# Exercise

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## Exercise 1.1 (7th grade chapter 1)

**1.Write down a pair of integers whose:**

(a) sum is –7 :

1.

2.

(b) difference is –10 :

1.

2.

(c) sum is 0

1.

2.

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**2.(a) Write a pair of negative integers whose difference gives 8 :**

1.

**(b) Write a negative integer and a positive integer whose sum is –5 .**

1.

**(c) Write a negative integer and a positive integer whose difference is –3.**

1.

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**3. In a quiz, team A scored – 40, 10, 0 and team B scored 10, 0, – 40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order?**

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**4. Fill in the blanks to make the following statements true:**

(i) (–5) + (– 8) = (– 8) + (

(ii) –53 +

(iii) 17 + (

(iv) [13 + (– 12)] + (

(v) (– 4) + [15 + (–3)] = [– 4 + 15] + (

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## Exercise 1.2 (7th grade chapter 1)

**1. Find each of the following products:**

(a) (–316) × (–1) =

(b) (–15) × 0 × (–18) =

(c) 9 × (–3) × (– 6) =

(d) (–1) × (–2) × (–3) × 4 =

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**2. Verify the following:**

(a) 18 × [7 + (–3)] = [18 × 7] + [18 × (–3)] =

(b) (–21) × [(– 4) + (– 6)] = [(–21) × (– 4)] + [(–21) × (– 6)] =

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**3. For any integer a,**

(i)what is **(–1) × a** equal to =

(ii) Determine the integer whose product with (–1) is:

(a) –22 =

(b) 37 =

(c) 0 =

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**4. Starting from (–1) × 5, write various products showing some pattern to show (–1) × (–1) = 1.**

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## Exercise 1.3 (7th grade chapter 1)

**1. Evaluate each of the following:**

(a) (–30) ÷ 10 =.

(b) (–36) ÷ (–9) =

(c) 13 ÷ [(–2) + 1] =

(d) (–31) ÷ [(–30) + (–1)] =

(e) [(– 6) + 5] ÷ [(–2) + 1] =

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**2. Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c.**

(a) a = 12, b = – 4, c = 2

- Now,Let us take LHS =
a ÷ b + c - Given a=
; b = ; c = - Subtitute the values of a,b,c in LHS
- LHS =
- repeat the same with RHS =
a ÷ b + a ÷ c - Subtitute the values of a,b,c in RHS
- RHS =
+ - RHS =
- RHS
LHS

**(b) a = (–10), b = 1, c = 1**

- Now, let's try out the second case
- Now,Let us take LHS =
a ÷ b + c - Given a =
; b = ; c = - Subtitute the values of a,b,c in LHS
- LHS=
- repeat the same with RHS=
a ÷ b + a ÷ c - Subtitute the value s of a,b,c in RHS
- RHS=
+ - RHS=
- RHS
LHS

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**3. Fill in the blanks:**

(a) 369 ÷

(b) (–75) ÷

(c) (–206) ÷

(d) – 87 ÷

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**4. Write five pairs of integers (a, b) such that a ÷ b = –3. One such pair is (6, –2) because 6 ÷ (–2) = (–3).(multiple choice)**

pair | a | b | a÷b |
---|---|---|---|

1 | -6 | -3 | |

2 | 9 | -3 | |

3 | -15 | -3 | |

4 | 21 | -3 | |

5 | -24 | -3 |

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**5. The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight:**

**a.At what time would the temperature be 8°C below zero?**

Determine Time to Reach -8°C.

Initial Temperature:10°C

Desired Temperature:-8°C

Total Temperature Change Needed:

ΔT=-8°C-10°C=

Rate of decrease:

Time to Reach -8°C:

t=ΔT/Rate

ss=

Time Calculation:

12noon + 9hours=

Therefore, the temperature will be -8°C at 9 PM.

**b.What would be the temperature at mid-night?(reveal next)**

**Solution:**

Hours from 9 PM to Midnight:

Midnight-9PM =

Additional Temperature Decrease:

Decrease=3hours×-2°C/hour=

Temperature at Midnight:

Temperature at 9 PM + Additional Decrease = -8°C + (-6°C) =

Therefore,The temperature at midnight will be -14°C.

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**6. In a class test (+ 3) marks are given for every correct answer and (–2) marks are given for every incorrect answer and no marks for not attempting any question.**

**(i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly?**

**Solution:**

Given scoring rules:

Correct Answer:

Incorrect Answer:

Unattempted Question:

We'll set up equations to find the number of incorrectly attempted questions.

(i) Radhika's Score

Total Marks:

Correct Answers:

Incorrect Answers: 𝑥

The equation for the total score is:

Total Score=(Correct Answers×3)+(Incorrect Answers×−2)

Substitute the values:

20=

Solve for 𝑥:

20=

Rearrange to isolate 𝑥:

20−36=−2x

x =

**Therefore,Radhika attempted 8 questions incorrectly.**

**(ii) Mohini scores –5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly?(reveal)**

**Solution:**

Mohini's Score:

Total Marks:

Correct Answers:

Incorrect Answers: y

The equation for the total score is:

Total Score=(Correct Answers×3)+(Incorrect Answers×−2)

Substitute the values:

Solve for y:

-5 =

Rearrange to isolate y:

-5 = 21 −2y

−26 = −2y

y = -26/-2 =

**Therefore,Mohini attempted 13 questions incorrectly.**

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**7. An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach – 350 m.**

**Solution:**

**Step 1:** Calculate the Total Distance to be Covered

**Initial Position:** 10 meters above ground level.

**Final Position:** -350 meters below ground level.

**Total Distance:** The total distance d is the sum of the distance to the ground level and the distance below ground level.

d=

**Step 2:** Calculate the Time Required to Descend.

**Rate of Descent:** 6 meters per minute

**Total Distance to Cover:** 360 meters.

**Time Required:** Time t can be found using the formula:

t=

t=

**Therefore,it will take 60 minutes for the elevator to descend to −350 meters.**