Maharashtra Board Class 6 Maths Chapter 3 Integers Set 4 Solutions

Question 1. Classify the following numbers as positive numbers and negative numbers. -5, +4, -2, 7, +26, -49, -37, 19, -25, +8, 5, -4, -12, 27
Answer:

In simple words: Positive numbers are those greater than zero, often indicated by a '+' sign or no sign at all, while negative numbers are less than zero and always have a '-' sign. Classifying them involves recognizing these signs.

🎯 Exam Tip: Pay close attention to the '+' and '-' signs to correctly categorize numbers as positive or negative. Numbers without a sign are inherently positive.

Question 2. Given below are the temperatures in some cities. Write them using the proper signs.
Answer:

In simple words: Temperatures below 0°C are represented with a negative sign, while temperatures above 0°C are represented with a positive sign. This helps differentiate between cold and hot conditions relative to freezing point.

🎯 Exam Tip: Remember that "below 0°C" means a negative temperature, and "above 0°C" means a positive temperature. Accurately applying these signs is crucial for representing temperature data.

Question 3. Write the numbers in the following examples using the proper signs.
(1) A submarine is at a depth of 512 meters below sea level.
(2) The height of Mt Everest, the highest peak in the Himalayas, is 8848 meters.
(3) A kite is flying at a distance of 120 meters from the ground.
(4) The tunnel is at a depth of 2 meters under the ground.
Answer:
(1) A submarine is at a depth of -512 meters from sea level.
(2) The height of Mt Everest, the highest peak in the Himalayas is +8848 meters.
(3) A kite is flying at a distance of +120 meters from the ground.
(4) The tunnel is at a depth of -2 meters from the ground.
In simple words: Locations below a reference point (like sea level or ground) are expressed with negative numbers, while locations above a reference point are expressed with positive numbers. This convention helps describe positions relative to a zero point.

🎯 Exam Tip: Understand that "below" or "under" implies a negative value, and "height" or "above" implies a positive value. Correctly assigning signs is key to representing real-world situations with integers.

Maharashtra Board Class 6 Maths Chapter 3 Integers Practice Set 4 Intext Questions And Activities
 

Question 1. Take warm water in one beaker, some crushed ice in another and a mixture of salt and crushed ice in a third beaker. Ask your teacher for help in measuring the temperature of the substance in each of the beakers using a thermometer. Note the temperatures. (Textbook pg. no. 13)
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र तीन बीकर दिखाता है। पहले बीकर में गर्म पानी है, दूसरे बीकर में कुचली हुई बर्फ है, और तीसरे बीकर में कुचली हुई बर्फ और नमक का मिश्रण है। यह छात्रों को तापमान के विभिन्न प्रभावों को समझने में मदद करता है।
Answer: (Students should attempt this activity on their own)
In simple words: This activity demonstrates how different substances (warm water, ice, and a salt-ice mixture) have different temperatures, which can be measured using a thermometer. It highlights the concept of varying temperature values.

🎯 Exam Tip: While this is an activity, understanding that ice-salt mixtures achieve lower temperatures than plain ice is an important concept. Be prepared to discuss temperature differences in such scenarios.

Question 2. Look at the picture of the kulfi man. Why do you think he keeps the kulfi moulds in a mixture of salt and ice? (Textbook pg. no. 14)
ℹ️ चित्र व्याख्या (Diagram Explanation): इस चित्र में एक कुल्फी वाला अपनी ठेले पर कुल्फी के सांचों को बर्फ और नमक के मिश्रण में रखता हुआ दिखाया गया है। यह दर्शाता है कि कुल्फी को ठंडा और जमा हुआ रखने के लिए इस मिश्रण का उपयोग कैसे किया जाता है।
Answer: Kulfi man keeps the kulfi moulds in a mixture of salt and ice because such a mixture helps in keeping the kulfi cool for a longer period of time. The kulfi kept in the said mixture relatively takes more time to melt. This mixture is Considered ideal as it has the temperature of -4°C as against the temperature of ice i.e. 0°C.
In simple words: A mixture of salt and ice creates a much colder temperature than ice alone (around -4°C compared to 0°C), which keeps the kulfi frozen for longer, preventing it from melting quickly. This is due to the freezing point depression effect of salt.

🎯 Exam Tip: This question tests your understanding of freezing point depression. Remember that adding salt to ice lowers its melting point, creating a colder mixture ideal for preserving frozen items like kulfi.

Question 3. My class, i.e. Std. VI, is a part of my school. My school is in my town. My town is a part of a taluka. In the same way, the taluka is a part of a district, and the district is a part of Maharashtra State. In the same way, what can you say about these groups of numbers? (Textbook pg. no. 15)
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र संख्याओं के विभिन्न समूहों को एक अंडाकार वेन आरेख के रूप में दर्शाता है। सबसे अंदर प्राकृतिक संख्याएँ (1, 2, 3...) हैं, जो पूर्ण संख्याओं (0, 1, 2, 3...) का हिस्सा हैं, और ये सभी पूर्णांकों (-1, -2, 0, 1, 2...) का हिस्सा हैं। यह संख्या प्रणालियों के पदानुक्रम को स्पष्ट करता है।
Answer: By observing the above given groups of numbers, we can infer that natural numbers are a part of whole numbers. In turn, whole numbers are a part of integers.
In simple words: Just as smaller geographical units are part of larger ones, natural numbers are a subset of whole numbers, and whole numbers are a subset of integers. This shows a hierarchical relationship between different number systems.

🎯 Exam Tip: Understand the nested relationship between natural numbers, whole numbers, and integers. Natural numbers are positive counting numbers, whole numbers include zero, and integers include all positive and negative whole numbers along with zero.