45 Challanging integers worksheet for class 7 with Answer - PDF

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 What is an integer in maths

Definition and examples of integers

In maths, an integer is a whole number that can be positive, negative, or zero. It doesn't have any fractional or decimal parts. So, the definition of integers includes numbers like -3, -2, -1, 0, 1, 2, 3, and so on.

Integers Meaning in Hindi:

In Hindi, integers are called "पूर्णांक" (Poornank). These are numbers that can be positive, negative, or zero and don't have any fractional or decimal parts.

Examples of an Integer:

• Positive Integers: 1, 2, 3, 4...
• Negative Integers: -1, -2, -3, -4...
• Zero: 0

Integers Addition and Subtraction with Examples:

Addition:

• Adding Positive Integers: $2+3=5$
• Adding Negative Integers: $-2+(-3)=-5$

Subtraction:

• Subtracting Positive from Positive: $5-3=2$
• Subtracting Negative from Positive: $5-(-3)=8$

Integers Multiplication:

Multiplying integers is pretty straightforward. The rule is simple:

• Positive x Positive = Positive $�\mathrm{.}�\mathrm{.},2�3=6$
• Negative x Negative = Positive $�\mathrm{.}�\mathrm{.},-2�-3=6$
• Positive x Negative = Negative $�\mathrm{.}�\mathrm{.},2�-3=-6$

Integer Questions for Class 7:

1. What is $2+3$?
2. What is $-5+3$?
3. What is $2�-4$?

Integers Division:

When you divide integers, the rules are similar to multiplication.

• Positive ÷ Positive = Positive $�\mathrm{.}�\mathrm{.},6÷3=2$
• Negative ÷ Negative = Positive $�\mathrm{.}�\mathrm{.},-6÷-3=2$
• Positive ÷ Negative = Negative $�\mathrm{.}�\mathrm{.},6÷-3=-2$

Integers Properties:

1. Closure: When you add or multiply two integers, the result is always an integer.
2. Associative: For addition and multiplication, the way integers are grouped doesn't affect the result. $(�+�)+�=�+(�+�)$
3. Commutative: The order in which integers are added or multiplied doesn't affect the result. $�+�=�+�$
4. Existence of Identity: For addition, zero is the identity. For multiplication, 1 is the identity.
5. Existence of Inverse: Every integer has an additive inverse. For example, the additive inverse of 5 is -5.

Integers Rules:

1. Addition:

   • Positive + Positive = Positive
   • Negative + Negative = Negative
   • Positive + Negative = Subtract the numbers and take the sign of the larger number.

2. Subtraction: Change the sign of the number to be subtracted and then add.

   $�-�=�+(-�)$

3. Multiplication & Division:

   • Positive x Positive = Positive
   • Negative x Negative = Positive
   • Positive x Negative = Negative

Integers Formula:

1. Addition: $�+�$
2. Subtraction: $�-�$
3. Multiplication: $���$
4. Division: $�÷�$, $�\mathrm{\ne }0$

Is Zero an Integer?

Yes, zero is an integer. It is neither positive nor negative and serves as the "identity element" for addition, meaning when you add zero to any integer, the number doesn't change.

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In a nutshell, our worksheet on integers for class 7 with answers is the one-stop solution for all your integers exercises for class 7 needs. Stop flipping through dozens of books and websites when you can find everything compiled in one easy-to-navigate package. Whether you're a student, a teacher, or a parent trying to help your child excel in math, our resources offer a comprehensive and interactive approach to understanding integers problems. So don't wait, dive into our class 7th integers worksheet today and turn those numbers into child's play!