07_CBSE_Integers_Notes
Integers
What are Integers?
Integers are whole numbers, either positive, negative,
or zero. They do not include fractions or decimals.
Types of Integers
- Positive Integers: 1, 2, 3, ...
- Negative Integers: -1, -2, -3, ...
- Zero: 0
Operations on Integers
Addition
- When we add two positive integers, the result is
always positive.
- Example: 2
+ 3 = 5
- When we add two negative integers, the result is
always negative.
- Example:
(-2) + (-3) = -5
- When we add a positive and a negative integer, the
result can be either positive or negative.
- Example: 2
+ (-3) = -1
Subtraction
- When we subtract a positive integer from another
positive integer, the result can be either positive or negative.
- Example: 5
- 3 = 2
- When we subtract a negative integer from a positive
integer, the result is always positive.
- Example: 5
- (-3) = 8
- When we subtract a positive integer from a negative
integer, the result is always negative.
- Example:
(-5) - 3 = -8
Multiplication
- When we multiply two positive integers, the result
is always positive.
- Example: 2
× 3 = 6
- When we multiply two negative integers, the result
is always positive.
- Example:
(-2) × (-3) = 6
- When we multiply a positive and a negative integer,
the result is always negative.
- Example: 2
× (-3) = -6
Division
- When we divide a positive integer by another
positive integer, the result can be either positive or negative.
- Example: 6
÷ 3 = 2
- When we divide a negative integer by a positive
integer, the result is always negative.
- Example:
(-6) ÷ 3 = -2
- When we divide a positive integer by a negative
integer, the result is always negative.
- Example: 6
÷ (-3) = -2
Properties of Integers
- Commutative Property: The order of the
integers does not change the result.
- Example: 2
+ 3 = 3 + 2
- Associative Property: The order in
which we perform operations does not change the result.
- Example:
(2 + 3) + 4 = 2 + (3 + 4)
- Distributive Property: We can
distribute a single operation over multiple integer.
- Example:
2(3 + 4) = 2 × 3 + 2 × 4
Important Points to Remember
- Always follow the order of operations (PEMDAS/BODMAS).
- Be careful when working with negative integers.
- Practice, practice, practice!
MM-30 Time- 45 Min
Section A(MCQ)
(Each question carries 1
mark)
Choose
the correct option.
1.
What is the sum of -5 and 3?
(a) -2 (b) 2` (c) -8 (d)
8
2.
What is the product of -4 and -6?
(a) 24 (b) -24` (c) 10 (d)
-10
3.
What is the result of 7 - (-3)?
(a) 4 (b) 10 (c) -4 (d)
-10
4.
What is the quotient of 12 ÷ (-4)?
(a) 3 (b) -3` (c) 4 (d)
-4
5.
What is the sum of 2, -3, and 5?
(a) 4 (b) -4` (c) 10 (d)
-10
Section B
(Each question carries 2
marks)
6.
Simplify: 5 + (-2)
7.
Evaluate: 8 - (-4)
8.
Simplify: (-6) × (-8)
9.
Find the quotient of 15 ÷ (-5)
Section C
(Each question carries 3
marks)
10.
A submarine is at a depth of -200 meters. If it rises by 50 meters, what is its
new depth?
11. A temperature of -5°C is
recorded. If the temperature rises by 8°C, what is the new temperature?
12. A student scored 75 marks in a
test, but then lost 15 marks for a negative marking. What is the student's new
score?
Section D
(Each question carries 4
marks)
13.
Ritu has ₹25 in his pocket. He spends ₹8 on a book and then gets ₹12 from her
mother How much money does Ritu have now?
14.
A bakery sells 250 loaves of bread per day. If he makes a profit of ₹0.50 per
loaf, but have to pay rent for his shop of ₹25 per day, what is the total
profit?
Answer
Key
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
-2 |
24 |
10 |
-3 |
4 |
3 |
12 |
48 |
-3 |
-150 |
3 |
60 |
29 |
100 |
Note- Pdf format of this Practice paper is available-
https://t.me/cgscbsesupportbypramodsir/42
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