RBSE Solutions Class 6 Maths Chapter 4 Negative Numbers and Integers Important Questions

Multiple Choice Questions

Question 1. Zero (0) is:
(a) Positive integer
(b) Negative integer
(c) Neutral
(d) All of the options
Answer: (c) Neutral
In simple words: Zero is neither a positive number nor a negative number. It sits in the middle on the number line.

🎯 Exam Tip: Remember that zero is a unique integer; it acts as the reference point for positive and negative numbers.

Question 2. Largest negative number is:
(a) -1
(b) -2
(c) -3
(d) -4
Answer: (a) -1
In simple words: When we talk about negative numbers, the number closest to zero is the largest. For example, -1 is bigger than -10 because -1 is closer to zero.

🎯 Exam Tip: On a number line, numbers increase as you move to the right. So, -1 is to the right of -2, making -1 larger.

Question 3. Smallest positive number is:
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (b) 1
In simple words: The smallest whole number that is greater than zero is 1. All other positive numbers are larger than 1.

🎯 Exam Tip: Positive numbers start from 1 and go up (1, 2, 3...). Zero is not positive, and numbers less than zero are negative.

Question 4. Each negative integer is each positive integer.
(a) large
(b) small
(c) equal
(d) none
Answer: (b) small
In simple words: Any negative number will always be smaller than any positive number. For instance, -5 is much smaller than 5.

🎯 Exam Tip: A good way to remember this is that all negative numbers are to the left of zero on a number line, while all positive numbers are to the right.

Question 6. Large number 3 or -7 is:
(a) 0
(b) 1
(c) -7
(d) 3
Answer: (d) 3
In simple words: Between 3 and -7, 3 is the larger number. Positive numbers are always greater than negative numbers.

🎯 Exam Tip: Always remember that any positive number is larger than any negative number, regardless of its numerical value.

Fill In The Blanks

(i) Numbers lie on right of zero on number line are _______.
Answer: positive integers.
In simple words: On a number line, numbers to the right of zero are always positive.

🎯 Exam Tip: Visualize the number line; moving right always means increasing value.

(ii) Numbers lie on left of zero on number line are _______.
Answer: Negative integers.
In simple words: Numbers to the left of zero on a number line are always negative.

🎯 Exam Tip: Moving left on the number line always means decreasing value.

(iii) _______ is called additive identity.
Answer: 0
In simple words: When you add zero to any number, the number stays the same. That's why zero is called the additive identity.

🎯 Exam Tip: The additive identity is the number that, when added to any other number, leaves the other number unchanged.

(iv) When a number is added to its additive identity, there result is _______.
Answer: 0
In simple words: Adding a number to its additive inverse always results in zero. For example, \( 5 + (-5) = 0 \).

🎯 Exam Tip: The additive inverse of a number is the number that when added to it yields zero.

(v) Each negative integer is smaller than _______.
Answer: zero
In simple words: All negative numbers, no matter how small they seem, are always less than zero. They are all to the left of zero on the number line.

🎯 Exam Tip: Zero acts as a dividing line; all numbers to its left are less than zero.

Question 1. Write suitable integers for given cases:
(i) 25 m below sea level.
(ii) 7 m above Earth
(iii) On heating milk at 20°C temperature
(iv) On freezing ice-cream at 5°C temperature
Answer:
(i) 25 m below sea level = -25 m. When something is below a reference point, it is represented with a negative sign.
(ii) 7 m above Earth = +7 m. When something is above a reference point, it is represented with a positive sign.
(iii) On heating milk at 20°C temperature = +20°C. Temperature increase or above zero is positive.
(iv) On freezing ice-cream at 5°C temperature = -5°C. Freezing temperature usually implies a drop, so it is negative here.
In simple words: We use positive numbers for things like 'above' or 'increase', and negative numbers for 'below' or 'decrease'.

🎯 Exam Tip: Always associate words like 'below', 'loss', 'decrease' with negative integers, and 'above', 'gain', 'increase' with positive integers.

Question 2. Use sign >, < or =
(i) 7 ___ 7
(ii) 0 ___ 4
(iii) -6 ___ -2
(iv) -8 ___ -4
Answer:
(i) 7 > -7. Positive numbers are always greater than negative numbers.
(ii) 0 < 4. Any positive number is greater than zero.
(iii) -6 < -2. On the number line, -6 is to the left of -2.
(iv) -8 < -4. On the number line, -8 is further to the left of -4, making it smaller.
In simple words: Remember that numbers get bigger as you move to the right on a number line, and smaller as you move to the left.

🎯 Exam Tip: Practice placing numbers on a mental number line to quickly determine greater than or less than relationships, especially for negative numbers.

Question 3. Write the following integers in ascending and descending order.
(i) 7, 2, -9, 0, -4
(ii) 5, -5, 6, 1, 3, -3
Answer:
(i) Given integers: 7, 2, -9, 0, -4
Ascending order: -9, -4, 0, 2, 7. We start with the smallest negative number and go up to the largest positive number.
Descending order: 7, 2, 0, -4, -9. We start with the largest positive number and go down to the smallest negative number.
(ii) Given integers: 5, -5, 6, 1, 3, -3
Ascending order: -5, -3, 1, 3, 5, 6. Always arrange from the smallest (most negative) to the largest (most positive).
Descending order: 6, 5, 3, 1, -3, -5. Arrange from the largest to the smallest.
In simple words: Ascending means going up from the smallest number to the biggest. Descending means coming down from the biggest number to the smallest.

🎯 Exam Tip: When ordering integers, always list all negative numbers first (smallest being furthest from zero), then zero, then positive numbers (largest being furthest from zero).

Short/Long Answer Type Questions

Question 1. Find the value of the following.
(i) 73 + (-85)
(ii) (-48) + (-39)
(iii) 56 + (-67) + (-47)
(iv) (-49) - (-28) + (-14)
Answer:
(i) \( 73 + (-85) = 73 - 85 = -12 \). When adding a negative number, it's the same as subtracting.
(ii) \( (-48) + (-39) = -48 - 39 = -87 \). When adding two negative numbers, sum their absolute values and keep the negative sign.
(iii) \( 56 + (-67) + (-47) = 56 - 67 - 47 = 56 - (67 + 47) = 56 - 114 = -58 \). Combine the negative numbers first for easier calculation.
(iv) \( (-49) - (-28) + (-14) = -49 + 28 - 14 \). Subtracting a negative number is equivalent to adding a positive number.
\( = -49 - 14 + 28 = -63 + 28 = -35 \). Group the negative numbers together before performing the final addition.
In simple words: When you add or subtract numbers with different signs, remember the rules: plus and minus make minus, minus and minus make plus. Also, always keep track of the sign of the bigger number in the result.

🎯 Exam Tip: A good strategy is to first convert all subtractions of negative numbers into additions of positive numbers (e.g., \( a - (-b) = a + b \)), then group all positive numbers and all negative numbers before adding them up.

Question 2. Solve the following using number line.
(i) (-8) + (-3)
(ii) (-8) - (-3)
(iii) 8 + (-3)
(iv) 8 - (-3)
Answer:
(i) \( (-8) + (-3) = -11 \)First, move 8 steps left from 0 to -8. Then, from -8, move another 3 steps left to reach -11.
(ii) \( (-8) - (-3) = -8 + 3 = -5 \)First, move 8 steps left from 0 to -8. Then, since we are subtracting -3 (which is like adding +3), move 3 steps right from -8 to reach -5.
(iii) \( 8 + (-3) = 8 - 3 = 5 \)First, move 8 steps right from 0 to 8. Then, since we are adding -3 (which is like subtracting 3), move 3 steps left from 8 to reach 5.
(iv) \( 8 - (-3) = 8 + 3 = 11 \)First, move 8 steps right from 0 to 8. Then, since we are subtracting -3 (which means adding +3), move 3 steps right from 8 to reach 11.
In simple words: To use a number line for adding or subtracting, start at the first number. If you add a positive number, move right. If you add a negative number (or subtract a positive number), move left. If you subtract a negative number, it's like adding, so move right.

🎯 Exam Tip: Always draw clear arrows on your number line. A movement to the right means addition or subtracting a negative, while a movement to the left means subtraction or adding a negative.