What Is Integers Class 7th: Definition and Complete Guide

Definition of Integers for Class 7 Students

Integers are a set of numbers that include:

• All positive whole numbers (1, 2, 3, ...)
• All negative whole numbers (-1, -2, -3, ...)
• Zero (0)

In simple words, integers are numbers without fractions or decimals. They extend the concept of natural numbers by including their negatives and zero. For Class 7 NCERT Mathematics, understanding integers is crucial as it forms the basis for many arithmetic operations.

Key points:

• Integers do not include fractions or decimals.
• Zero is an integer but is neither positive nor negative.

This definition helps students solve problems involving temperatures, elevations, and financial calculations where negative values occur.

Types of Integers and Their Properties

Integers can be classified into three types:

Properties of Integers:

• Closure: Addition, subtraction, and multiplication of integers always result in an integer.
• Commutative Property: $a + b = b + a$ and $a \times b = b \times a$ for integers.
• Associative Property: $(a + b) + c = a + (b + c)$ and $(a \times b) \times c = a \times (b \times c)$.
• Additive Identity: Adding zero to any integer leaves it unchanged ($a + 0 = a$).
• Additive Inverse: For every integer $a$, there is an integer $-a$ such that $a + (-a) = 0$.

Understanding these properties helps in solving integer problems efficiently.

How to Add and Subtract Integers: Rules and Examples

Adding and subtracting integers follow specific rules:

Addition Rules:

• Same signs: Add their absolute values and keep the sign.
• Example: $3 + 5 = 8$, $-4 + (-7) = -11$
• Different signs: Subtract smaller absolute value from larger absolute value and keep the sign of the larger.
• Example: $7 + (-3) = 4$, $-9 + 5 = -4$

Subtraction Rules:

• Change subtraction to addition by adding the opposite.
• Example: $5 - 3 = 5 + (-3) = 2$
• Example: $-4 - (-6) = -4 + 6 = 2$

Worked Example:

Calculate $(-7) + 12 - 5$:

Step 1: $(-7) + 12 = 5$ (different signs, subtract 7 from 12)

Step 2: $5 - 5 = 0$

Answer: $0$

Mastering these rules is essential for Class 7 students to solve integer problems confidently.

Real-Life Applications of Integers for Class 7 Students

Integers are not just theoretical; they are used daily in many real-life situations:

• Temperature: Temperatures below zero are negative integers, e.g., -5 °C.
• Banking: Deposits and withdrawals can be represented by positive and negative integers.
• Elevation: Heights above sea level are positive integers; depths below sea level are negative.
• Sports: Scoring systems sometimes use positive and negative points.

Example: If the temperature is -3 °C in the morning and rises by 7 °C, the new temperature is:

$$-3 + 7 = 4 °C$$

This shows how integers help describe changes and differences in everyday life, making the concept practical and easy to understand.

Comparing Integers: Understanding Greater and Smaller Values

Comparing integers involves understanding their position on the number line.

• Integers to the right on the number line are greater.
• Integers to the left are smaller.

Tips for comparing:

• Any positive integer is greater than any negative integer.
• Among negatives, the one with the smaller absolute value is greater. For example, -2 > -5.

Worked Example: Compare $-7$ and $-3$:

Since $-3$ is to the right of $-7$, we have:

$$-3 > -7$$

This skill is vital for solving inequality problems in Class 7 Mathematics.

Practice Problems on Integers for Class 7 NCERT

Practicing integer problems helps reinforce concepts. Here are some exercises:

1. Find the sum: $-8 + 15$ 2. Subtract: $12 - (-7)$ 3. Compare: Which is greater, $-4$ or $3$? 4. Calculate: $(-5) + (-6) + 11$ 5. Real-life: If a submarine is at -200 m and rises 150 m, what is its new depth?

Solutions:

1. $-8 + 15 = 7$ 2. $12 - (-7) = 12 + 7 = 19$ 3. $3 > -4$ 4. $(-5) + (-6) + 11 = (-11) + 11 = 0$ 5. $-200 + 150 = -50$ m (new depth)

Try these problems regularly to prepare well for your Class 7 NCERT Mathematics exams.