GSEB Class 7 Maths Solutions Chapter 1 Integers Exercise 1.2

Question 1. Write down a pair of integers whose:
(a) sum is -7
(b) difference is -10
(c) sum is 0
Answer:
(a) We can use \( (-2) + (-5) = -7 \). So, -2 and -5 form a suitable pair.
(b) We can take \( (-15) - (-5) = -15 + 5 = -10 \). So, -15 and -5 create a suitable pair.
(c) We can use \( (-15) + 15 = 0 \). So, -15 and 15 form a suitable pair.
In simple words: For each part, find two whole numbers that, when you add them or subtract them, give you the target number. There can be many correct answers for each.

Exam Tip: When asked for a "pair" of integers, remember that multiple combinations might satisfy the condition. Always show your chosen pair and the calculation.

Question 2.
(a) Write a pair of negative integers whose difference gives 8.
(b) Write a negative integer and a positive integer whose sum is – 5.
(c) Write a negative integer and a positive integer whose difference is – 3.
Answer:
(a) Since, \( (-2) - (-10) = -2 + 10 = 8 \). Hence, -2 and -10 are a pair of negative integers whose difference is 8.
(b) Since, \( (-6) + 1 = -5 \). Therefore, -6 and 1 are a pair of integers whose sum is -5, and one of these is a negative number.
(c) Since, \( (-1) - (2) = -1 - 2 = -3 \). Therefore, -1 and 2 are a pair of integers whose difference is -3, with one being positive and the other negative.
In simple words: For each question, find two numbers that fit the rules. For (a), pick two negative numbers that, when subtracted, equal 8. For (b), choose a negative and a positive number that add up to -5. For (c), find a negative and a positive number whose subtraction equals -3.

Exam Tip: Pay close attention to the signs (+ or -) of the integers and the operation (sum or difference) required. A common error is mixing up the order of subtraction with negative numbers.

Question 3. In a quiz, team A scored – 40, 10, 0 and team B scored 10, 0, – 40 in three successive rounds. Which team scored morel Can we say that we can add integers in any order?
Answer: Total score for team A is calculated as \( (-40) + 10 + 0 = -30 \). Total score for team B is calculated as \( 10 + 0 + (-40) = -30 \). So, the scores of both teams are the same, both being -30. Yes, we can add integers in any sequence.
In simple words: Team A and Team B both got a score of -30. This means their scores were equal. Also, when you add numbers, you can change their order, and the answer will still be the same.

Exam Tip: Remember the commutative property of addition, which states that changing the order of addends does not change the sum. This applies to integers as well.

Question 4. Fill in the blanks to make the following statements true:
(i) \( (-5) + (- 8) = (-8) + (\text{ }) \)
(ii) \( - 53 + (\text{ }) = - 53 \)
(iii) \( 17 + (\text{ }) = 0 \)
(iv) \( [13 + (-12)] + (\text{ }) = 13 + [(- 12) + (- 7)] \)
(v) \( (- 4) + [15 + (- 3)] = [- 4 + 15] + (\text{ }) \)
Answer:
(i) Because integers can be summed in any sequence, \( (-5) + (-8) = (-8) + (-5) \).
(ii) If we add zero to any integer, the integer remains unchanged. So, \( -53 + 0 = -53 \).
(iii) We understand that the total of an integer and its additive inverse is zero. Thus, \( 17 + (-17) = 0 \).
(iv) Since, integer addition is associative. For any three integers a, b, and c, we know that \( (a + b) + c \) is the same as \( a + (b + c) \). Therefore, \( [13 + (-12)] + (-7) = 13 + [(-12) + (-7)] \).
(v) The equation \( (-4) + [15 + (-3)] = [(-4) + 15] + (-3) \).
In simple words: These blanks need to be filled using rules of addition. (i) uses the rule that numbers can be added in any order. (ii) shows that adding zero doesn't change a number. (iii) uses the rule that a number plus its opposite is zero. (iv) and (v) use the rule that when you add three numbers, you can group them differently, and the total stays the same.

Exam Tip: This question tests your knowledge of fundamental integer properties: commutative property of addition (i), additive identity (ii), additive inverse (iii), and associative property of addition (iv, v). Memorizing these properties helps in quickly solving such fill-in-the-blank questions.