These notes cover the Integers chapter from NCERT CBSE Class 7 Mathematics. Understand the basics of integers, their properties, and operations.
Integers are fundamental in maths, representing positive, negative, and zero whole numbers. This chapter builds foundation for advanced concepts.
Integers are a set of whole numbers that include positive numbers, negative numbers, and zero. Examples: -3, -2, -1, 0, 1, 2, 3. They are used in various real-life scenarios like temperature measurements, bank balances, and elevations.
Integers can be represented on a number line where zero is the origin. Positive integers are to the right, and negative integers are to the left. This visual aid helps in understanding order and operations.
Integers follow specific properties under addition, subtraction, multiplication, and division.
For any two integers a and b, their sum (a + b), difference (a - b), and product (a * b) are always integers. However, division may not always yield an integer.
Addition and multiplication of integers are commutative: a + b = b + a and a * b = b * a. Subtraction and division are not commutative.
Addition and multiplication are associative: (a + b) + c = a + (b + c) and (a * b) * c = a * (b * c). This property does not hold for subtraction and division.
Multiplication distributes over addition: a * (b + c) = a * b + a * c. This is useful in simplifying expressions.
Zero is the additive identity: a + 0 = a. One is the multiplicative identity: a * 1 = a.
Understanding rules for operations is crucial for solving problems.
To add integers, consider signs: same signs add and keep the sign; different signs subtract and take the sign of the larger absolute value. Example: (-5) + (-3) = -8; 7 + (-4) = 3.
Subtracting an integer is equivalent to adding its additive inverse: a - b = a + (-b). Example: 5 - (-2) = 5 + 2 = 7.
Multiply absolute values and determine sign: same signs yield positive; different signs yield negative. Example: (-6) * 4 = -24; (-3) * (-5) = 15.
Divide absolute values and assign sign similar to multiplication. Example: (-12) ÷ 3 = -4; 20 ÷ (-5) = -4; (-18) ÷ (-6) = 3. Division by zero is undefined.
Integers are applied in solving real-world problems. Practice with examples like profit-loss calculations, distance differences, and temperature changes. For instance, if temperature drops by 5°C from 3°C, it becomes -2°C, using integer subtraction.
