Lets start the Integers chapter from NCERT book of Class 7. This chapter is going to deal with some concepts that you might find new and challenging. As you start solving the questions, you would be able to understand it better.
| Class: | 7 |
| Chapter and Exercise: | 1 – 1.1 |
| Chapter Name: | Integers |
| Academic Session: | 2023-24 (CBSE) |
| Medium: | English |
| Book Name: | NCERT: Mathematics (Textbook for Class VII) |
| Edition: | December 2022 Agrahayana 1944 (latest) |
| Page Number: | 5 |
Let’s do a quick revision before we go into solving the questions –
- Adding Integers:
- When adding two integers with the same sign, add their absolute values and give the result the same sign.
- Example: -3 + -5 = -8 (both are negative, add 3 and 5 to get 8, result is negative).
- When adding two integers with different signs, subtract the smaller absolute value from the larger absolute value and give the result the sign of the integer with the larger absolute value.
- Example: -7 + 4 = -3 (subtract 4 from 7 to get 3, result is negative because 7 is larger and negative).
- Subtracting Integers: To subtract an integer, add its opposite.
- Example: 5 – (-3) = 5 + 3 = 8.
- Properties of Addition:
- Commutative Property: a + b = b + a
- Associative Property: (a + b) + c = a + (b + c)
- Identity Property: a + 0 = a
NCERT Class 7 Maths Chapter 1 Other Exercises
Example 1: Write a pair of integers whose sum is -7.
Step 1: Choose two negative numbers whose absolute values add up to 7.
Step 2: -3 + (-4) = -3 – 4 = -7.
Example 2: Write a pair of negative integers whose difference is 8.
Step 1: Choose two negative numbers.
Step 2: Ensure the larger number’s absolute value is 8 more than the smaller’s.
Step 3: -4 – (-12) = -4 + 12 = 8.
Example 3: In a quiz, team A scored -40, 10, 0 and team B scored 10, 0, -40. Which team scored more?
Step 1: Calculate the sum of team A’s scores: -40 + 10 + 0 = -30.
Step 2: Calculate the sum of team B’s scores: 10 + 0 – 40 = -30.
Step 3: Compare both sums. Both teams scored -30, demonstrating the commutative property of addition.
NCERT Solutions Class 7 Maths Chapter 1 Exercise 1.1 Integers
Question 1. Write down a pair of integers whose:
(a) Sum is –7:
A pair could be –3 and –4 because –3 + (–4) = –7. (Adding two negative numbers)
(b) Difference is –10:
A pair could be 5 and 15 because 5 – 15 = –10. (Subtracting a larger number from a smaller number gives a negative result)
(c) Sum is 0:
A pair could be 7 and –7 because 7 + (–7) = 0. (A number and its negative add up to zero)
Question 2. (a) Write a pair of negative integers whose difference gives 8.
A pair could be –4 and –12 because –4 – (–12) = 8. (Subtracting a smaller negative number from a larger negative number)
(b) Write a negative integer and a positive integer whose sum is –5.
A pair could be –8 and 3 because –8 + 3 = –5. (Adding a larger negative number to a smaller positive number)
(c) Write a negative integer and a positive integer whose difference is –3.
A pair could be 2 and 5 because 2 – 5 = –3. (Subtracting a larger number from a smaller number)
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 more? Can we say that we can add integers in any order?
Team A’s total score: (–40) + 10 + 0 = –30.
Team B’s total score: 10 + 0 + (–40) = –30.
Both teams scored the same, –30 points.
Yes, we can add integers in any order. This is due to the commutative property of addition, which states that changing the order of the numbers does not change the sum.
Question 4. Fill in the blanks to make the following statements true:
(i) (–5) + (– 8) = (– 8) + (…………)
(–5) + (–8) = (–8) + (-5) (Commutative property of addition: a + b = b + a)
-13 = -13
Blank Space: -5 (Ans)
(ii) –53 + ………… = –53
-53 + 0 = -53 (Adding 0 to a number leaves it unchanged)
Blank Space: 0 (Ans)
(iii) 17 + ………… = 0
17 + (-17) = 0 (A number added to its negative equals zero)
Blank Space: -17 (Ans)
(iv) [13 + (–12)] + (…………) = 13 + [(–12) + (–7)]
[13 + (-12)] + ………… = 13 + [-12 + (-7)] (Associative property of addition)
1 + ………… = 13 + (-19)
1 + (-7) = 13 + (-19)
Blank Space: -7 (Ans)
(v) (–4) + [15 + (–3)] = [–4 + 15] + …………
(-4) + [15 + (-3)] = [(-4) + 15] + ………… (Associative property of addition)
(-4) + 12 = 11 + …………
(-4) + 12 = 11 + (-3)
Blank Space: -3 (Ans)
Worksheet for Practice – Exercise 1.1 Chapter 1 Integers
Here’s a worksheet based on the types of questions we’ve just worked on:
1. Write down a pair of integers whose:
(a) Sum is –9
(b) Difference is 5
(c) Sum is 0
(d) Sum is 15
(e) Difference is –15
(f) Sum is –12
(g) Difference is 8
(h) Sum is 5
(i) Difference is –7
(j) Sum is –3
Solution
(a) Sum is –9:
Pair can be -4 and -5 because -4 + (-5) = -9.
(b) Difference is 5:
Pair can be 3 and -2 because 3 – (-2) = 5.
(c) Sum is 0:
Pair can be 5 and -5 because 5 + (-5) = 0.
(d) Sum is 15:
Pair can be 7 and 8 because 7 + 8 = 15.
(e) Difference is –15:
Pair can be -5 and 10 because -5 – 10 = -15.
(f) Sum is –12:
Pair can be -7 and -5 because -7 + (-5) = -12.
(g) Difference is 8:
Pair can be 10 and 2 because 10 – 2 = 8.
(h) Sum is 5:
Pair can be 2 and 3 because 2 + 3 = 5.
(i) Difference is –33:
Pair can be -10 and 23 because -10 – 23 = -33.
(j) Sum is –3:
Pair can be -1 and -2 because -1 + (-2) = -3.
2. For each scenario, write a pair of integers:
(a) A pair of negative integers whose difference is 5.
(b) A negative integer and a positive integer whose sum is –8.
(c) A negative integer and a positive integer whose difference is 10.
(d) A pair of positive integers whose difference is 2.
(e) A pair of negative integers whose sum is –10.
(f) A negative integer and a positive integer whose sum is 3.
(g) A negative integer and a positive integer whose difference is –6.
(h) A pair of positive integers whose sum is 20.
(i) A pair of negative integers whose difference is –3.
(j) A negative integer and a positive integer whose sum is –2.
Solution
(a) A pair of negative integers whose difference is 5:
Pair can be -3 and -8 because -3 – (-8) = 5.
(b) A negative integer and a positive integer whose sum is –8:
Pair can be -10 and 2 because -10 + 2 = -8.
(c) A negative integer and a positive integer whose difference is 10:
Pair can be -5 and 5 because -5 – 5 = 10.
(d) A pair of positive integers whose difference is 2:
Pair can be 5 and 3 because 5 – 3 = 2.
(e) A pair of negative integers whose sum is –10:
Pair can be -6 and -4 because -6 + (-4) = -10.
(f) A negative integer and a positive integer whose sum is 3:
Pair can be -2 and 5 because -2 + 5 = 3.
(g) A negative integer and a positive integer whose difference is –6:
Pair can be 4 and 10 because 4 – 10 = -6.
(h) A pair of positive integers whose sum is 20:
Pair can be 10 and 10 because 10 + 10 = 20.
(i) A pair of negative integers whose difference is –3:
Pair can be -7 and -4 because -7 – (-4) = -3.
(j) A negative integer and a positive integer whose sum is –2:
Pair can be -5 and 3 because -5 + 3 = -2.
3. For the given scores, determine which team scored more and answer the additional question:
(a) Team A: –20, 15, 5; Team B: 15, 5, –20
(b) Team A: –30, 20, 10; Team B: 20, 10, –30
(c) Can we add integers in any order and still get the same total score for each team?
4. Fill in the blanks to make the following statements true:
(a) (–7) + (–9) = (–9) + (…………)
(b) –45 + ………… = –45
(c) 23 + ………… = 0
(d) [15 + (–16)] + (…………) = 15 + [(–16) + (–9)]
(e) (–6) + [14 + (–5)] = [–6 + 14] + …………
(f) (–3) + (–6) = (–6) + (…………)
(g) –65 + ………… = –65
(h) 19 + ………… = 0
(i) [18 + (–17)] + (…………) = 18 + [(–17) + (–8)]
(j) (–2) + [12 + (–4)] = [–2 + 12] + …………
Solution
(a) (–7) + (–9) = (–9) + (…………):
The correct number is -7 because (–7) + (–9) = (–9) + (–7).
(b) –45 + ………… = –45:
The correct number is 0 because –45 + 0 = –45.
(c) 23 + ………… = 0:
The correct number is -23 because 23 + (-23) = 0.
(d) [15 + (–16)] + (…………) = 15 + [(–16) + (–9)]:
The correct number is -9 because [15 + (–16)] + (-9) = 15 + [(–16) + (–9)].
(e) (–6) + [14 + (–5)] = [–6 + 14] + …………:
The correct number is -5 because (–6) + [14 + (–5)] = [–6 + 14] + (-5).
(f) (–3) + (–6) = (–6) + (…………):
The correct number is -3 because (–3) + (–6) = (–6) + (–3).
(g) –65 + ………… = –65:
The correct number is 0 because –65 + 0 = –65.
(h) 19 + ………… = 0:
The correct number is -19 because 19 + (-19) = 0.
(i) [18 + (–17)] + (…………) = 18 + [(–17) + (–8)]:
The correct number is -8 because [18 + (–17)] + (-8) = 18 + [(–17) + (–8)].
(j) (–2) + [12 + (–4)] = [–2 + 12] + …………:
The correct number is -4 because (–2) + [12 + (–4)] = [–2 + 12] + (-4).
