Operations with Integers
Key Concepts
Integers are numbers that can be positive, negative, or zero. They do not include fractions or decimals. The four basic operations with integers are addition, subtraction, multiplication, and division.
Addition of Integers
When adding integers, follow these rules:
- If both numbers have the same sign, add their absolute values and keep the same sign.
- If the numbers have different signs, subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value.
Example:
(+5) + (+3) = +8
(-5) + (-3) = -8
(+5) + (-3) = +2
(-5) + (+3) = -2
Subtraction of Integers
To subtract integers, change the subtraction sign to addition and change the sign of the number being subtracted. Then, follow the rules for addition.
Example:
(+5) - (+3) = (+5) + (-3) = +2
(-5) - (-3) = (-5) + (+3) = -2
(+5) - (-3) = (+5) + (+3) = +8
(-5) - (+3) = (-5) + (-3) = -8
Multiplication of Integers
When multiplying integers, follow these rules:
- If both numbers have the same sign, the product is positive.
- If the numbers have different signs, the product is negative.
Example:
(+5) × (+3) = +15
(-5) × (-3) = +15
(+5) × (-3) = -15
(-5) × (+3) = -15
Division of Integers
When dividing integers, follow the same rules as multiplication:
- If both numbers have the same sign, the quotient is positive.
- If the numbers have different signs, the quotient is negative.
Example:
(+15) ÷ (+3) = +5
(-15) ÷ (-3) = +5
(+15) ÷ (-3) = -5
(-15) ÷ (+3) = -5
Analogies to Understand Operations with Integers
Think of integers as steps on a vertical number line. Positive numbers are steps up, and negative numbers are steps down. Adding integers is like taking steps in the same direction, while subtracting is like reversing direction. Multiplication and division can be thought of as repeated addition or subtraction, where the sign determines the direction of the steps.
Conclusion
Mastering operations with integers is crucial for solving more complex mathematical problems. By understanding the rules and applying them consistently, you can confidently perform calculations involving positive and negative numbers.