Final answer:
The sign of a number indicates whether it is positive or negative, which is essential for performing arithmetic operations. When adding or subtracting, the sign of the result depends on whether the numbers are like-signed or opposite-signed. For multiplication and division, like-signed numbers yield a positive result while opposite-signed numbers yield a negative result.
Step-by-step explanation:
Understanding the sign of a number is essential in mathematics as it indicates whether a number is positive or negative. This is crucial when performing operations such as addition, subtraction, multiplication, and division, as different rules apply depending on the signs of the numbers involved.
Rules for Addition and Subtraction
- When two positive numbers add, the result is positive, e.g., 3 + 2 = 5.
- When two negative numbers add, the result is negative, e.g., -4 + (-2) = -6.
- For numbers with opposite signs, subtract the smaller number from the larger ones and the answer has the sign of the larger number, e.g., -5 + 3 = -2.
- In subtraction, change the sign of the number being subtracted and follow addition rules, e.g., 5 - 3 is the same as 5 + (-3) = 2.
Rules for Multiplication and Division
- When two positive numbers multiply, the result is positive, e.g., 2 x 3 = 6.
- When two negative numbers multiply, the result is also positive, e.g., (-4) x (-3) = 12.
- If the numbers multiplied have opposite signs, the result is negative, e.g., (-3) x 2 = -6.
- Division follows the same sign rules as multiplication, e.g., (-6) / 2 = -3, and (-6) / (-3) = 2.
Understanding these rules will help you calculate the correct sign when dealing with both positive and negative numbers and perform arithmetic operations accurately.