Operations with Rational Numbers and Integers Math A College Prep
Module #2 Homework 2016 - 2017
Created in collaboration with Utah Middle School Math Project A University of Utah Partnership Project
San Dieguito Union High School District
2.1A Homework: Additive Inverse in Context and Chip/Tile Model* Name:
Period:
Fill in the table below.
Context
1. The Helium atom had two protons and two electrons.
Model/Picture
Net Result in Words
How Many Zero Pairs?
-
2. The treasure map said to take ten steps north, then eight steps south.
3. Jen earned $6 working in the garden, and then she spent $5 on a toy.
4. The elevator started on the 8th floor, went up five floors, and then went down two floors.
SDUHSD Math A College Prep Module #2 – HOMEWORK 2016-2017
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Circle the operation you will be performing. Draw a chip/tile model for each sum. Record the sum. For the following exercises, use the key below: =1
= –1
5. 7 + (–4)
6. –3 + 8
7. 4 + 6
8. –5 + 8
9. –4 + (–2)
10. –6 + (–3)
11. 7 + (–6)
12. 4 + (–8)
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13. Suppose a + b = c. Can c be less than zero (c < 0)? Explain. a. What must you know about a and b relative to each other?
b. What must you know about a and b relative to c?
Spiral Review For #14-19, answer the following questions. 14. Which number is less? 15. Which number is more? -27 or -36 -85 or -89
16. Which number is less? -78 or -44
17. Which number is more? -49 or -53
19. Which number is more? -91or 0
18. Which number is less? -52 or -53
For #20-21, simplify each expression without the use of a calculator. 20. 40 ÷ 1 + 3 − 3×7 + 7 − 5 21. 1 − 5 + 1×(4×4 − 31)×8
For #22-24, find each using a bar model. 22. 8 is 25% of what number? 23. What percent of 40 is 30?
SDUHSD Math A College Prep Module #2 – HOMEWORK 2016-2017
24. What is 40% of 60?
4
2.1B Homework: Adding Integers Using a Number Line* Name:
Period:
Circle the operation you are going to perform. Model the following expressions using a number line and write the answer. 1.
–7 + 5
2.
9 + (– 9)
4.
–15 + (–4)
5.
11 + 9
6.
7 + (–16)
3.
–11 + (–5)
SDUHSD Math A College Prep Module #2 – HOMEWORK 2016-2017
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7.
You borrowed $25 from your mom to buy clothes. A week later you repaid her $13. a. Write an addition expression to show how much money YOU owe.
b. Label the number line and model the expression.
c. Write your answer in context using a complete sentence.
8.
Given the following addition expression: – 15 + 18 a. Write a context (your own word problem) for the expression.
b. Model the context using the number line.
c. Simplify your expression.
d. Write your answer in context using a complete sentence.
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Circle the operation you are going to perform. Model each integer addition problem with chips/tiles AND with a number line. Record the sum. Chips/Tiles 9.
Number Line
5+8
10. – 4 + (– 3)
11. 7 + (– 9)
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Circle the operation you are going to perform. Draw a chip/tile model or number line model for each. Record the sum. 12. 4 + (– 4)
13. – 3 + 11
14. – 3 + (– 3)
15. 0 + (– 5)
16. 4 + – 3 + 5
17. – 7 + – 4 + (−3)
Write an addition expression to represent the word problem and simplify. Write your answer in context using a complete sentence. Models are optional. 18. The Golf Tournament shows that Todd’s score was 1 on his first round and –3 on his second round. What is his total score for the first two rounds?
19. A stunt plane started a maneuver 35 feet below the top of a skyscraper. If he traveled an additional 60 feet down, where is the stunt plane compared to the top of the skyscraper?
20. What patterns have you noticed when adding integers? Explain why each pattern works. Be sure to reference zero pairs where applicable. a. 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 =____________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ b. 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 + 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 =___________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ c. 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 + 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 =___________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ SDUHSD Math A College Prep Module #2 – HOMEWORK 2016-2017
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2.1C Homework: Model Subtraction of Integers with Chips/Tiles* Name:
Period:
Circle the operation you are going to perform. Draw a chip/tile model for each and state the difference.
1. – 4 − (– 3)
2. 8 − 3
3. – 5 − 8
4. 7 − (– 7)
5. – 4 − (– 5)
6. 3 − 10
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Use a chip model to solve each of the following. Write a numerical expression that models your solution and then write a complete sentence stating your answer. 7. Nick has $6 in his bank account. After he went shopping, he looked at his account again and he had –$8. How much did he spend shopping?
8. On the first play of a possession, Drew Brees was sacked 4 yards behind the line of scrimmage. He then threw a pass for a 12 yard gain. Did the Saints get a first down? (A team must move forward 10 yards to get a first down.)
9. There is a Shaved Ice Shack on 600 South Street. Both Mary and Lina live on 600 South Street. Mary lives 5 blocks west of the shack and Lina lives 3 blocks east of it. How far apart do they live?
10. Mitchell owes his mom $11. He’s been helping around the house a lot, so his mom decided to forgive $5 of his debt. How much does he owe now?
11. Eva went miniature golfing with Taylor. Eva’s score was −4 and Taylor’s score was −2. By how many shots is Eva in the lead?
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2.1D Homework: Number Line Model for Subtraction* Name: Circle the operation you will be performing. Use the method for subtraction to model the following problems to find the difference. 1. 4 – 17
Period: Circle the operation you will be performing. Think of a number line to find the difference for each. Draw a number line if helpful. 6.
7 – (–3)
7.
8 – (–4)
8.
5 – 12
9.
6 – 18
2. 5 – (–10)
3. –7 – 6 10. 14 – 3
11. 21 – 5
4. –8 – (–9) 12. –13 – 17
13. –8 – 3
5. 9 – 4 14. –9 – (–4)
15. –2 – (–6)
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Use a number line to solve each of the following. Write a numerical expression that models your solution and then write a complete sentence stating your answer. 16. Steve found a treasure map that said to take ten steps north, then ten steps south. Where is Steve in relationship to where he started?
Spiral Review: A number line is shown below. The numbers 0 and 1 are marked on the line, as are two other numbers a and b.
2 Determine if each expression is negative or positive. Explain your reasoning. 17. 𝑎 − 1
18. 𝑎 − 2
19. 𝑎 + 𝑏
20. 𝑎 − 𝑏
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2.1E Homework: Subtraction and Integers Review* Name:
Period:
Circle the operation you will be performing. Write an equivalent addition expression for each subtraction expression, and then simplify the expression. Subtraction Expression
Addition Expression
Simplify
1. – 7 − 3 2. 6 − 11 3. 12 − (– 3) 4. – 6 − (– 8) 5. 14 − 10 6. – 2 − 7 7. – 8 − (– 10) 8. 5 − (– 9)
Circle the operation you are going to perform. Find the indicated sum or difference. Draw a number line or chip/tile model if helpful. 9. 3 − (– 9) 10. – 4 + (– 1)
11.
– 3 − (– 7)
12.
8−5
13.
4−9
14.
5 − (– 2)
15.
–3 − 4
16.
– 5 + (– 2)
17.
3 − (– 1)
18.
2−6
19.
– 5 + 10
20.
– 2 − (– 9)
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Section 2.1 Review* Name:
Period:
Read each set of directions carefully.
= 1 and
= -1. You must show ALL of your work.
1. Find the value for each labeled point on the number line. Then use the values to simplify the expression. A B C -25
-35
-15
-5
A = ______
15
5 B = ______
25
35
C = ______
d. A + B
e. A + C
f.
B–A
g. C – B
Expression:_______
Expression:_______
Expression:_______
Expression:_______
Sum:________
Sum:________
Difference:________
Difference:________
2. Which statement below is equivalent to −17 − 11? a. −11 + 17
b. −11 − 17
c. −17 + 11
d. −11 − (−17)
Explain your choice______________________________________________________________________ _____________________________________________________________________________________ 3. Complete the expressions illustrated by the three situations below.
_____ + _____ = _____
_____+ _____ = _____
_____+ _____= _____
The rule for adding two negative numbers is:
4. Complete the expressions illustrated by three situations below.
_____ + _____ = _____
_____ + _____ = _____
_____ + _____ = _____
The rule for adding two positive numbers is:
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5. Show a model that proves the following statement to be false: The sum of a positive number and a negative number is always positive.
6. Mike borrows $13 from Sara to buy a movie ticket. Mike gives Sara $5 to begin to pay back his debt. How much does Mike still owe Sara? a. Draw a chip/tile model or a horizontal or vertical number line to solve each of the following.
b. Write an addition equation to show the sum.
c. Write a complete sentence stating your answer.
7. Model and solve –3 + 6 using the number line shown below.
Write a different addition problem which has the same sum as the problem above.
8. Draw a chip/tile model for −6 − (−3) and simplify. Answer: _____ Chip/Tile Model Write a different subtraction problem which has the same difference as −6 − (−3). _____________
9. Simplify each expression. a. 12 − (−6)
b. −4 − 9
c. −17 + 5 + (−2)
SDUHSD Math A College Prep Module #2 – HOMEWORK 2016-2017
d. −3 + 12
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2.2A Homework: Multiply Integers Using a Chip Model* Name:
Period:
1. Model the following problems. State the product. Then rewrite each as an equivalent addition or subtraction expression. a) 2 ∙ 4 b) 3 ∙ (−7)
c)
(−2) ∙ 5
d)
(−7) ∙ (−1)
e)
2 ∙ (−4)
f)
(−2) ∙ (−7)
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2. What patterns have you noticed when multiplying integers? Explain any patterns you have observed from the previous page. Explain why each shortcut works. You should reference how multiplication relates to addition/subtraction and how and why you can use zero pairs. a. 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 ∙ 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 =__________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ b. 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 ∙ 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 =__________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ c. 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 ∙ 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 =_________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 3. How do the rules for multiplication above compare to the rules for addition? Are there similarities? Are there differences? _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Spiral Review For #4-7, simplify each expression without the use of a calculator. 4. 4 + 9 + 16 ÷ 4 − 8 − 3×5 5. 7×7 + 1 + 16 ÷ 8 − (6 − 7)
6.
2! − 2! ×4 − 3!
7.
(3! + 4) ÷ 5
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2.2B Homework: Rules and Structure for Multiplying & Dividing Integers* Name:
Period:
Find each product. 1. −2(3)
2. −4(−7)
3. 8(−4)
4. 9 ∙ 7
5. −3(7)
6. −12(−3)
7. 15(−3)
8. 15(4)
9. 10(−12)
10. −13(−3)
11. −1 ∙ (4)
12. −4(13)
13. −24(3)
14. 15(−8)
15. −8(7)(−3)
16. −2(5)(10)
17. 3(−8)(−4)
18. −1 ∙ (−3) ∙ (−6)
Write a multiplication expression for each situation. Write the answer in a complete sentence. 19. Karla borrowed $5 each from 4 different friends. How much money does Karla owe her friends altogether? Expression:
Answer:
20. Jim was deep sea diving last week. He descends 3 feet every minute. How many feet will he descend in 10 minutes? Expression:
Answer:
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Find each quotient. 21.
20 ÷ (−4)
22.
72 ÷ (−6)
23. −82 ÷ (−2)
24.
56 ÷ 4
25.
−54 ÷ (−6)
26.
90 ÷ (−5)
27.
−36 ÷ 9
28.
65 ÷ (−5)
29.
160 ÷ 20
30.
63 ÷ (−7)
31.
−60 ÷ (−12)
32.
28 ÷ −4
Write a division expression for each situation. Write the answer in a complete sentence. 33. Keith borrowed a total of $30 by borrowing the same amount of money from 5 different friends. How much money does Keith owe each friend? Expression:
Answer:
34. The temperature fell 12ºF over 4 hours. What was the average change in temperature per hour? Expression:
Answer:
35. Siegfried borrowed $4 a day until he had borrowed a total of $88. How many days did Siegfried borrow money? Expression:
Answer:
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Section 2.2 Review* Name:
Period:
Read each set of directions carefully. You must show ALL of your work to earn credit. 1. Draw a chip model for each multiplication. Rewrite as an equivalent repeated addition expression. 2 ∙ (−3) Rewrite 2 ∙ (−3) as an equivalent Chip Model repeated addition expression Product
2. Draw a chip model for each multiplication. Rewrite as an equivalent repeated subtraction expression. (−2) ∙ (3) Rewrite(−2) ∙ (3) as an equivalent Chip Model repeated subtraction expression Product
Find each product or quotient. 3. (– 7)(– 8)
4.
!" (!!)
5. 3 ∙ (−10)
6. (−48) ÷ (−6)
7. (– 1)(– 3)(– 7)
8. (−2) ∙ 3 ∙ (−8)
9. 36 ÷ −4
10. −56 ÷ (−4)
11. −72 ÷ 9
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Simplify. 12. – 1– 5
15. 14 + (– 8) + (– 12)
13. 72 ÷ (−6)
14. 6 − (– 4)
16. 3 − 15
17. 3(−15)
18. Explain the difference between #16 and #17 above?
Write an expression for each situation. Answer the question in a complete sentence. 19. Bryan went flying in Catalina. He ascended 40 feet every minute. How many feet will he ascend in 12 minutes? Expression:
Answer:
20. Frank paid $6 a day until he paid back $72. For how many days did he pay money? Expression:
Answer:
21. Which of the following situations could be represented by the expression (– 4) + (– 7)? Circle all that apply. a. b. c. d. e. f.
Katrina dove 4 feet down in the water and then went up 7 feet. Robert scored 4 points on Tuesday and 7 on Wednesday. Melissa made $4 at her job and spent $7 on lunch. Chloe gave 4 books to her cousin and then gave 7 books to the library. Ana bought 4 yogurt cups and gave 7 to her younger sister. Matt owes $4 to his mom and $7 to his friend.
22. Which of the following expressions are equal to –18? Circle all that apply. a. – 15 − 3 b. – 13 − (– 5) c. – 16 − 2 d. – 9 − (– 9) e. 1 − 17 f. 9 − (– 9) SDUHSD Math A College Prep Module #2 – HOMEWORK 2016-2017
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23. Big Cat started a new diet. After the first week, Big Cat lost 2 pounds. The veterinarian weighed Big Cat after the second week and noticed he had gained 2 pounds! What is Big Cat’s net weight change after two weeks?
24. Choose all of the following numerical expression(s) that result in a negative number. Circle all that apply. a. (– 12) ÷ (– 3) b. (– 50) + (– 60) c. – 15 − (– 20) d. (– 4) ∙ (– 5) e. (4) ∙ (−5)
A number line is shown below. The numbers 0 and 1 are marked on the line, as are two other numbers a and b.
3 Determine if each expression is negative or positive. Explain your reasoning. 25. 𝑎 − 2
26. −𝑏
27. 𝑎𝑏
28. 𝑎𝑏 + 1
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2.3A Homework: Number Line City* Name: Period: In Number Line City, there is one straight road. All the residents of number line city live either East (+) or West (−) of Town Hall (0). All addresses are given as positive or negative rational numbers. Mark the location (with a dot and first letter) of the following addresses on the map of Number Line City below: Betsy: −1
! !
Allyson: −2 Chris: 5
! !
! !
David: 6
Frank: 2
!
Emily: 7
!
Number Line School: 1
!
!
Town Hall: 0
!
Hannah: 6
!
!
Store: −4
!
George: −6
! !
! !
Post Office: −10
Answer the following questions. 1. How far is it from Allyson’s house to Betsy’s house? Answer: 2. How far is it from Chris’ house to Betsy’s house?
Answer: 3. How far is it from David’s house to Chris’ house?
Answer: 4. How far is it from Emily’s house to George’s house?
Answer: 5. Who lives closer to the Store, Allyson or George? Explain. Answer:
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6. The mailman leaves the post office and makes a delivery to Hannah, picks up a package from George, and then delivers the package to Frank before returning to the post office. How far did the mailman travel?
Answer:
7. Every morning, Betsy walks to Allyson’s house and they walk together to school. How far does Betsy walk each morning? How much further does Betsy walk than Allyson?
Answer:
8. Jake moves into Number Line City. He moves into a home 2 ½ units from Chris’ home. Where could Jake live?
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2.3B Homework: Adding and Subtracting Fractions Name:
Period:
Evaluate each expression. Write each answer in simplest form. ! ! ! 1. − 2. − + 0.25 !
3. 6 −
!
!
!
4. −2.75 −
!
!
!
!
!"
5. − +
7. −
!" !
+
! !
6.
8.
! !
! !
− −
!
+ −
!
! !
!
!
SDUHSD Math A College Prep Module #2 – HOMEWORK 2016-2017
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9.
−
!
− −
!
!
!
!
!
11. −3 − 4
!
!
!
15. −1
!
17. −3
!
!
!
10. −1 + −2
!
−4
! !
! !
!
!
!
!
!
!
!
!
14. 2 + −1
+ −3
!
!
12. 3 + −1
!
13. 1 + −3
!
16. −2
! !
− −1
!
!
!
!
18. 1 − −3
SDUHSD Math A College Prep Module #2 – HOMEWORK 2016-2017
! !
26
Write an expression to solve each word problem. Answer the question in a complete sentence. !
19. During the day, the temperature increases by 3 degrees in San Jose. At night, the temperature !
!
decreases by 7 degrees. What is the overall change in temperature? !
!
20. Jamal is practicing tricks on his skateboard. One trick takes him forward 6 feet then backward 8 feet, !
!
then he moves forward again for 3 feet. Overall, how far did Jamal move and in what direction? !
Spiral Review For #21-22, answer the following questions. 21. Which letter best shows -98?
A
-75
B
0
22. Which letter best shows -43?
C
-62
SDUHSD Math A College Prep Module #2 – HOMEWORK 2016-2017
D
0
27
2.3C Homework: Operations with Rational Numbers* Name:
Period:
Perform the indicated operations. Show your work. Write any fraction answers in simplest form. 1. 6 − 3.98 2. 1.8 − (−3.7)
3.
−0.8 + −7.2 − 5.4
!
!
!
!
5. − +
7.
9.
! !
! !
− −
6.
! !
+ 0.3 − 0.6
! !
11. − ∙
! !
!
13. −2 ∙ −1.75 !
4. 1.7 − −0.8 + 4.013
8.
! !
−
!
−
!
+
!
! !
!
!
10. − − (−1.4) !
12. −2 ∙
! !
14. −1.25 ∙
! !
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15. −3.6 ÷ 3
17. −3.7 ÷ 2
!
!
!
!
!
!"
!
!
16. 1 ÷ 5
!
18. − ∙ −
!
∙ 0.8
Write an expression to solve each word problem. Answer the question in a complete sentence. 19. A baby whale was weighed on Monday by his trainer. Exactly one week later, the trainer finds that the ! baby whale has gained 4 ounces each day. If the baby whale continues to gain weight at the same ! rate, how much weight did the whale gain after 7 days?
!!
!
20. To avoid a hurricane, a pilot descended mile in minute. What was the plane’s average change of !" ! altitude per minute?
!
21. The running back for the Chargers football team carried the ball 7 times for a total loss of 15 yards. ! Find the average change in field position on each run.
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2.3D Homework: Word Problems with Multiplying and Dividing Rational Numbers* Name:
Period:
For questions #1-5, do the following. a. Write an expression. b. Show your work to calculate your answer. c. Write your answer in context in a complete sentence. !
1. Fernando entered a weight-loss contest. The first week he lost 5 pounds, the next week he lost 4.59 ! pounds and the last week he lost 2.31 pounds. What was his total change in weight? Expression:
Answer: 2. A marathon is 26.2 miles. June wants to run the distance of a marathon in a month, but she thinks that ! she can only run of a mile each day. About how many days will she need to run? Will she be able to ! finish in a month? Expression:
Answer: 3. Reynold just got hired to paint fences this summer. He gets paid $0.60 for every foot of fencing that he ! paints. If Reynold paints an average of 135 feet of fencing a week, how much can he earn in 8 weeks? !
Expression:
Answer: 4. A super freezer can change the internal temperature of a 10 pound turkey by −2.4° F every 10 minutes. ! How much can the freezer change the temperature of the turkey in 3 hours? !
Expression:
Answer:
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5. I want to use a recipe for muffins that calls for 3 cups of flour and 2 eggs. If I only have 1 egg, how much flour should I use? Expression:
Answer: Spiral Review: Simplify. Be sure to show your work. !
!
!
!"
6. − +
10.
6 − 17
!
!
!
!
13.
7 − 4
16.
2 −5
!
!
!"
12.
− − −
!
!
!
1 +5
!
!
!
5 + −2
9.
15.
!
7.
!
!
!
!
∙ ∙
!
11.
!
!
!
!
!"
!
!
!
!
8.
14.
SDUHSD Math A College Prep Module #2 – HOMEWORK 2016-2017
17.
! !
!
!!
!
!
+ +
!
!
!
!
18 − 10
!! !
∙
! !
!
!
!
!
6 (−15)
31
Module 2 Review Name:
Period:
Read each of the directions carefully. You must show ALL of your work to earn credit. 1.
Based on the number line above, decide whether each of the following values is positive or negative and circle your choice. Explain your reasoning. a.) a – 2 Positive/Negative Explain: b.) – b
Positive/Negative Explain:
c.) ab + 1
Positive/Negative Explain:
For #2-3, draw a chip model for each multiplication problem. Then rewrite the multiplication expression as an equivalent addition expression. 2. 3 ∙ (2) Chip Model Equivalent addition expression Answer
3.
(−3) ∙ (2) Chip Model
Equivalent addition expression
Answer
For #4-9, simplify each expression. Write your answer in simplest form. !
!
!
!
4. −2 +
!
!
!
!
5. 16 − 9
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!
!
!
!
6. 1 +
!
!
!
!!
7. − ÷
!
8. 1 ⋅ −0.75
!
!
!
!"
9. − +
!
− 0.8
Draw a chip model and a horizontal or vertical number line for each problem, and state answer. Chips/Tiles
1. 10. 7 + (–3) 2.
Number Line 7 + (–3)
11. –8 + 5
–8 + 5
12.
–2 – (–7)
–2 – (–7)
For #13-14, draw a number line model and write your answer in a complete sentence. 13. Adam owes his brother eight dollars. His brother forgives 5 dollars of the debt. How much does Adam owe his brother?
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14. A submarine is submerged 8 feet below the surface of the water. It then dives 5 feet deeper. How many feet below the surface of the water is the submarine at this point?
For #15-21, write an expression and solve the word problem. Write your answer in a complete sentence. 15. Brandon has $76 in his bank account. After he went shopping, he looked at his account again and he had - $11. How much did he spend shopping?
!
!
!
!
16. One day you rode your bicycle for 3 hours and ran for 1 hours. How many hours did you exercise?
!
!
!
!
17. A toy maker cuts a piece of fabric 7 in long from a piece that is 9 in long. How much fabric is left?
!
!
!
18. There were three rainstorms last February. The storms dropped 3 in, 5 in, and 11 in of rain. What ! !" ! was the combined rainfall of the three storms?
SDUHSD Math A College Prep Module #2 – HOMEWORK 2016-2017
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!
!
19. Roy is hiking along a trail that is 13 miles long. He plans to stop every 2 miles. How many stops will ! ! he make?
!
20. A bread recipe calls for cup of chocolate chips. Marly wants to triple the recipe. How many cups of ! chocolate chips does she need?
21. Sammy the seal is sitting on a cliff that is 5 feet from the surface of the sea. He then dives into the sea to catch a fish that is 3 feet below the surface of the water, then he comes back up to the surface of the water. How many total feet has Sammy traveled?
SDUHSD Math A College Prep Module #2 – HOMEWORK 2016-2017
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