# Texas Go Math Grade 6 Lesson 6.3 Answer Key Applying integer Operations

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## Texas Go Math Grade 6 Lesson 6.3 Answer Key Applying integer Operations

Question 1.
Reggie lost 3 spaceships in level 3 of a video game. He lost 30 points for each spaceship. When he completed level 3, he earned a bonus of 200 points. By how much did his score change?
Use negative integer to represent lost points for each spaceship. The product
3 × (- 30)
shows how many points he lost for 3 spaceships.
Add positive integer that represents bonus he earned when he completed level 3.
The expression you get is:
3 × (- 30) + 200
First, calculate the product using rules for multiplying integers:
– 90 + 200
Then, find the sum using rules for adding integers:
– 90 + 200 = 110
His score increased by 110 points when he completed level 3

His score increased by 110 points.
Use rules for multiplying integers and rules for adding integers to find the change in his score.

Question 2.
Simplify: – 6(13) – 21
The expression you want to simplify ¡S:
– 6(13) – 21
First, calculate the product using rules for multiplying integers:
– 78 – 21
Then, find the difference using rules for subtracting integers:
– 78 – 21 = – 99
The expression is equal to – 99

The expression – 6(13) – 21 is equal to – 99
Use rules for multipLying integers and rules for subtracting integers to simplify it

Reflect

Question 3.
What If? Suppose there were four brothers in Example 2. How much would the youngest brother need to pay?
Use positive integers because you want to calculate how much money he would need to pay.
The quotient
72 ÷ 4
represents equal parts that each brother needs to pay.
Add 15 to that quotient to find the final result.
The value of the expression:
72 ÷ 4 + 15
is the amount that youngest brother would need to pay.
First, calculate the quotient using rules for dividing integers:
18 + 15
Then, find the sum using rules for adding integers:
18 + 15 = 33
Youngest brother would need to pay $33 to his parents. Use rules for dividing integers and rules for adding integers to calculate the amount Your Turn Simplify each expression. Question 4. (- 12) ÷ 6 + 2 ___________ Answer: The expression you want to simplify is: (-12) ÷ 6 + 2 First calculate the quotient using rules for dividing integers: – 2 + 2 Then, find the sum using rules for adding integers: – 2 + 2 = 0 The expression is equal to 0. The expression (- 12) ÷ 6 + 2 is equal to 0. Use rules for dividing integers and rules for adding integers to simplify it. Question 5. – 87 ÷ (- 3) – 9 _________ Answer: The expression you want to simplify is: (- 87) ÷ (- 3) – 9 First, calculate the quotient using rules for dividing integers: 29 – 9 Then, find the difference using rules for subtracting integers: 29 – 9 = 20 The expression is equal to 20. The expression (- 87) ÷ (- 3) – 9 is equal to 0. Use rules for dividing integers and rules for adding integers to simplify it. Question 6. 40 ÷ (- 5) + 30 ___________ Answer: The expression you want to simplify is: 40 ÷ (- 5) + 30 First, calculate the quotient using rules for dividing integers: – 8 + 30 Then, find the difference using rules for subtracting integers: – 8 + 30 = 20 The expression is equal to 22. The expression 40 ÷ (- 5) + 30 is equal to 22. Use rules for dividing integers and rules for adding integers to simplify it. Question 7. – 39 ÷ 3 – 15 ____________ Answer: The expression you want to simplify is: – 39 ÷ 3 – 15 First, calculate the quotient using rules for dividing integers: – 13 – 15 Then, find the difference using rules for subtracting integers: – 13 – 15 = – 28 The expression is equal to – 28. The expression – 39 ÷ 3 – 15 is equal to – 28. Use rules for dividing integers and rules for adding integers to simplify it. Question 8. Amber and Will are in line together to buy tickets. Amber moves back by 3 places three times to talk to friends. She then is invited to move 5 places up in line. Will moved back by 4 places twice, and then moved up in line by 3 places. Overall, who moved farther back in line? Answer: Write the expression that represents Amber’s change in position in the line: 3(- 3) + 5 First calculate the quotient using rules for dividing integers: – 9 + 5 Then, find the sum using rules for adding integers: – 9 + 5 = – 4 Amber moves back 4 places. Now, write the expression that represents Will’s change in position in the line: 2(- 4) + 3 Calculate the quotient using rules for dividing integers: – 8 + 3 Then, find the sum using rules for adding integers: – 8 + 3 = – 5 Will moves back 5 places. Compare absolute values of the results to find who moved farther in line: |- 4| < |- 5| Will moved farther back in tine. Find change in position for Amber and Will using rules for multiplying integers and rules for adding integers and then compare results. Evaluate each expression. Circle the expression with the greater value. Question 9. (- 10) ÷ 2 – 2 = ____________ (- 28) ÷ 4 + 1 = ____________ Answer: First expression is: (-10) ÷ 2 – 2 First calculate the quotient using rules for dividing integers: – 5 – 2 Then, find the difference using rules for subtracting integers: – 5 – 2 = – 7 Second expression is: (- 28) ÷ 4 + 1 Calculate the quotient using rules for dividing integers: – 7 + 1 Then find the sum using rules for adding integers – 7 + 1 = – 6 Compare values: – 7 < – 6 The expression with the greater value is (- 28) ÷ 4 + 1. Find values of both expressions using rules for dividing, subtracting and adding integers and compare them. Question 10. 42 ÷ (-3) + 9 = ____________ (- 36) ÷ 9 – 2= ____________ Answer: First expression is: 42 ÷ (- 3) + 9 First calculate the quotient using rules for dividing integers: – 14 + 9 then, find the sum using rules for adding integers: – 14 + 9 = – 5 Second expression is: (- 36) ÷ 9 – 2 Calculate the quotient using rules for dividing integers: – 4 – 2 then, find the difference using rules for subtracting integers: – 4 – 2 = – 6 Compare values: – 5 > – 6 The expression with the greater value is 42 ÷ (-3) + 9. Find values of both expressions using rules for dividing, subtracting and adding integers and compare them. Texas Go Math Grade 6 Lesson 6.3 Guided Practice Answer Key Evaluate each expression. (Example 1) Question 1. -6 (-5) + 12 ______________ Answer: The expression is: – 6(- 5) + 12 First calculate the product using rules for multiplying integers: 30 + 12 Then, find the sum using rules for adding integers: 30 + 12 = 42 Therefore: – 6(- 5) + 12 = 42 The value of the expression is 42 Use rules for multiplying integers and rules for adding integers to find the value of the expression. Question 2. 3(-6) – 3 ______________ Answer: The expression is: 3(-6) – 3 First calculate the product using rules for multiplying integers: – 18 – 3 Then, find the sum using rules for adding integers: – 18 – 3 = – 21 Therefore: 3(- 6) – 3 = – 21 The value of the expression is – 21 Use rules for multiplying integers and rules for adding integers to find the value of the expression. Question 3. – 2(8) + 7 ______________ Answer: The expression is: – 2(8) + 7 First calculate the product using rules for multiplying integers: – 16 + 7 Then, find the sum using rules for adding integers: – 16 + 7 = – 9 Therefore: – 2(8) + 7 = – 9 The value of the expression is – 9 Use rules for multiplying integers and rules for adding integers to find the value of the expression. Question 4. 4(-13) + 20 ______________ Answer: The expression is: 4(-13) + 20 First calculate the product using rules for multiplying integers: – 52 + 20 Then, find the sum using rules for adding integers: – 52 + 20 = – 32 Therefore: 4(- 13) + 20 = – 32 The value of the expression is – 32 Use rules for multiplying integers and rules for adding integers to find the value of the expression. Question 5. (- 4)(0) – 4 ______________ Answer: The expression is: (- 4)(0) – 4 First calculate the product using rules for multiplying integers: 0 – 4 Then, find the sum using rules for adding integers: 0 – 4 = – 4 Therefore: – 4(0) – 4 = – 4 The value of the expression is – 4 Use rules for multiplying integers and rules for adding integers to find the value of the expression. Question 6. – 3(- 5) – 16 ______________ Answer: The expression is: – 3(- 5) – 16 First calculate the product using rules for multiplying integers: 15 – 16 Then, find the sum using rules for adding integers: 15 – 16 = – 1 Therefore: – 3(- 5) – 16 = – 1 The value of the expression is – 1 Use rules for multiplying integers and rules for adding integers to find the value of the expression. Write an expression to represent the situation. Evaluate the expression and answer the question. Question 7. Bella pays 7 payments of$5 each to a game store. She returns one game and receives $20 back. What is the change to the amount of money she has? Answer: Use negative integer to represent each payment and use positive integer to represent the amount of money she receives back. The expression you get is: 7(- 5) + 20 First, calculate the product using rules for multiplying integers: – 35 + 20 Then, find the sum using rules for adding integers: – 35 + 20 = – 15 The change to the amount of money Bella has is –$15.
Use rules for multiplying integers and rules for adding integers to find the change.

Question 8.
Ron lost 10 points seven times playing a video game. He then lost an additional 100 points for going over the time limit. What was the total change in his score?
Use negative integers to represent points he lost
The expression you get is:
7(- 10) – 100
First, calculate the product using rules for multiplying integers:
– 70 – 100
Then, find the difference using rules for subtracting integers:
– 70 – 100 = – 170
Total, change in Ron’s score was – 170 points.
Use rules for multiplying integers and rules for adding integers to find the change.

Question 9.
Ned took a test with 25 questions. He lost 4 points for each of the 6 questions he got wrong and earned an additional 10 points for answering a bonus question correctly. How many points did Ned receive or lose overall?
Negative integer represents points he lost and positive integer represents additional points he earned.
The expression you get is:
6(- 4) + 10
First, calculate the product using rules for multiplying integers:
– 24 + 10
Then, find the sum using rules for adding integers:
– 24 + 10 = – 14
Ned lost 14 points.
Use rules for multiplying integers and rules for adding integers to find how many points he received or lost

Question 10.
Mr. Harris has some money in his wallet. He pays the babysitter $12 an hour for 4 hours of babysitting. His wife gives him$10, and he puts the money in his wallet. By how much does the amount in his wallet change?
Negative integer represents the money he pays the babysitter and positive integer represents the money he gets from his wife.
The expression you get is:
4(- 12) + 10
First calculate the product using rules for multiplying integers:
-48 + 10
Then, find the sum using rules for adding integers:
– 48 + 10 = – 38
The amount changes by – $38. Use rules for multiplying integers and rules for adding integers to find by how much the amount changes. Compare the values of the two expressions using <, =, or >. Question 11. – 3(- 2) + 3 _______ 3(- 4) + 9 Answer: First expression is: – 3(- 2) + 3 First, calculate the product using rules for multiplying integers: 6+3 Then, find the sum using rules for adding integers: 6 + 3 = 9 Second expression is: 3(- 4) + 9 Calculate the product using rules for multiplying integers: – 12 + 9 Find the sum using rules for adding integers: – 12 + 9 = – 3 Compare results you got: 9 > – 3 Therefore: – 3(- 2) + 3 > 3(- 4) + 9 Use rules form multiplying integers and rules far adding integers to find the values of the expressions and then compare those values. Question 12. – 8(- 2) – 20 _______ 3(- 2) + 2 Answer: First expression is: – 8(- 2) – 20 First, calculate the product using rules for multiplying integers: 16 – 20 Then, find the difference using rules for subtracting integers: 16 – 20 = – 4 Second expression is: 3(- 2) + 2 Calculate the product using rules for multiplying integers: – 6 + 2 Find the sum using rules for adding integers: – 6 + 2 = – 4 Compare results you got: – 4 = – 4 Therefore: – 8(-2) – 20 = 3(-2) + 2 Use rules form multiplying integers and rules far adding integers to find the values of the expressions and then compare those values. Question 13. – 7(5) 9 ________ – 3(20) + 10 Answer: First expression is: – 7(5) – 9 First calculate the product using rules for multiplying integers: – 35 – 9 Then, find the difference using rules for subtracting integers: – 35 – 9 = – 44 Second expression is: – 3(20) + 10 Calculate the product using rules for multiplying integers: – 60 + 10 Find the sum using rules for adding integers: – 60 + 10 = – 50 Compare results you got: – 44 > – 50 Therefore: – 7(5) – 9 > – 3(20) + 10 Use rules form multiplying integers and rules far adding integers to find the values of the expressions and then compare those values. Question 14. – 16(0) – 3 ________ – 8(- 2) – 3 Answer: First expression is: – 16(0) – 3 First calculate the product using rules for multiplying integers: 0 – 3 Then, find the difference using rules for subtracting integers: 0 – 3 = – 3 Second expression is: – 8(- 2) – 3 Calculate the product using rules for multiplying integers: 16 – 3 Find the difference using rules for subtracting integers: 16 – 3 = 13 Compare results you got: – 3 < 13 Therefore: – 16(0) – 3 < – 8(- 2) – 3 Use rules form multiplying integers and rules far adding integers to find the values of the expressions and then compare those values. Essential Question Check-In Question 15. When you solve a problem involving money, what can a negative answer represent? Answer: There are several possible situations. A negative solution for a problem involving money can represent the amount of money that some person spent (for example shopping) or withdrew from account. It can represent by how much someone’s savings changed after payment (returning debt paying bills,…). Another possibility is that it represents how much price of some product reduced over the time. There are several possibilities. It can represent the amount of money that some person spent (for example shopping) or how much someone’s savings changed after payment, how much price of some product reduced over the time Evaluate each expression. Question 16. – 12(- 3) + 7 ____________ Answer: The expression is: – 12(- 3) + 7 First, calculate the product using rules for multiplying integers: 36 + 7 Then, find the sum using rules for adding integers: 36 + 7 = 43 Therefore: – 12(- 3) + 7 = 43 The value of the expression is 43. Use rules for multiplying integers and rules for adding integers to find the value of the expression. Question 17. – 42 ÷ (- 6) + 5 – 8 _____________ Answer: The expression is: – 42 ÷ (- 6) + 5 – 8 First, calculate the product using rules for multiplying integers: 7 + 5 – 8 Then, find the sum using rules for adding integers: 12 – 8 Finally, find the difference using rules for subtracting integers: 12 – 8 = 4 Therefore: – 42 ÷ (- 6) + 5 – 8 = 4 The value of the expression is 4. Use rules for dividing, adding and subtracting integers to find the value of the expression. Question 18. 10(- 60) – 18 _____________ Answer: The expression ¡s: 10(- 60) – 18 First calculate the product using rules for multiplying integers: – 600 – 18 Then, find the difference using rules for subtracting integers: – 600 – 18 = – 618 Therefore: 10(- 60) – 18 = – 618 The value of the expression is – 618. Use rules for multiplying integers and rules for subtracting integers to find the value of the expression. Question 19. (- 11) (- 7) + 5 – 82 _____________ Answer: The expression is: (- 11) (- 7) + 5 – 82 First calculate the product using rules for multiplying integers: 77 + 5 – 82 Then, use Associative Property and rules for adding integers: 82 – 82 Finally, find the difference using rules for subtracting integers: 82 – 82 = 0 Therefore: (- 11) (- 7) + 5 – 82 = 0 The value of the expression is 0. Use rules for multiplying, adding and subtracting integers to find the value of the expression. Question 20. 35 ÷ (- 7) + 6 ___________ Answer: The expression is: 35 ÷ (- 7) + 6 First calculate the quotient using rules for dividing integers: – 5 + 6 Then, find the sum ‘using rules for adding integers: – 5 + 6 = 1 Therefore: 35 ÷ (- 7) + 6 = 1 The value of the expression is 1. Use rules for dividing integers and rules for adding integers to find the value of the expression. Question 21. – 13(- 2) – 16 – 8 _____________ Answer: The expression is: – 13 (- 2) – 16 – 8 First calculate the product using rules for multiplying integers: 26 – 16 – 8 Then, use Associative Property and rules for subtracting integers: 10 – 8 Finally, find the difference using rules for subtracting integers: 10 – 8 = 2 Therefore: – 13(- 2) – 16 – 8 = 2 The value of the expression is 2. Use rules for multiplying integers and rules for subtracting integers to find the value of the expression Question 22. Multistep Lily and Rose are playing a game. In the game, each player starts with O points and the player with the most points at the end wins. Lily gains 5 points two times, loses 12 points, and then gains 3 points. Rose loses 3 points two times, loses 1 point, gains 6 points, and then gains 7 points. a. Write and evaluate an expression to find Lily’s score. Answer: The expression that represents lily’s score 5: 2(5) – 12 + 3 First, calculate the product using rules for multiplying integers: 10 – 12 + 3 Then, use Commutative Property and rules for adding integers: 10 + 3 – 12 13 – 12 Finally, find the difference using rules for subtracting integers: 13 – 12 = 1 Lily’s score is 1 point b. Write and evaluate an expression to find Rose’s score. Answer: The expression that represents Rose’s score is: 2(-3) – 1 + 6 + 7 First calculate the product using rules for multiplying integers: – 6 – 1 + 6 + 7 Then, use Associative Property and rules for subtracting and adding integers: (- 6 – 1) + (6 + 7) – 7 + 13 Finally, find the sum using rules for adding integers: – 7 + 13 = 6 Rose’s score is 6 points. c. Who won the game? Answer: Compare results to find who won the game: 1 < 6 Rose won the game. Use rules for multiplying, adding and subtracting integers to calculate their scores and compare results to find who won the game. Write an expression from the description. Then evaluate the expression. Question 23. 8 less than the product of 5 and – 4 Answer: The expression a less than b represents a value of b less a: b – a so you get: 5(- 4) – 8 First, calculate the product using rules for multiplying integers: – 20 – 8 Then, find the difference using rules for subtracting integers: – 20 – 8 = – 28 Therefore: 5(- 4) – 8 = – 28 The value of the expression 5(- 4) – 8 is – 28. The expression a less than b represents a value of b less a: b – a. Use rules for multiplying and subtracting integers to find the value. Question 24. 9 more than the quotient of – 36 and – 4. Answer: The expression more than indicates addition so you get: First calculate the quotient using rules for dividing integers: 9 + 9 Then, find the sum using rules for adding integers: 9 + 9 = 18 Therefore: (- 36) ÷ (- 4) + 9 = 18 The value of the expression (- 36) + (- 4) + 9 is 18 The expression ‘more than’ indicates addition. Use rules for dividing integers and rules for adding integers to find the value Question 25. Multistep Arleen has a gift card for a local lawn and garden store. She uses the gift card to rent a tiller for 4 days. It costs$35 per day to rent the tiller. She also buys a rake for $9. a. Find the change to the value on her gift card. Answer: Use negative integer to represent how much renting a tiller costs and subtract integer that represents price of a rake. The expression you get is: 4(- 35) – 9 First, calculate the product using rules for multiplying integers: – 140 – 9 Then, find the difference using rules for subtracting integers: – 140 – 9 = – 149 The change to the value is –$149.

b. The original amount on the gift card was $200. Does Arleen have enough left on the card to buy a wheelbarrow for$50? Explain.
Add the change to the value you got, – $149. to the original amount on gift card,$200. to find how much money Arleen has left on the card.
The expression you get is:
200 + (- 149)
Find the sum using rules for adding integers;
200 + (- 149) = 51
She has $51 left on the card. Now, compare that amount with the price of a wheelbarrow,$ 50;
51 > 50
Arleen has enough money left on the card because she has $51 left on it after renting tiller and buying rake. Use rules for multiplying, subtracting and adding integers to find the change to the value. Question 26. Carlos made up a game where, in a deck of cards, the red cards (hearts and diamonds) are negative and the black cards (spades and clubs) are positive. All face cards are worth 10 points, and number cards are worth their value. a. Samantha has a king of hearts, a jack of diamonds, and a 3 of spades. Write an expression to find the value of her cards. Answer: Represent king of hearts with – 10, jack of diamonds with – 10 and 3 of spades with 3. The expression you get is: 2(- 10) + 3 First, calculate the product using rules for multiplying integers: – 20 + 3 Then, find the sum using rules for adding integers: – 20 + 3 = – 17 The value of Samantha’s cards is – 17. b. Warren has a 7 of clubs, a 2 of spades, and a 7 of hearts. Write an expression to find the value of his cards. Answer: Represent 7 of clubs with 7, 2 of spades with 2 and 7 of hearts with – 7. The expression you get is: 7 + 2 – 7 Use Associative Property and rules for adding integers: 9 – 7 Then, find the sum using rules for adding integers: 9 – 7 = 2 The value of Warren’s cards is 2. c. If the greater score wins, who won? Answer: Compare their scores to find who won the game: – 17 < 2 Therefore, Warren won the game. d. If a player always gets three cards, describe two different ways to receive a score of 7. Answer: One possibility is that the player gets a king of clubs, a 5 of hearts and a 2 of spades. The expression that represents the value of his cards is: 10 – 5 + 2 Use rules for subtracting and adding integers to calculate the value: 10 – 5 + 2 = 7 Another possibility is that the player gets a 4 of diamonds, a jack of clubs and a 1 of spades. The expression that represents the value of his cards is: – 4 + 10 + 1 Use rules for adding integers to calculate the value: – 4 – 10 + 1 = 7 Another possibility is that he gets a 4 of diamonds, a jack of clubs and a 1 of spades. H.O.T. Focus On Higher Order Thinking Question 27. Represent Real-World Problems Write a problem that the expression 3(-7) – 10 + 25 = – 6 could represent. Answer: Jenny wants to buy three shirts that cost$7 each and a pair of jeans that costs $10 She has$25 in her wallet Does she have enough money to buy everything she wants?
Use negative integers to represent prices of clothes and positive integer for the amount of money she has.
The expression you get is:
3(- 7) – 10 + 25
First, find the product using rules for multiplying integers:
– 21 – 10 + 25
Use Associative Property and rules for subtracting integers:
– 31 + 25
Find the sum using rules for adding integers:
– 31 + 25 = – 6
Jenny doesn’t have enough money because she has $6 less than total cost,$31.

Jenny wants to buy three shirts that cost $7 each and a pair of jeans that costs$10. She has $25 in her wallet. Does she have enough money to buy everything she wants? Jenny doesn’t have enough money because she has$6 less than total cost, \$31.

Question 28.
Critique Reasoning Jim found the quotient of two integers and got a positive integer. He added another integer to the quotient and got a positive integer. His sister Kim says that all the integers Jim used to get this result must be positive. Do you agree? Explain.
His sister is wrong.
One possibility is that Jim found the quotient of two negative integers and added positive integer to that quotient.

Since the quotient of two negative integers is positive, the sum of two positive integers would be positive.

Another possibility is that he found the quotient of two negative integers and added negative integer with condition that the absolute value of the negative integer he added is lesser than the absolute value of the quotient.

Since absolute value of positive integer (the quotient of two negative integers is positive)
is greater than the absolute value of the negative integer, the sum of those two integers would be positive.

He could also find the quotient of two positive integers and added negative integer with condition that the absolute value of the negative integer he added is lesser than the absolute value of the quotient.

Since absolute value of positive integer (the quotient of two positive integers is positive)
is greater than the absolute value of the negative integer, the sum of those two integers would be positive.

Question 29.
Persevere in Problem Solving Lisa is standing on a dock beside a lake. She drops a rock from her hand into the lake. After the rock hits the surface of the lake, the rock’s distance from the lake’s surface changes at a rate of -5 Inches per second. If Lisa holds her hand 5 feet above the lake’s surface, how far from Lisa’s hand is the rock 4 seconds after it hits the surface?
First note that 1 feet is equal to 12 inches
so the product:
5 × 12 = 60
shows that 5 feet is equal to 60 inches.
The expression
4(-5) – 60
represents how far from her hand the rock is.
First find the product using rules for multiplying integers:
– 20 – 60
Then, find the difference using rules for subtracting integers:
– 20 – 60 = -80
The rock is 80 inches far from Lisa’s hand.

The rock is 80 inches far from Lisa’s hand 4 seconds after it hits the surface of the Lake
Use rules for multiplying and subtracting integers to find the solution and the fact that 1 feet is equal to 12 inches.

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