**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.

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

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

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

Multiplying integers is pretty straightforward. The rule is simple:

- Positive x Positive = Positive $\ufffd\mathrm{.}\ufffd\mathrm{.},2\ufffd3=6$
- Negative x Negative = Positive $\ufffd\mathrm{.}\ufffd\mathrm{.},-2\ufffd-3=6$
- Positive x Negative = Negative $\ufffd\mathrm{.}\ufffd\mathrm{.},2\ufffd-3=-6$

- What is $2+3$?
- What is $-5+3$?
- What is $2\ufffd-4$?

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

- Positive ÷ Positive = Positive $\ufffd\mathrm{.}\ufffd\mathrm{.},6\xf73=2$
- Negative ÷ Negative = Positive $\ufffd\mathrm{.}\ufffd\mathrm{.},-6\xf7-3=2$
- Positive ÷ Negative = Negative $\ufffd\mathrm{.}\ufffd\mathrm{.},6\xf7-3=-2$

Integers Properties:

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

Addition:

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

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

$\ufffd-\ufffd=\ufffd+(-\ufffd)$

Multiplication & Division:

- Positive x Positive = Positive
- Negative x Negative = Positive
- Positive x Negative = Negative

- Addition: $\ufffd+\ufffd$
- Subtraction: $\ufffd-\ufffd$
- Multiplication: $\ufffd\ufffd\ufffd$
- Division: $\ufffd\xf7\ufffd$, $\ufffd\mathrm{\ne}0$

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!

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