The World of Numbers • Class 9 Mathematics • Ganita Manjari
Practice Mode: पहले question खुद solve करें। समझ न आए तो 🇮🇳 हिंदी में समझें दबाएँ। उसके बाद Solution देखें से diagram और पूरा solution check करें.
Focus: Integers, positive/negative numbers, Brahmagupta's laws और real-life applications.
Question 1
Temperature in Ladakh
The temperature in the high-altitude desert of Ladakh is recorded as 4°C at noon. By midnight, it drops by 15°C. What is the midnight temperature.
हिंदी में समझें:Drop means subtract. Starting temperature = 4°C. Therefore 4 − 15 = −11°C. The number line shows movement 15 units to the left from 4.
Step-by-Step Solution:
Visual: इस diagram को देखकर positive और negative quantities की direction/meaning समझें।
Drop means subtract. Starting temperature = 4°C. Therefore 4 − 15 = −11°C. The number line shows movement 15 units to the left from 4.
✅ Final Answer: −11°C
Question 2
Debt, Profit and Loss
A spice trader takes a loan (debt) of ₹850. The next day, he makes a profit (fortune) of ₹1,200. The following week, he incurs a loss of ₹450. Write this sequence as an equation using integers and calculate his final financial standing.
हिंदी में समझें:Debt = −₹850, profit = +₹1200, loss = −₹450. Equation: (−850) + 1200 + (−450) = 350 − 450 = −100. A negative final balance means a debt.
Step-by-Step Solution:
Visual: इस diagram को देखकर positive और negative quantities की direction/meaning समझें।
Debt = −₹850, profit = +₹1200, loss = −₹450. Equation: (−850) + 1200 + (−450) = 350 − 450 = −100. A negative final balance means a debt.
✅ Final Answer: −₹100, i.e. a debt of ₹100
Question 3
Brahmagupta's Laws
Calculate the following using Brahmagupta’s laws: (i) (−12) × 5 (ii) (−8) × (−7) (iii) 0 − (−14) (iv) (−20) ÷ 4.
हिंदी में समझें:(i) Negative × positive = negative, so (−12)×5 = −60. (ii) Negative × negative = positive, so (−8)×(−7)=56. (iii) Subtracting a negative adds the positive: 0−(−14)=14. (iv) Negative ÷ positive = negative, so (−20)÷4=−5.
Step-by-Step Solution:
Visual: इस diagram को देखकर positive और negative quantities की direction/meaning समझें।
(i) Negative × positive = negative, so (−12)×5 = −60. (ii) Negative × negative = positive, so (−8)×(−7)=56. (iii) Subtracting a negative adds the positive: 0−(−14)=14. (iv) Negative ÷ positive = negative, so (−20)÷4=−5.
✅ Final Answer: (i) −60 (ii) 56 (iii) 14 (iv) −5
Question 4
Subtracting a Negative
Explain, using a real-world example of debt, why subtracting a negative number is the same as adding a positive number, for example 10 − (−5) = 15.
हिंदी में समझें:Think of −₹5 as a debt of ₹5. Starting with ₹10, if we remove or cancel a debt of ₹5, your financial position increases by ₹5. Hence 10 − (−5) = 10 + 5 = 15.
Step-by-Step Solution:
Visual: इस diagram को देखकर positive और negative quantities की direction/meaning समझें।
Think of −₹5 as a debt of ₹5. Starting with ₹10, if we remove or cancel a debt of ₹5, your financial position increases by ₹5. Hence 10 − (−5) = 10 + 5 = 15.