Equivalent expressions with distributive property combining like terms

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)

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?

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

Equivalent Expressions

Equivalent Expressions using the Distributive Property (Grandma Property)

Equivalent Expressions 2

Equivalent Expressions 1

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