RBSE Solutions Class 6 Maths Chapter 4 Negative Numbers and Integers Exercise 4.1

Question 1. Write the appropriate integer according to the following -
(i) The temperature of hot water is 45°C.
(ii) A matter freezes at 10°C below 0°C.
(iii) Reena earned a profit of Rs 300 by selling book.
(iv) Withdraw Rs 500 from the bank account.
Answer:
(i) +45°C or 45°C
(ii) -10°C
(iii) +Rs 300
(iv) -Rs 500. Integers help us represent real-world situations like temperature changes or money transactions easily.
In simple words: We write positive numbers for things above zero or money coming in, and negative numbers for things below zero or money going out.

🎯 Exam Tip: Remember that "below zero" or "withdraw" indicates a negative integer, while "above zero" or "profit" indicates a positive integer.

Question 2. Represent the following on the number line.
(i) + 5
(ii) - 4
(iii) 0
(iv) - 2
Answer:
(i) +5
(ii) -4
(iii) 0
(iv) -2 When drawing a number line, ensure the tick marks are evenly spaced to accurately represent integer values.
In simple words: To show a number on a number line, draw a line with marks for whole numbers, then put a special dot or circle on the mark for the number you need to show.

🎯 Exam Tip: Always use a ruler to draw straight lines and ensure equal spacing between each integer on the number line.

Question 3. Compare the following numbers by putting the correct sign (>, <, or =).
Answer:
(i) 3 > -5
(ii) -2 > -4
(iii) 7 > -7
(iv) 0 > -3
(v) 0 < 3
(vi) 1 > -50. Remember, numbers on the right side of the number line are always greater than numbers on the left.
In simple words: Look at each pair of numbers and decide if the first one is bigger than, smaller than, or equal to the second one.

🎯 Exam Tip: When comparing negative numbers, the number closer to zero is greater. For example, -2 is greater than -4.

Question 4. Write true or false for the following statements.
(i) - 4 is located to the right side of - 3 on the number line.
(ii) Zero is a negative number.
(iii) The smallest negative integer is - 1.
(iv) 0 is located between - 1 and 1 on number line.
Answer:
(i) False. On a number line, -4 is to the left of -3, meaning -4 is smaller than -3.
(ii) False. Zero is neither a positive nor a negative number; it is a neutral integer.
(iii) False. There is no smallest negative integer, as numbers like -2, -3, and so on are smaller than -1.
(iv) True. Zero is indeed located between any negative number and any positive number, including -1 and 1.
In simple words: We check if each statement about numbers is correct or not. Remember that negative numbers get smaller as they move further away from zero.

🎯 Exam Tip: Understand the properties of zero (neither positive nor negative) and the concept of "smallest" or "largest" negative/positive integers for accurate True/False answers.

Question 5. Write the integers in ascending order between the pair of numbers given below:
(i) 0, -4
(ii) -3, -5
(iii) -2, 2
(iv) -10, -6
Answer:
(i) Integers from -4 to 0 (inclusive) are:
-4
\( \implies \) -3
\( \implies \) -2
\( \implies \) -1
\( \implies \) 0
(ii) Integers from -5 to -3 (inclusive) are:
-5
\( \implies \) -4
\( \implies \) -3
(iii) Integers from -2 to 2 (inclusive) are:
-2
\( \implies \) -1
\( \implies \) 0
\( \implies \) 1
\( \implies \) 2
(iv) Integers from -10 to -6 (inclusive) are:
-10
\( \implies \) -9
\( \implies \) -8
\( \implies \) -7
\( \implies \) -6. When listing integers in ascending order, remember to start with the smallest number and go towards the largest, especially with negative numbers.
In simple words: Find all the whole numbers that come between the two given numbers, making sure to list them from smallest to biggest.

🎯 Exam Tip: Be careful with the term "between"; usually, it means *excluding* the given numbers, but if the solution includes them, follow that pattern for consistency. Always clarify if endpoints are included or excluded.

Question 6. Write the following sets of integers in both ascending and descending order.
(i) -7, -3, 3, 5
(ii) -2, -1, 0, 3
(iii) 6, 1, 3
(iv) -5, -1, 2, 4
Answer:
(i) Given integers: -7, -3, 3, 5
Ascending order: -7, -3, 3, 5
Descending order: 5, 3, -3, -7
(ii) Given integers: -2, -1, 0, 3
Ascending order: -2, -1, 0, 3
Descending order: 3, 0, -1, -2
(iii) Given integers: 6, 1, 3
Ascending order: 1, 3, 6
Descending order: 6, 3, 1
(iv) Given integers: -5, -1, 2, 4
Ascending order: -5, -1, 2, 4
Descending order: 4, 2, -1, -5. Always remember that ascending means from smallest to largest, and descending means from largest to smallest.
In simple words: To put numbers in ascending order, arrange them from the smallest to the biggest. To put them in descending order, arrange them from the biggest to the smallest.

🎯 Exam Tip: When dealing with both positive and negative numbers, always place the largest negative number (closest to zero) before smaller negative numbers when ordering ascendingly.