CBSE Class 7 Mathematics Integers Notes Set 06

Integers and the Number Line

Integers are the numbers ... -3, -2, -1, 0, 1, 2, 3 ... On the number line they increase towards the right, so -2 is greater than -4 and every positive integer is greater than every negative integer.
The absolute value |a| is the distance of a from 0 and is never negative: |-6| = 6. Zero is neither positive nor negative.

Addition and Subtraction

Adding two integers with the same sign: add the numbers and keep the sign. With different signs: subtract the smaller number from the larger and take the sign of the larger.
The additive identity is 0 and the additive inverse of a is -a. Subtraction is addition of the inverse: a - b = a + (-b), so subtracting -9 is the same as adding 9.

Multiplication and Division

The product or quotient of two integers with like signs is positive and with unlike signs is negative. A product of negative integers is positive when the count of negatives is even and negative when odd.
The multiplicative identity is 1. Division by zero is not defined and 0 divided by a non-zero integer is 0.

Properties

Closure: integers are closed under addition, subtraction and multiplication but not under division. Commutative: a + b = b + a and a × b = b × a. Associative: (a + b) + c = a + (b + c), and the same for multiplication.
Distributive: a × (b + c) = a × b + a × c, and similarly over subtraction. Subtraction and division are not commutative or associative.

Worked Example

A test gives +3 for each correct and -2 for each wrong answer. A student with 12 correct answers scores 20.
Marks from correct answers = 36. Loss from wrong answers = 36 - 20 = 16. Number of wrong answers = 16 ÷ 2 = 8.