 4 units Length = 6 + x units We know that, Area of a rectangle = l × w A = (6 + x) × 4 A = 24 + 4x Thus the area of the rectangle is 4x + 24

For Problems 26-31, find an equivalent expression using the Distributive Property.

Question 26. 25w + 30x Answer: 25w + 30x The distributive property is multiplying a number by a sum or difference is the same as multiplying by each number in the sum or difference and then adding or subtracting. Take 5 as a common multiple to write the equivalent expression. 25w + 30x = 5(5w + 6x)

Question 27. x(4 + y) Answer: x(4 + y) The distributive property is multiplying a number by a sum or difference is the same as multiplying by each number in the sum or difference and then adding or subtracting. x(4 + y) = 4x + 4y

Question 28. 0.25(8r – 4m) Answer: 0.25(8r – 4m) The distributive property is multiplying a number by a sum or difference is the same as multiplying by each number in the sum or difference and then adding or subtracting. 0.25 × 8r – 0.25 × 4m 2r – 1m 0.25(8r – 4m) = 2r – m

Question 29. 24 + 8k Answer: 24 + 8k The distributive property is multiplying a number by a sum or difference is the same as multiplying by each number in the sum or difference and then adding or subtracting. Take 8 as a common number to simplify the expression. 24 + 8k = 8(3 + k)

Question 30. 4xy – 16x Answer: 4xy – 16x The distributive property is multiplying a number by a sum or difference is the same as multiplying by each number in the sum or difference and then adding or subtracting. Take 4x as a common factor to simplify the expression. 4xy – 16x = 4x(y – 4)

Question 31. g 3 (7 + h) Answer: g 3 (7 + h) The distributive property is multiplying a number by a sum or difference is the same as multiplying by each number in the sum or difference and then adding or subtracting. g 3 (7 + h) = 7g 3 + 7h

For Problems 32-33, determine if the expressions are equivalent.

Question 32. 7(x + 4) is _____________ to 7x + 4. Answer: 7(x + 4) = (7 × x) + (7 × 4) = 7x + 28 7(x + 4) is not equivalent to 7x + 4.

Question 33. 3r + 11 + 5r is _____________ to 2(4r + 3) + 5. Answer: 2(4r + 3) + 5 8r + 6 + 5 = 8r + 11 = 3r + 11 + 5r 3r + 11 + 5r is equivalent to 2(4r + 3) + 5.

Lesson 8.5 More Practice/Homework

Question 3. Critique Reasoning Trisha says that since 4(3s + 2) and 5(7s – 3) both equal 20 when s = 1, the expressions are equivalent. Is she correct? Explain. Answer: 4(3s + 2) s = 1 4(3(1) + 2) = 4(3 + 2) = 4(5) = 20 5(7s – 3) s = 1 5(7(1) – 3) = 5(7 – 3) = 5(4) = 20 Hence Trisha is correct.

Question 5. The surface area of a rectangular prism with length l, width w, and height h is given by the expression 2lw + 2lh + 2wh. Write an equivalent expression using the Distributive Property. Answer: The surface area of a rectangular prism with length l, width w, and height h is given by the expression 2lw + 2lh + 2wh. By using Distributive Property we can write the equivalent expression. 2lw + 2lh + 2wh = 2(lw + lh + wh)

Math on the Spot For Problems 6-7, identify the property.

Question 6. 3(6 • 5) = (3 • 6)5 ________________ Property of Multiplication Answer: Associative Property of Multiplication: When multiplying more than two numbers, the grouping of the numbers does not change the product. 3(6 • 5) = (3 • 6)5 In this case the product is same for both the numbers. 3 (6 × 5) = 3 × 30 = 90 (3 × 6) × 5 = 18 × 5 = 90

Question 7. w + z = z + w ________________ Property of Addition Answer: w + z = z + w is Commutative property of addition. Definition: Commutative property of addition states that when adding the numbers or expressions, changing the order of the numbers does not change the sum.

For Problems 8-9, determine whether the expressions are equivalent.

Question 8. 6r + 3w – 2r + 5w is _______________ to 4(r + 2w). Answer: 6r + 3w – 2r + 5w 6r – 2r + 3w + 5w 4r + 8w Let us take 4 as a common factor. 4(r + 2w) So, 6r + 3w – 2r + 5w is equivalent to 4(r + 2w).

Question 9. 12d + 8r is ______________ to 2(5d + 4r) + 4d. Answer: 2(5d + 4r) + 4d 10d + 8r + 4d 10d + 4d + 8r 14d + 8r So, 12d + 8r is not equivalent to 2(5d + 4r) + 4d.

Question 10. What property of operations can be used to justify that the two expressions in this equation are equivalent? 6x 2 + 4x = 4x + 6x 2 Answer: The commutative property of operations is used to justify that the two expressions in this equation are equivalent. 6x 2 + 4x = 4x + 6x 2 x(6x + 4) = x(4 + 6x) The order of the equation is different but the equation is the same.

Question 13. Which expressions are equivalent to 6(h + 4)? Select all that apply. (A) 6h + 4 (B) 6h + 24 (C) h + 10 (D) 4(h + 4) + 2(h + 4) (E) 2(3h + 12) Answer: Given, 6(h + 4) It can be written as 6h + 24 Take 2 as common factor It becomes 2(3h + 12) (D) 4(h + 4) + 2(h + 4) = 4h + 16 + 2h + 8 = 6h + 24 Thus Option B, D and E are the correct answers.

Question 14. Write an expression that is equivalent to 24x + 36y. Answer: Given expression 24x + 36y We can simplify by taking 6 as the common factor. 6(4x + 6y) or We can simplify by taking 12 as the common factor. 12(2x + 3y) So, the expression that is equivalent to 24x + 36y is 12(2x + 3y).

Spiral Review

Question 15. Penny is 100 centimeters tall. Jeremy is 38 inches tall. Who is taller? Show how you know. [Note: 1 centimeter ≈ 0.394 inches] Answer: Penny is 100 centimeters tall. Jeremy is 38 inches tall. 1 centimeter ≈ 0.394 inches 100 × 0.394 = 39.4 inches 39.4 inches is greater than 38 So, Penny is taller than Jeremy.

Question 16. What integer is the opposite of 12? Answer: The integer opposite of 12 is -12.

Question 17. Write 5 × 5 × 5 × 5 × 5 × 5 × 5 as an expression with an exponent. Answer: 5 × 5 × 5 × 5 × 5 × 5 × 5 = 5 7

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Simplify Radical Expressions | Radicals Lesson | Video | Homework | Algebra

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Teach your Algebra students how to to simplify radical expressions with this comprehensive lesson on radicals! Includes lesson notes, instructional video, and homework problems. Perfect for your middle or high school math class.

The lesson includes 30 problems in 19 easy to adapt slides in Google Slides. The skills covered in this lesson are:

• Simplify radical expression without variables
• Simplify radical expression with variables
• Finding a missing piece of a radical expression/equation
• Adding/Subtracting Radicals
• Multiplying Radicals

Also included with this lesson is a full length YouTube video of this lesson being taught. The video is great for:

• students that are absent
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• to show parents what is being taught in class

You also get a skill check/homework worksheet that can be used as for the lesson. The questions are based of the lesson and range from easy to challenging questions.

Finally, you also get answer keys and worked out solutions to both the lesson and the skill check.

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