RBSE Solutions Class 7 Maths Chapter 1 Integers Exercise 1.1

Question 1. The temperature in Churu is measured in \(^{\circ}\text{C}\) at different times and represented on a number line.
(i) The temperature of Churu on the following dates from the above number line:
(a) 26 January
(b) 25 December
(c) 25 February
(d) 25 March
(ii) What is the difference in temperature between the hottest and the coldest day?
(iii) The temperature of 26 January is how much less than the temperature of 25 February?
(iv) Can we say that the sum of temperature of 25 December and 25 February is greater than the temperature of 26 January?
Answer:
(i) The temperature of Churu on the number line for each date is:
(a) 26 January: \( -11^{\circ}\text{C} \)
(b) 25 December: \( -6^{\circ}\text{C} \)
(c) 25 February: \( 4^{\circ}\text{C} \)
(d) 25 March: \( 14^{\circ}\text{C} \)
(ii) To find the difference between the hottest and coldest days, we identify the hottest temperature as \( 14^{\circ}\text{C} \) (on 25 March) and the coldest as \( -11^{\circ}\text{C} \) (on 26 January).
Difference in temperature \( = 14^{\circ}\text{C} - (-11^{\circ}\text{C}) \)
\( = 14^{\circ}\text{C} + 11^{\circ}\text{C} \)
\( = 25^{\circ}\text{C} \)
This means there is a \( 25^{\circ}\text{C} \) change between the two extreme temperatures. This range helps understand the weather variations in Churu.
(iii) The temperature of 26 January is \( -11^{\circ}\text{C} \). The temperature of 25 February is \( 4^{\circ}\text{C} \).
To find how much less \( -11^{\circ}\text{C} \) is than \( 4^{\circ}\text{C} \), we calculate the difference:
Difference \( = 4^{\circ}\text{C} - (-11^{\circ}\text{C}) \)
\( = 4^{\circ}\text{C} + 11^{\circ}\text{C} \)
\( = 15^{\circ}\text{C} \)
So, 26 January is \( 15^{\circ}\text{C} \) colder than 25 February.
(iv) First, find the sum of temperatures for 25 December and 25 February:
Temperature on 25 December \( = -6^{\circ}\text{C} \)
Temperature on 25 February \( = 4^{\circ}\text{C} \)
Sum of temperatures \( = -6^{\circ}\text{C} + 4^{\circ}\text{C} = -2^{\circ}\text{C} \)
Next, compare this sum with the temperature of 26 January:
Temperature on 26 January \( = -11^{\circ}\text{C} \)
Since \( -2^{\circ}\text{C} \) is greater than \( -11^{\circ}\text{C} \), we can say that the sum of the temperatures of 25 December and 25 February is greater than the temperature of 26 January. This shows how combining values can change the overall comparison.
In simple words: First, find the temperature for each date from the number line. Then, calculate the difference between the highest and lowest temperatures. For comparing "how much less", subtract the colder temperature from the warmer one. Finally, add the temperatures for the given dates and see if that sum is bigger than the temperature of the last date.
🎯 Exam Tip: Always pay attention to the negative signs when calculating differences in temperature, especially when dealing with values below zero degrees. Subtracting a negative number is the same as adding a positive number.

Question 2. Sheela deposits Rs.5000 in a post office and withdraws Rs.3700 after one month. If the amount withdrawn is represented as a negative number, how will we represent the deposited amount? What is the amount left in the account after withdrawal?
Answer: If the amount withdrawn is shown as a negative number, then the amount deposited will be shown as a positive number. This is a common way to represent money going into or out of an account.
Amount deposited \( = \text{Rs.}5000 \)
Amount withdrawn \( = -\text{Rs.}3700 \)
Amount remaining after withdrawal \( = (\text{Rs.}5000) + (-\text{Rs.}3700) \)
\( = \text{Rs.}(5000 - 3700) \)
\( = \text{Rs.}1300 \) (Positive)
So, Sheela has Rs.1300 left in her account.
In simple words: Money put in is a positive number, and money taken out is a negative number. To find out how much is left, you add the positive deposited amount and the negative withdrawn amount.
🎯 Exam Tip: When dealing with financial transactions, deposits are usually positive values, and withdrawals are negative values. This helps in keeping track of the balance correctly.

Question 3. Solve the following:
(i) \( (-4) + (-3) \)
(ii) \( 15 - 8 + (-9) \)
(iii) \( 400 + (-1000) + (-500) \)
(iv) \( 23 - 41 - 11 \)
(v) \( -27 + (-3) + 30 \)
Answer:
(i) \( (-4) + (-3) = -4 - 3 = -7 \)
(ii) \( 15 - 8 + (-9) = 7 + (-9) = 7 - 9 = -2 \)
(iii) \( 400 + (-1000) + (-500) \)
\( = 400 - 1000 - 500 \)
\( = 400 - 1500 \)
\( = -1100 \)
(iv) \( 23 - 41 - 11 \)
\( = 23 - 52 \)
\( = -29 \)
(v) \( -27 + (-3) + 30 \)
\( = -27 - 3 + 30 \)
\( = -30 + 30 \)
\( = 0 \)
Adding and subtracting integers requires careful attention to the signs, especially when combining negative numbers.
In simple words: Follow the rules for adding and subtracting positive and negative numbers. When you add two negative numbers, the answer is a bigger negative number. When you subtract a larger number from a smaller one, the answer is negative.
🎯 Exam Tip: Remember that adding a negative number is the same as subtracting a positive number (e.g., \( a + (-b) = a - b \)). Also, when you have multiple operations, work from left to right unless there are parentheses.

Question 4. Compare the following expressions using \( < \), \( > \), or \( = \):
(i) \( (-14) + 11 + 5 \) and \( 14 - 11 - 5 \)
(ii) \( 30 + (-5) + (-8) \) and \( (-5) + (-8) + 30 \)
(iii) \( 7 + 11 + (-5) \) and \( (-7) - 11 + 5 \)
(iv) \( (-14) + 11 + (-12) \) and \( 14 + 11 + 12 \)
(v) \( 6 + 7 - 13 \) and \( 6 + 7 + (-13) \)
Answer:
(i) First, calculate each side:
\( (-14) + 11 + 5 = -14 + 16 = 2 \)
\( 14 - 11 - 5 = 14 - 16 = -2 \)
Since \( 2 > -2 \), then \( (-14) + 11 + 5 > 14 - 11 - 5 \).
(ii) Calculate each side:
\( 30 + (-5) + (-8) = 30 - 5 - 8 = 30 - 13 = 17 \)
\( (-5) + (-8) + 30 = -5 - 8 + 30 = -13 + 30 = 17 \)
Since \( 17 = 17 \), then \( 30 + (-5) + (-8) = (-5) + (-8) + 30 \). This shows the commutative property of addition.
(iii) Calculate each side:
\( 7 + 11 + (-5) = 18 - 5 = 13 \)
\( (-7) - 11 + 5 = -18 + 5 = -13 \)
Since \( 13 > -13 \), then \( 7 + 11 + (-5) > (-7) - 11 + 5 \).
(iv) Calculate each side:
\( (-14) + 11 + (-12) = -14 + 11 - 12 = -26 + 11 = -15 \)
\( 14 + 11 + 12 = 37 \)
Since \( -15 < 37 \), then \( (-14) + 11 + (-12) < 14 + 11 + 12 \).
(v) Calculate each side:
\( 6 + 7 - 13 = 13 - 13 = 0 \)
\( 6 + 7 + (-13) = 13 - 13 = 0 \)
Since \( 0 = 0 \), then \( 6 + 7 - 13 = 6 + 7 + (-13) \).
In simple words: First, solve the math problem on each side of the comparison. After you have a single number for both sides, look at which number is bigger, smaller, or if they are equal. Then, put in the correct sign (\( < \), \( > \), or \( = \)).
🎯 Exam Tip: Always simplify both sides of the expression completely before attempting to compare them. Be careful with signs, especially when you have multiple negative numbers or subtraction operations.

Question 5. Write two integers whose:
(i) sum is \( (-7) \)
(ii) difference is \( 4 \)
(iii) sum is \( 0 \)
(iv) difference is \( -2 \)
Answer:
(i) Two integers whose sum is \( (-7) \) could be \( (-1) \) and \( (-6) \). For example:
\( (-1) + (-6) = -7 \)
(ii) Two integers whose difference is \( 4 \) could be \( 6 \) and \( 2 \). For example:
\( 6 + (-2) = 4 \) (or \( 6 - 2 = 4 \))
(iii) Two integers whose sum is \( 0 \) could be \( (1) \) and \( (-1) \). For example:
\( (1) + (-1) = 0 \). These are called additive inverses.
(iv) Two integers whose difference is \( -2 \) could be \( (-3) \) and \( (-1) \). For example:
\( (-3) - (-1) = -3 + 1 = -2 \)
There can be many pairs of integers that fit these conditions, depending on the chosen numbers. Understanding how integers work helps find these pairs easily.
In simple words: For each question, pick two numbers that either add up to the target sum or subtract to give the target difference. Remember that many different pairs of numbers can work.
🎯 Exam Tip: When finding pairs of integers, consider both positive and negative numbers. For a sum of zero, remember that any number and its opposite will work. For differences, subtracting a negative number can make the result larger.

Question 6. Fill in the blanks:
(i) \( (-3) + 5 = 5 + .... \)
(ii) \( 17 + .... = 17 \)
(iii) \( .... + (-5) = 0 \)
(iv) \( -11 + [(-12) + 4] = [(-11) + (-12)] + .... \)
Answer:
(i) \( (-3) + 5 = 5 + (-3) \)
This shows the Commutative Property of Addition.
(ii) \( 17 + 0 = 17 \)
This shows the Additive Identity Property.
(iii) \( 5 + (-5) = 0 \)
This shows the Additive Inverse Property.
(iv) \( -11 + [(-12) + 4] = [(-11) + (-12)] + 4 \)
This shows the Associative Property of Addition.
Filling in these blanks helps us practice and understand the basic properties of integer addition, such as the commutative, associative, additive identity, and additive inverse properties.
In simple words: For each blank, find the number that makes the equation true. Think about the rules of addition, like changing the order of numbers or adding zero, to find the missing part.
🎯 Exam Tip: Recognize the properties of addition when filling blanks: Commutative property (order doesn't matter), Associative property (grouping doesn't matter), Additive Identity (adding zero), and Additive Inverse (adding opposites equals zero).