07_CBSE_Integers_Notes & Practice paper

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!

Practice Paper

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