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QuestionMathematics
What are the rules for adding, subtracting, multiplying, and dividing integers?
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Step 1:I'll explain the rules for operations with integers step by step:
Step 2:: Addition of Integers
- Example: $$(-5) + 3 = -2
- When adding integers with the same sign, add the absolute values and keep the sign - When adding integers with different signs, subtract the smaller absolute value from the larger and take the sign of the larger number
Step 3:: Subtraction of Integers
- $$a - b = a + (-b)
- Subtracting an integer is the same as adding its opposite - The key rule is: Change the subtraction to addition of the opposite
Step 4:: Multiplication of Integers
- Example: $$3 \times (-4) = -12
- Positive × Positive = Positive - Negative × Negative = Positive - Positive × Negative = Negative - Negative × Positive = Negative
Step 5:: Division of Integers
- Example: $$12 \div (-3) = -4
- Positive ÷ Positive = Positive - Negative ÷ Negative = Positive - Positive ÷ Negative = Negative - Negative ÷ Positive = Negative
Final Answer
- Addition: Add absolute values, keep sign of larger number - Subtraction: Add the opposite of the second number - Multiplication: Positive × Positive = Positive, Negative × Negative = Positive, Mixed signs = Negative - Division: Similar sign results in positive, different signs result in negative
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