Class 7th Math Ex 1.3 Solved By PREM SIR

🟦 प्रश्नावली 1.3 | Exercise 1.3

Q1. निम्नलिखित में से प्रत्येक का मान ज्ञात कीजिए:

Let’s solve each part step by step.

(a) (–30) ÷ 10

Method 1 (Direct Division): 👉
क्योंकि एक negative number को positive number से divide करने पर result negative आता है।

Method 2 (Using sign rules): Rule:
(+ ÷ + = +)
(- ÷ + = -)
तो,

✅ Answer = -3

(b) 50 ÷ (–5)

Method 1 (Direct Division):
👉

Method 2 (Sign Rule):

(Positive ÷ Negative = Negative)

✅ Answer = -10

(c) (–36) ÷ (–9)

Method 1 (Direct):
👉

Method 2 (Rule):
Negative ÷ Negative = Positive
Toh

✅ Answer = +4

(d) (–49) ÷ (–49)

Method 1 (Same Numbers):
👉

Method 2 (Trick):
Kisi bhi number ka same negative se division hamesha +1 hota hai.
(-x ÷ -x = +1)

✅ Answer = +1

(e) 13 ÷ [–(–2) + 1]

Step by Step Method 1:
First solve the bracket:
–(–2) = +2
So:
13 ÷ (2 + 1) = 13 ÷ 3

❗ Yeh 13 ÷ 3 = 4.33 (decimal)
Par yeh answer fractions mein acceptable hoga.

Method 2 (Fraction form):

✅ Answer = 13/3 or approx. 4.33

(f) 0 ÷ (–12)

Method 1:
Zero ko kisi bhi number se divide karo (except zero), answer hamesha 0 hota hai.
👉

Method 2 (Rule):
0 ÷ x = 0 (Jab x ≠ 0)

✅ Answer = 0

Q2. निम्नलिखित अभिव्यक्तियों में से प्रत्येक को हल कीजिए:

(i) [–6] ÷ 3

Method 1:

Method 2 (Sign rule):
Negative ÷ Positive = Negative
Toh

✅ Answer = -2

(ii) {[(–6) + 5]} ÷ [–(–2) + 1]

Step-by-step Method 1:

Inner bracket: (–6) + 5 = –1
Next: –(–2) = +2 → +2 + 1 = 3
So, expression becomes: –1 ÷ 3 = –1/3

Method 2 (Direct substitution):
— keep as a fraction.

✅ Answer = –1/3

Q3. निम्नलिखित रिक्त स्थानों में उपयुक्त संख्याएँ भरिए:

Let’s fill in the blanks:

(a) –206 ÷ ____ = 1

✅

(b) ____ ÷ –1 = 87

⇒ Blank = –87 ✅

(c) –87 ÷ ____ = 87

Only possible if ÷ –1
✅

(d) ____ ÷ 87 = –1

Only possible if numerator = –87
✅

(e) ____ ÷ 1 = –87

Answer = –87 ✅

(f) ____ ÷ 48 = –1

Answer = –48 ✅

(g) 20 ÷ ____ = –2

Answer = –10 ✅ (Because 20 ÷ –10 = –2)

(h) ____ ÷ (4) = –3

Answer = –12 ✅ (Because –12 ÷ 4 = –3)

Q4. पाँच ऐसे पूर्णांक युग्म (a, b) लिखिए, ताकि a ÷ b = –3 हो।

Hum aise numbers chahte hain jinka division –3 aaye.

Formula/Rule:
a ÷ b = –3
Toh a = –3 × b

Let’s take some examples:

a = –6, b = 2 → –6 ÷ 2 = –3
a = 6, b = –2 → 6 ÷ –2 = –3
a = –9, b = 3 → –9 ÷ 3 = –3
a = 9, b = –3 → 9 ÷ –3 = –3
a = –15, b = 5 → –15 ÷ 5 = –3

✅ Final Pairs:
(–6, 2), (6, –2), (–9, 3), (9, –3), (–15, 5)

✅ प्रश्न 5.

प्रश्न (Q):
दोपहर 12 बजे तापमान शून्य से 10°C ऊपर था। यदि यह आधी रात तक 2°C प्रति घंटे की दर से कम होता है, तो किस समय तापमान शून्य से 8°C नीचे होगा? आधी रात को तापमान क्या होगा?

🔍 समझो (Understand the situation):

12 बजे दिन में तापमान = +10°C
तापमान हर घंटे 2°C कम हो रहा है (decreasing)
हमें वो समय निकालना है जब तापमान –8°C हो जाएगा
और साथ में यह भी पता करना है कि 12 बजे रात (midnight) को कितना तापमान होगा

➡️ Method 1: Table Method

Starting at +10°C, temperature drops 2°C per hour:

Time	Temp (°C)
12 PM	+10
1 PM	+8
2 PM	+6
3 PM	+4
4 PM	+2
5 PM	0
6 PM	–2
7 PM	–4
8 PM	–6
9 PM	–8 ✅

🟢 Answer 1: शाम 9 बजे तापमान –8°C होगा

Now, how much will temp be at midnight (12 AM)?

From 12 PM to 12 AM = 12 hours
So drop = 12 × 2 = 24°C
Starting from 10°C → Final temp = 10 – 24 = –14°C

🟢 Answer 2: आधी रात को तापमान –14°C होगा

➡️ Method 2: Equation Method

Let time = x hours after 12 noon
Then,
Final Temp = 10 – 2x
Set this to –8:
→ 10 – 2x = –8
→ –2x = –18
→ x = 9

🟢 Answer 1: 9 घंटे बाद = रात 9 बजे

To find temp at 12 AM (x = 12):
Temp = 10 – 2×12 = –14°C
🟢 Answer 2: –14°C

✅ प्रश्न 6.

Q: एक टेस्ट में सही उत्तर पर +3 अंक, गलत पर –2 अंक, न दिए गए उत्तर पर 0 अंक मिलते हैं।
(i) रवीना को 20 अंक मिले। उसने 8 उत्तर सही दिए, कितने गलत दिए होंगे?
(ii) मोहिनी को –5 अंक मिले। उसने 3 उत्तर सही दिए, कितने गलत दिए?

➡️ Method 1 (Using Equation)

🔷 Part (i)

Let गलत उत्तर = x

Ravina’s score = 20
Correct answers = 8 → 8 × 3 = 24
Wrong = x → x × (–2) = –2x

Total = 24 – 2x = 20
Solve:
24 – 2x = 20
→ –2x = –4
→ x = 2

🟢 Answer: रवीना ने 2 उत्तर गलत दिए

🔷 Part (ii)

Let गलत उत्तर = y

Mohini’s score = –5
Correct = 3 × 3 = 9
So:
9 – 2y = –5
→ –2y = –14
→ y = 7

🟢 Answer: मोहिनी ने 7 उत्तर गलत दिए

➡️ Method 2 (Trial & Error)

Part (i) Ravina:

Correct = 8 → 8×3 = 24
Try wrong = 2 → 24 – (2×2) = 20 ✅

Part (ii) Mohini:

Correct = 3 → 3×3 = 9
Try wrong = 7 → 9 – (7×2) = 9 – 14 = –5 ✅

✅ प्रश्न 7.

Q: एक सुरंग 6 मीटर प्रति मिनट की दर से नीचे जाती है। यदि शुरुआत भूमि तल से 10 मीटर ऊपर से होती है, तो –350 मीटर की गहराई पर पहुंचने में कितना समय लगेगा?

➡️ Method 1: Using Equation

Start height = +10 m
Final depth = –350 m

Total distance to cover =
= 10 (upar se ground tak) + 350 (ground se neeche)
= 360 meters

Speed = 6 m/min
Time = Distance ÷ Speed = 360 ÷ 6 = 60 min

🟢 Answer: 60 मिनट लगेंगे

➡️ Method 2: Using number line or logic

From +10 to 0 = 10 m
Then 0 to –350 = 350 m
Total = 10 + 350 = 360 m
At 6 m/min, time = 360 ÷ 6 = 60 min

🟢 Answer: 1 घंटा या 60 मिनट

✅ Chapter 1 – पूर्णांक (Integers) | MCQ Questions with Answers

🔹 Q1. –25 ÷ 5 = ?

(a) –5
(b) +5
(c) 0
(d) –20

✅ Answer: (a) –5
Explanation: Negative ÷ Positive = Negative

🔹 Q2. What is the result of (–36) ÷ (–9)?

(a) –4
(b) 4
(c) –27
(d) 27

✅ Answer: (b) 4
Trick: Negative ÷ Negative = Positive

🔹 Q3. What will be the value of: 0 ÷ (–12)?

(a) –12
(b) 0
(c) Undefined
(d) 1

✅ Answer: (b) 0
Rule: Zero divided by any non-zero number = 0

🔹 Q4. Which of the following is the correct pair (a, b) so that a ÷ b = –3?

(a) (9, 3)
(b) (6, 2)
(c) (–9, 3)
(d) (–6, –2)

✅ Answer: (c) (–9, 3)
Explanation: –9 ÷ 3 = –3

🔹 Q5. 369 ÷ ____ = 369

(a) 0
(b) –1
(c) 1
(d) –369

✅ Answer: (c) 1
Rule: Any number ÷ 1 = That number

🔹 Q6. Which of the following is true?

(a) –100 ÷ 10 = –10
(b) –100 ÷ –10 = –10
(c) 100 ÷ –10 = 10
(d) –100 ÷ 5 = +20

✅ Answer: (a) –100 ÷ 10 = –10
Explanation: Negative ÷ Positive = Negative

🔹 Q7. Which of the following will result in a positive number?

(a) –25 ÷ 5
(b) –36 ÷ –6
(c) 18 ÷ –3
(d) –45 ÷ 5

✅ Answer: (b) –36 ÷ –6
Rule: Negative ÷ Negative = Positive

🔹 Q8. Mohini scored 3 correct answers (+3 each) and total marks = –5. How many wrong answers (–2 each) she gave?

(a) 3
(b) 5
(c) 7
(d) 6

✅ Answer: (c) 7
Explanation: 3×3 = 9, Let x wrong answers → 9 – 2x = –5 → x = 7

🔹 Q9. If temperature decreases 2°C per hour, and it was 10°C at noon, when will it be –8°C?

(a) 6 PM
(b) 8 PM
(c) 9 PM
(d) 10 PM

✅ Answer: (c) 9 PM
Explanation:
From +10 to –8 = Drop of 18°C → 18 ÷ 2 = 9 hours → 12 PM + 9 = 9 PM

🔹 Q10. What is the result of (–48) ÷ (–1)?

(a) 48
(b) –48
(c) 0
(d) 1

✅ Answer: (a) 48
Explanation: Negative ÷ Negative = Positive

🎁 Bonus Trick:

🧠 Sign Rules for Division:

- ÷ + = +
– ÷ – = +
- ÷ – = –
– ÷ + = –