math 6 homework (8.1)

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Texas Go Math Grade 6 Lesson 8.1 Answer Key Comparing Additive and Multiplicative Relationships

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 8.1 Answer Key Comparing Additive and Multiplicative Relationships.

Texas Go Math Grade 6 Lesson 8.1 Explore Activity Answer Key

Discovering Additive and Multiplicative Relationships

(A) Every state has two U.S. senators. The number of electoral votes a state has is equal to the total number of U.S. senators and U.S. representatives.

The number of electoral votes is _________________ the number of representatives.

(B) Frannie orders three DVDs per month from her DVD club. Complete the table.

Question 1. Look for a Pattern What operation did you use to complete the tables in (A) and (B)? Answer: Adding and multiplying

The relationship is additive because Ky’s age = Lu’s age + 7

Texas Go Math Grade 6 Lesson 8.1 Guided Practice Answer Key

Total number of dogs = Number of dogs they already have + Adopted dogs

List the ordered pairs from the table: (1, 3), (2, 4), (3. 5). (4, 6) and graph them on a coordinate plane.

Days of class = Weeks ∙ Three days

List the ordered pairs from the table: (1, 3), (2, 6), (3, 9), (4, 12) and graph them on a coordinate plane.

Cost = Pages printed ∙ 10 cents The relationship is multiplicative.

List the ordered pairs from the table: (1, 10), (2, 20), (3, 30), (4, 40), (5, 50) and graph them on a coordinate plane.

Essential Question Check-In

Question 6. How do you represent, describe, and compare additive and multiplicative relationships? Answer: We use tables and ordered pairs to represent and describe additive and multiplicative relationships. You can compare these relationships by graphing them on a coordinate plane.

An additive relationship involves a constant that is added to another number. A multiplicative relationship involves a constant that is multiplied by another number.

The tables give the price of a kayak rental from two different companies.

Question 7. Is the relationship shown in each table multiplicative or additive? Explain. Answer: First table: Cost = Hours ∙ 9 The relationship is multiplicative.

Second table Cost = Hours + 40 The relationship is additive.

Go Math Lesson 8.1 6th Grade Multiplicative Relationships Question 8. Yvonne wants to rent a kayak for 7 hours. How much would this cost to each company? Which one should she choose? Answer: First company: Cost = Hours ∙ 9 She wants to rent it for 7 hours, so: Cost = 7 ∙ 9 = 64

Second Company: Cost = Hours + 40 She wants to rent it for 7 hours, so: Cost = 7 + 40 = 47 She should choose the second company.

Question 9. After how many hours is the cost for both kayak rental companies the same? Explain how you found your answer. Answer: Let y represent the cast and z represents the hours. First company: y 1 = 9x Second company: y 2 = x + 40 If the casts are the same, y 1 = y 2 Substitute y 1 with 9x and y 2 with x + 40: y 1 = y 2 9x = x + 40 9x – x = 40 8x = 40 x = 5

Check the answer After 5 hours, in the first company the cost is: y = 9 ∙ 5 = 45 and in the second company: y = 5 + 40 = 45. After 5 hours.

The graph represents the distance traveled by a car and the number of hours it takes.

Lesson 8.1 Answer Key Additive and Multiplicative Relationships Worksheets Pdf Question 10. Persevere in Problem Solving Based on the graph, was the car traveling at a constant speed? At what speed was the car traveling? Answer: The ordered pairs on the graph are: (1, 60), (2, 120), (3, 180), (4, 240) Distance = Time ∙ 60 The car was traveling at a constant speed. Speed = \(\frac{\text { Distance }}{\text { Time }}\) = 60 mi per hour

Constant speed; 60 mi per hour

Question 11. Make a Prediction If the pattern shown in the graph continues, how far will the car have traveled after 6 hours? Explain how you found your answer. Answer: Distance = Time ∙ 60 After 6 hours, distance is equal to Distance = 6 ∙ 60 = 360 = 360 mi

Question 12. What If? If the car had been traveling at 40 miles per hour, how would the graph be different? Answer: Distance = Time ∙ 40

Use the graph for Exercises 13 – 15.

Go Math Grade 6 Lesson 8.1 Answer Key Multiplicative Relationship Graph Question 13. Which set of points represents an additive relationship? Which set of points represents a multiplicative relationship? Answer: Ordered pairs on the graph: (1, 6), (2, 12), (3, 18), (4, 24) y = 6x This set of points represents a multiplicative relationship.

(1, 9), (2, 10), (3, 11), (4. 12) y = x + 8 This set of points represents an additive relationship.

Question 14. Represent Real-World Problems What is a real-life relationship that might be described by the red points? Answer: Ana is 8 years older than Ben How old is he if she is 11 years old?

Question 15. Represent Real-World Problems What is a real-life relationship that might be described by the black points? Answer: In Gunther’s class there are 6 times more girls than boys. If there are 24 girls, how many boys there are?

H.O.T. Focus On Higher Order Thinking

This is a multiplicative relationship, not an additive. If an elevator rises three feet per second, that means, in 2 seconds it will rise 3 + 3 = 2 ∙ 3 = 6 seconds, instead of 5

First table. B = A ∙ 16

The second table shows equivalent ratios because \(\frac{1}{16} \cdot \frac{2}{2}=\frac{2}{32}\) \(\frac{1}{16} \cdot \frac{3}{3}=\frac{3}{48}\)

Lesson 8.1 Answer Key 6th Grade Additive or Multiplicative Question 18. Represent Real-World Problems Describe a real-world situation that represents an additive relationship and one that represents a multiplicative relationship. Answer: Additive relationship: Cart is 2 years older than his sister Julie. If she is 9 years old, how old is he? Carl’s age = Julie’s age + 2

Multiplicative relationship: One apple pie costs $3. Find the price of 4 pies. Price = Pies ∙ 3

Additive relationship: Carl is 2 years older than his sister Julie. If she is 9 years old, how old is he? Multiplicative relationship: One apple pie costs $3. Find the price of 4 pies.

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8th grade (Illustrative Mathematics)

Unit 1: rigid transformations and congruence, unit 2: dilations, similarity, and introducing slope, unit 3: linear relationships, unit 4: linear equations and linear systems, unit 5: functions and volume, unit 6: associations in data, unit 7: exponents and scientific notation, unit 8: pythagorean theorem and irrational numbers.

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Into Math Grade 6 Module 8 Lesson 1 Answer Key Understand and Apply Exponents

We included  HMH Into Math Grade 6 Answer Key  PDF   Module 8 Lesson 1 Understand and Apply Exponents to make students experts in learning maths.

HMH Into Math Grade 6 Module 8 Lesson 1 Answer Key Understand and Apply Exponents

I Can write and evaluate numerical expressions involving whole-number exponents.

Spark Your Learning

Turn and Talk Is there another way to solve this problem? Explain. Answer:

Build Understanding

Connect to Vocabulary When a number is raised to a power, the number that is used as a factor is the base. An exponent is a number that indicates how many times the base is used as a factor.

Turn and Talk When is it useful to write an expression using a base and an exponent? Give an example. Answer: In Mathematics, there are different laws of exponents. All the rules of exponents are used to solve many mathematical problems which involve repeated multiplication processes. The laws of exponents simplify the multiplication and division operations and help to solve the problems easily. For example, a m  = a × a × a × a…m times. b 4  = b × b × b × b. 5 3  = 5 × 5 × 5. The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Rewrite 7 × 7 × 7 × 7 × 7 × 7, using an exponent. solution: Step 1: The number 7 appears six times in the multiplication. Step 2: So 7 × 7 × 7 × 7 × 7 × 7 = 7 6 Step 3: The expression 7 6  has a base of 7 and an exponent of 6.

Step It Out

Question 2. An exponent tells how many times a number is used in an expression. Look at the expression 5 • 5 • 5 • 5. A. How many times is the factor 5 used? Answer: The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as a raised to the power m or just  a  to the power m. Step 1: The number 5 appears four times in the multiplication. Step 2: So 5 x 5 x 5 x 5 = 5^4 Step 3: The expression 5^4 has a base of 5 and an exponent of 4.

Check Understanding

On Your Own

Question 5. Write each expression in exponential form. A. 9 • 9 • 9 • 9 • 9 = _____________ Answer: The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Step 1: The number 9 appears five times in the multiplication. Step 2: So 9 x 9 x 9 x 9 x 9 = 9^5 Step 3: The expression 9^5 has a base of 9 and an exponent of 5. Step 4: The value of 9^5 is 59049

B. \(\frac{1}{8}\) • \(\frac{1}{8}\) • \(\frac{1}{8}\) = _____________ Answer: The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Step 1: The number 1/8 appears three times in the multiplication. Step 2: So 1/8 x 1/8 x 1/8 = (1/8)^3 Step 3: The expression (1/8)^3 has a base of 1/8 and an exponent of 3. Step 4: The value of (1/8)^3 is 1/512

For Problems 6-7, write the exponential expression as an equivalent repeated multiplication expression and then evaluate the expression.

Question 6. 6 3 = ___________ Answer: In Mathematics, there are different laws of exponents. All the rules of exponents are used to solve many mathematical problems which involve repeated multiplication processes. The laws of exponents simplify the multiplication and division operations and help to solve the problems easily. For example, a m  = a × a × a × a…m times. b 4  = b × b × b × b. 5 3  = 5 × 5 × 5. The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Step 1: The number 6 appears three times in the multiplication. Step 2: So 6 x 6 x 6 = 6^3 Step 3: The expression 6^3 has a base of 6 and an exponent of 3. Step 4: The value of 6^3 is 216

Question 7. 2 6 = _____________ Answer: In Mathematics, there are different laws of exponents. All the rules of exponents are used to solve many mathematical problems which involve repeated multiplication processes. The laws of exponents simplify the multiplication and division operations and help to solve the problems easily. For example, a m  = a × a × a × a…m times. b 4  = b × b × b × b. 5 3  = 5 × 5 × 5. The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Step 1: The number 2 appears six times in the multiplication. Step 2: So 2 x 2 x 2 x 2 x 2 x 2 = 2^6 Step 3: The expression 2^6 has a base of 2 and an exponent of 6. Step 4: The value of 2^6 is 64

I’m in a Learning Mindset!

What facts about exponents can I talk about? Answer: Zero raised to any power is zero (e.g. 0 5  = 0) One raised to any power is one (e.g. 1 5  = 1) Any number raised to the zero power is one (e.g. 7 0  = 1) Any number raised to the first power is that number (e.g. 7 1  = 7)

Lesson 8.1 More Practice/Homework

B. Write an expression to represent the number of people called at 8 o’clock using a base and an exponent. Answer: The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Step 1: The number 6 appears six times in the multiplication. Step 2: So 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6  = 6^8 Step 3: The expression 6^8 has a base of 6 and an exponent of 8. Step 4: The value of 6^8 is 1679616

C. How many people were called in all? Explain. Answer: As I mentioned above. At 8 o’clock, each of those friends called 6 of their other friends. This was the end. Step 1: The number 6 appears six times in the multiplication. Step 2: So 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6  = 6^8 Step 3: The expression 6^8 has a base of 6 and an exponent of 8. Step 4: The value of 6^8 is 1679616 Therefore, 1679616 were called.

Question 3. Reason Compare the expressions 3 8 and 3 5 × 3 3 using the properties of multiplication. What do you notice? Answer: As per the multiplication law of exponents, the product of two exponents with the same base and different powers equals to base raised to the sum of the two powers or integers. a m  × a n   = a m+n The above-given 3 5 × 3 3 According to the multiplication law of exponents: 3^5 x 3^3 = 3^(5 +3) = 3^8

Question 4. Math on the Spot Write the expression in exponential form. A. 7 • 7 • 7 • 7 = ___________ Answer: The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Step 1: The number 7 appears four times in the multiplication. Step 2: So 7 x 7 x 7 x 7 = 7^4 Step 3: The expression 7^4 has a base of 7 and an exponent of 4. Step 4: The value of 7^4 is 2401

B. 3 • 3 • 3 • 3 • 3 • 3 = ____________ Answer: The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Step 1: The number 3 appears six times in the multiplication. Step 2: So 3 x 3 x 3 x 3 x 3 x 3 = 3^6 Step 3: The expression 3^6 has a base of 3 and an exponent of 6. Step 4: The value of 3^6 is 729

For Problems 5-6, write the exponential expression as an equivalent repeated multiplication expression and then evaluate the expression.

Question 5. 2 8 = ___________ Answer: In Mathematics, there are different laws of exponents. All the rules of exponents are used to solve many mathematical problems which involve repeated multiplication processes. The laws of exponents simplify the multiplication and division operations and help to solve the problems easily. For example, a m  = a × a × a × a…m times. b 4  = b × b × b × b. 5 3  = 5 × 5 × 5. The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Step 1: The number 2 appears eight times in the multiplication. Step 2: So 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2^8 Step 3: The expression 2^8 has a base of 2 and an exponent of 8. Step 4: The value of 2^8 is 256

Question 6. 5 5 = ___________________ Answer: In Mathematics, there are different laws of exponents. All the rules of exponents are used to solve many mathematical problems which involve repeated multiplication processes. The laws of exponents simplify the multiplication and division operations and help to solve the problems easily. For example, a m  = a × a × a × a…m times. b 4  = b × b × b × b. 5 3  = 5 × 5 × 5. The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Step 1: The number 5 appears five times in the multiplication. Step 2: So 5 x 5 x 5 x 5 x 5 = 5^5 Step 3: The expression 5^5 has a base of 5 and an exponent of 5. Step 4: The value of 5^5 is 3125

For Problems 7 and 8, write the repeated multiplication expression using a single exponent.

Question 7. 8 • 8 • 8 • 8 • 8 = __________ Answer: In Mathematics, there are different laws of exponents. All the rules of exponents are used to solve many mathematical problems which involve repeated multiplication processes. The laws of exponents simplify the multiplication and division operations and help to solve the problems easily. For example, a m  = a × a × a × a…m times. b 4  = b × b × b × b. 5 3  = 5 × 5 × 5. The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Step 1: The number 8 appears five times in the multiplication. Step 2: So 8 x 8 x 8 x 8 x 8 = 8^5 Step 3: The expression 8^5 has a base of 8 and an exponent of 5. Step 4: The value of 8^5 is 32768

Question 8. 4 • 4 • 4 • 4 • 4 • 4 • 4 = ____________ Answer: In Mathematics, there are different laws of exponents. All the rules of exponents are used to solve many mathematical problems which involve repeated multiplication processes. The laws of exponents simplify the multiplication and division operations and help to solve the problems easily. For example, a m  = a × a × a × a…m times. b 4  = b × b × b × b. 5 3  = 5 × 5 × 5. The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Step 1: The number 4 appears seven times in the multiplication. Step 2: So 4 x 4 x 4 x 4 x 4 x 4 x 4 = 4^7 Step 3: The expression 4^7 has a base of 4 and an exponent of 7. Step 4: The value of 4^7 is 16384

Question 9. Select all expressions equivalent to 3 • 3 • 3 • 3 • 3 • 3 • 3 • 3. (A) 8 3 (B) 3 8 (C) 3 5 • 3 3 (D) 3 4 • 3 4 (E) 3 7 • 3 2 Answer: Option B, C, D are the possible expressions. Option B: 3 • 3 • 3 • 3 • 3 • 3 • 3 • 3 = 3^8 3 is used as a repeated factor of 8 times. Option C: As per the multiplication law of exponents, the product of two exponents with the same base and different powers equals to base raised to the sum of the two powers or integers. a m  × a n   = a m+n The above-given 3 5 × 3 3 According to the multiplication law of exponents: 3^5 x 3^3 = 3^(5 +3) = 3^8 Option D: According to the multiplication law of exponents: 3^4 x 3^4 = 3^(4 +4) = 3^8

Question 10. Select all expressions equivalent to 11 • 11 • 11. (A) 11 3 (B) 3 11 (C) 11 1 • 11 3 (D) 3 5 • 3 6 (E) 11 1 • 11 2 Answer: Option A and E are the possible expressions. Option A: 11. 11. 11 = 11^3 3 is used as a repeated factor of 8 times. Option E: As per the multiplication law of exponents, the product of two exponents with the same base and different powers equals to base raised to the sum of the two powers or integers. a m  × a n   = a m+n The above-given 11^1. 11^2 According to the multiplication law of exponents: = 11^(1 +2) = 11^3

Question 11. Write two equivalent expressions, one exponential and one a product of factors, for “4 to the 5th power.” Evaluate the expressions. Answer: 4 to the 5th power can be written as 4^5 4^5 can be written as: 4 x 4 x 4 x 4 x 4 In Mathematics, there are different laws of exponents. All the rules of exponents are used to solve many mathematical problems which involve repeated multiplication processes. The laws of exponents simplify the multiplication and division operations and help to solve the problems easily. For example, a m  = a × a × a × a…m times. b 4  = b × b × b × b. 5 3  = 5 × 5 × 5. The number a is known as base and m is said to be the exponent and a m  is said to be the exponent form of the number. Exponents are also called powers or indices. We read a m  as  a  raised to the power m or just  a  to the power m. Step 1: The number 4 appears five times in the multiplication. Step 2: So 4 x 4 x 4 x 4 x 4 = 4^5 Step 3: The expression 4^5 has a base of 4 and an exponent of 5. Step 4: The value of 4^5 is 1024 2nd method: We can go for the multiplication law of exponents: As per the multiplication law of exponents, the product of two exponents with the same base and different powers equals to base raised to the sum of the two powers or integers. a m  × a n   = a m+n According to the multiplication law of exponents: 4^1 x 4^4 = 4^(1 +4) = 4^5

Spiral Review

Question 13. Letty answered 15 out of 20 questions correctly on her history quiz. What is her grade as a percent? Answer: The number of questions Letty answered = 15 The total number of questions = 20 The grade as a percent = P P = 15/20 x 100 P = 75% therefore, Letty grade is 75%.

Question 15. Which is the better buy, a 31-ounce bottle of ketchup for $2.53 or a 64-ounce bottle for $5.05? Answer: I think a 64-ounce bottle is better to buy. The cost of 31-ounce bottle = $2.53 The cost of 64-ounce bottle = $5.05 If we buy 2 31-ounce bottles then we need to spend $5.06 which e get 62-ounces. But if we buy a 64-ounce bottle, we get 2-ounces more with 0.1 less. So definitely better worth buying a 64-ounce bottle.

Question 16. A pancake recipe calls for 4\(\frac{1}{2}\) cups of whole-wheat flour. If the chef wants to split the recipe into 3 equal batches, how much flour should be in each batch? Answer: 4 1/2 can be written as 9/2 which is an improper fraction Now, this 9/2 should be divided into 3 equal batches. Then we get to know the flour should be in each batch. Let it be E. E = 9/2 x 3 E = 27/2 E = 13.5 Therefore, each batch would get 13.5 cups of flour.

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Unit 1: Rigid Transformations and Congruence

Unit 2: dilations, similarities and introducing slope, unit 3: linear relationships, unit 4: linear equations and linear systems, unit 5: functions and volume, unit 6: associations in data, unit 7: exponents and scientific notation, unit 8: pythagorean theorem and irrational numbers.

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