RBSE Solutions Class 6 Maths Chapter 4 Negative Numbers and Integers More Ques

Rajasthan Board RBSE Class 6 Maths Chapter 4 Negative Numbers and Integers In Text Exercise

Pg. No. 48

Question 1. Write using appropriate symbols
1. Any 2 numbers smaller than 0.
2. 50 meters below sea level.
3. 10° C temperature below 0°C.
4. 15°C temperature above 0°C.
Answer:
1. Any two numbers smaller than zero are written as -1 and -2. Negative numbers always show values less than zero.
2. 50 meters below sea level is shown as -50 meters. When we go below a certain point, we use negative numbers.
3. A temperature of 10°C below 0°C is written as -10°C. This means the temperature is very cold.
4. A temperature of 15°C above 0°C is written as +15°C. This shows a warm temperature.
In simple words: We use negative numbers for things that are less than zero, like temperatures below freezing or depths below sea level. Positive numbers are for values greater than zero, like temperatures above freezing.

🎯 Exam Tip: Remember that "below" or "less than" usually means a negative sign, while "above" or "more than" means a positive sign in mathematics.

Question 2. Mark - 3, 5, -1, 0, - 5, 6 on the number line
Answer: The numbers -3, 5, -1, 0, -5, and 6 are marked correctly on the number line. The number line helps us visualize the order and position of these numbers.

In simple words: A number line shows numbers in order. Negative numbers are to the left of zero, and positive numbers are to the right. We put a dot on the line for each number we need to mark.

🎯 Exam Tip: Always draw your number line with clear, even spacing between numbers and extend it far enough to include all the numbers you need to mark.

Pg. No. 50

Question 1. Solve the following
(i) \( (-7) + (+8) \)
(ii) \( (-3) + 5 \)
(iii) \( (-3) + (-2) \)
(iv) \( (+7) + (-2) \)
Answer:
(i) \( (-7) + (+8) = 1 \). When adding a positive and a negative number, find the difference between their absolute values and use the sign of the larger absolute value. In this case, 8 - 7 = 1, and since 8 is positive, the result is positive.
(ii) \( (-3) + 5 = -3 + 5 = 5 - 3 = 2 \). Adding 5 to -3 moves three units from -3 towards the positive side, ending at 2.
(iii) \( (-3) + (-2) = -3 - 2 = -5 \). When adding two negative numbers, we add their absolute values and keep the negative sign. Moving 2 units further left from -3 brings us to -5.
(iv) \( (+7) + (-2) = 7 - 2 = 5 \). Adding a negative number is the same as subtracting its positive value. Subtracting 2 from 7 gives 5.
In simple words: Adding numbers means moving on a number line. If you add a positive number, you move right. If you add a negative number, you move left.

🎯 Exam Tip: When dealing with additions and subtractions of positive and negative numbers, remember that adding a negative number is the same as subtracting, and subtracting a negative number is the same as adding.

Pg. No. 52

Question 1. Fill in the following table.
Answer: The table is completed by performing the addition operations for each row and determining if the result is positive or negative.

🎯 Exam Tip: Always double-check your calculations, especially with negative numbers, to ensure the correct sum and sign are identified.

Pg. No. 53

Question 1. Subtract the following with the number line.
(i) \( (+ 7) - (+3) \)
(ii) \( (+ 3) - (+7) \)
(iii) \( (+7) - (-3) \)
(iv) \( (-7) - (-3) \)
Answer:
(i) \( (+ 7) - (+3) = 7 - 3 = 4 \). First, move from 0 to 7 on the number line. Then, subtract 3 by moving 3 units to the left from 7, which lands you at 4.

(ii) \( (+ 3) - (+7) = 3 - 7 = - 4 \). Start at 0 and move to 3 on the number line. Then, subtract 7 by moving 7 units to the left from 3, which results in -4.

(iii) \( (+7) - (-3) = 7 + 3 = 10 \). Start at 0 and move to 7 on the number line. Subtracting -3 means adding 3, so move 3 units to the right from 7, which brings you to 10.

(iv) \( (-7) - (-3) = - 7 + 3 = - 4 \). Start at 0 and move to -7 on the number line. Subtracting -3 means adding 3, so move 3 units to the right from -7, which leads to -4.

In simple words: When you subtract a positive number, you move left on the number line. When you subtract a negative number, it is like adding a positive number, so you move right on the number line.

🎯 Exam Tip: Always remember that subtracting a negative number changes the operation to addition, moving you towards the right on the number line.

Pg. No. 45

Question 1. Mahesh is studying and he is staying in a tribal hostel. His father gives him Rs 100 every month as pocket money which he deposits with his warden. He transacts the money according to his needs which is recorded on a paper by the warden. Mahesh took Rs 50 in the first week, Rs 30 in the second week, Rs 20 in the third week and asked for Rs 20 in the fourth week. The warden says that he has returned the complete amount. Ramesh tells him to deduct it in the next month. The warden gives him Rs 20 and denotes in on amount received the number-line as follows: much of Mahesh's money is now left deposited with the wardens? The same day he got prize of Rs 50 for essay writing, now how much total money of Mahesh is deposited with the warden ? Look at the number line and answer the following questions -
1. How much money did Mahesh spend in the first month?
2. How much money did the warden give him in the fourth week?
3. In which direction has the warden shown above amount on the number line?
4. What is the difference between the Rs 20 written on the right side and the Rs 20 written on the left side of the zero?
5. On which side of the number line Rs 100 and Rs 50 received in the second month is denoted?
6. If Mahesh has to spend Rs 200 due to illness in the second month, how much money will remain with the warden and where on the number line will it be denoted?
Answer:

1. Mahesh spent a total of Rs 120 in the first month. This is calculated by adding his expenses: Rs 50 + Rs 30 + Rs 20 + Rs 20.
2. The warden gave Mahesh Rs 20 in the fourth week. This amount was given back to him by the warden.
3. The warden has shown the amount given in the fourth week on the left side of the number line. This means it is a deduction or an amount taken out.
4. The difference between Rs 20 on the right side (positive money, like earnings) and Rs 20 on the left side (negative money, like spending) of zero is Rs 40. The right side denotes Mahesh's money, while the left side shows the warden's money.
5. The Rs 100 received and the Rs 50 prize in the second month are both positive amounts. These would be shown on the right side of zero on the number line, indicating money coming in.
6. If Mahesh has to spend Rs 200 due to illness in the second month, the warden will deduct Rs 70 from his account. This deduction will be shown on the left side of the zero on the number line, as it represents money taken out.
In simple words: Mahesh spent money in four weeks and also got a prize. We track money spent as negative (left on number line) and money received as positive (right on number line). His total spending and earnings help us understand how much money is left with the warden.

🎯 Exam Tip: For problems involving money, always define what is positive (money received, income) and what is negative (money spent, expenses). This makes tracking easier.

Pg. No. 46-47

Question 1. Write predecessor and successor of the following table.
Answer: The table shows the predecessor (number before) and successor (number after) for each given number. The predecessor is found by subtracting 1, and the successor is found by adding 1.

🎯 Exam Tip: Be careful with negative numbers: for example, the successor of -5 is -4 (which is greater), and its predecessor is -6 (which is smaller).

Pg. No. 52

Question 1. What will be the sum of two positive integers?
Answer: The sum of two positive integers will always be a positive integer. For instance, if you add 2 and 3, both positive, the result is 5, which is also positive.
In simple words: When you add two numbers that are both positive, the answer will always be positive too.

🎯 Exam Tip: Remember this basic rule: Positive + Positive = Positive. It's a fundamental property of addition.

Question 2. What is the result of addition for more than two negative integers? Positive/ Negative/Zero.
Answer: The result of adding more than two negative integers will always be a negative integer. For example, if you add -2, -3, and -4, the sum is -9, which is negative.
In simple words: If you add many negative numbers together, the final answer will always be a bigger negative number.

🎯 Exam Tip: When you add several negative numbers, think of it as moving further and further to the left on the number line, always resulting in a more negative value.