Equivalent Expressions 1

8.AR.1.1 Identify equivalent algebraic expressions that have monomial bases with one variable or two variables by applying the Laws of Exponents: ➢ using 1 law of exponents with integer exponents (L2) ➢ using 2 or 3 laws of exponents with positive exponents (L3)

GSE Grade 6 Math - MGSE6.EE.1 Equivalent Numerical Expressions

Here’Transformation,Ratio,Proportion, Fractions and Algebraic Expressions,Transformation 1. Translation 2. Reflection 3. Rotation 4. Enlargement 5. Transformation 6. Congruence 7. Similarity 8. Scale Factor 9. Image 10. Pre-image 11. Symmetry 12. Isometry 13. Ratio 14. Proportion 15. Equivalent Ratios 16. Simplify 17. Unit Ratio 18. Scale 19. Part-to-Part 20. Part-to-Whole 21. Rate 22. Comparison 23. Proportional Relationship 24. Cross Multiplication 25. Direct Proportion 26. Inverse Proportion 27. Constant of Proportionality 28. Golden Ratio 29. Linear Relationship 30. Equal Proportions 31. Proportional Constant 32. Scale Drawing 33. Word Problems 34. Unitary Method 35. Percentage 36. Double Number Line 37. Fraction 38. Numerator 39. Denominator 40. Improper Fraction 41. Proper Fraction 42. Mixed Number 43. Simplified Fraction 44. Reciprocal 45. Least Common Denominator (LCD) 46. Greatest Common Factor (GCF) 47. Equivalent Fractions 48. Decimal 49. Variable 50. Coefficient 51. Constant 52. Algebraic Term 53. Polynomial 54. Monomial 55. Binomial 56. Expression 57. Equation 58. Like Terms 59. Simplify 60. Substitution -

8.AR.1.3 Identify a common monomial factor in the sum of two algebraic expressions (L2) Given a sum of two algebraic expressions, identify the equivalent expression having a common monomial factor as a common factor multiplied by the sum of two algebraic expressions (L3) Rewrite the sum of two algebraic expressions having a common monomial factor: ➢ with a common factor multiplied by the sum of two algebraic expressions (L4)

Select all the numbers that can be used as a common denominator to rewrite the fractions __ 2 6 and __ 1 2 . A 3 D 12 B 6 E 16 C 8 2 Aaron ran __ 5 8 mile to his friend’s house. Then he ran another __ 1 4 mile to the park. 1 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 4 Which equation shows how many miles Aaron ran? A __ 5 8 – __ 1 4 = __ 2 8 C __ 5 8 + __ 1 4 = __ 7 8 B __ 5 8 – __ 1 4 = __ 3 8 D __ 5 8 + __ 1 4 = __ 8 8 3 Select all the expressions that can be used to find the sum of __ 6 8 and ___9 12. A ___ 36 48 + ___ 36 48 D ___ 18 20 + ___ 17 20 B ___ 24 36 + ___ 27 36 E ___ 18 24 + ___ 18 24 C ___ 14 16 + ___ 13 16 4 Write a pair of equivalent fractions for __ 3 4 and __ 2 5 using a common denominator of 20. __ 3 4 = __ 2 5 = 5 Katie spent __ 4 5 hour painting and __ 1 2 hour drawing. ? 1 1 2 1 5 1 5 1 5 1 5 How much more time in hours did she spend painting than drawing? 6 Dave is planting a garden. He plants cucumbers in ___2 12 of his garden and tomatoes in __ 2 3 of his garden. What fraction of his garden does Dave plant with cucumbers and tomatoes? 7 Of the students in Maria’s class, __ 2 5 have dogs and __ 1 3 have cats. No students have both a dog and a cat. What fraction represents how many more students in Maria’s class have dogs? 52 © Houghton Mifflin Harcourt Publishing Company Module 6 • Form A Name Module Test DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-C 9 Mr. Gonzales used __ 3 4 quart of broth and __ 1 2 quart of milk to make soup. How many quarts of liquid did he use? Part A Complete the fraction model to represent the problem. 1 1 2 1 4 1 4 1 4 Part B Write an equation to show how many quarts of liquid Mr. Gonzales used to make soup. 10 A bowl of cereal contains __ 2 3 cup of oats and __ 2 8 cup of raisins. Write a numerical expression using equivalent fractions with a common denominator of 24 to model how many more cups of oats than raisins there are in the bowl. 11 Jessica read __ 1 6 of her book on Thursday, __ 2 9 of her book on Friday, and __ 1 2 of her book on Saturday. Part A Write a numerical expression using equivalent fractions to model how much of her book she has read so far. Part B What fraction of her book has Jessica read?

math 1_equivalent expression

Based on the PowerPoint you shared, here is a simple quiz focusing on vocabulary, exponent laws, and identifying function types. --- Quiz: Exponent Laws & Rational Exponents (3.1–3.3) Multiple Choice (5 questions) Choose the correct answer. 1. In the expression 5^3, the number 3 is called the a) base b) power c) exponent d) coefficient 2. Which law of exponents would you use to simplify (x^2)^3? a) Product rule b) Quotient rule c) Power of a power rule d) Zero exponent rule 3. According to the zero exponent law, 7^0 = a) 0 b) 1 c) 7 d) undefined 4. If the first differences in a table of values are constant, the function is a) linear b) quadratic c) exponential d) not a function 5. Which expression is equivalent to \frac{2^5}{2^3}? a) 2^2 b) 2^8 c) 2^{15} d) 2^{-2} True or False (5 questions) Write T for true or F for false. 1. When multiplying powers with the same base, you add the exponents. 2. A negative exponent means the answer will always be negative. 3. For an exponential function, the ratios of consecutive y-values are constant. 4. The power 16^{\frac{1}{2}} is equal to 8. 5. The quotient rule for exponents says \frac{x^a}{x^b} = x^{a-b}. Completion (2 questions) Fill in the blank with the correct term. 1. The _____________ rule states that when raising a power to another power, you multiply the exponents. 2. If the second differences in a table of values are constant, the function is ______________. --- Answer Key Multiple Choice 1. c) exponent 2. c) Power of a power rule 3. b) 1 4. a) linear 5. a) 2^2 True or False 6. T 7. F (a negative exponent indicates a reciprocal, not a negative value) 8. T 9. F (16^{\frac{1}{2}} = \sqrt{16} = 4) 10. T Completion 11. power of a power (or power rule) 12. quadratic

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