Sign Rules

Definition

Sign rules are a set of guidelines that govern the behavior of positive and negative numbers, especially when performing mathematical operations such as addition, subtraction, multiplication, and division. These rules help in understanding and predicting the signs of the results of various calculations involving integers.

5 Must Know Facts For Your Next Test

1. When adding or subtracting two numbers with the same sign, the result will have the same sign.
2. When adding or subtracting two numbers with different signs, the result will have the sign of the number with the larger absolute value.
3. When multiplying or dividing two numbers with the same sign, the result will be positive.
4. When multiplying or dividing two numbers with different signs, the result will be negative.
5. The sign of a number raised to an even power will always be positive, while the sign of a number raised to an odd power will be the same as the original number.

Review Questions

• Explain the sign rules for addition and subtraction of integers.
  • The sign rules for addition and subtraction of integers state that when adding or subtracting two numbers with the same sign, the result will have the same sign. For example, $+3 + (+5) = +8$ and $-7 - (-2) = -5$. However, when adding or subtracting two numbers with different signs, the result will have the sign of the number with the larger absolute value. For instance, $+4 - (-3) = +7$ and $-6 + (+2) = -4$.
• Describe the sign rules for multiplication and division of integers.
  • The sign rules for multiplication and division of integers state that when multiplying or dividing two numbers with the same sign, the result will be positive. For example, $(-2) \times (+3) = -6$ and $(-10) \div (+2) = -5$. Conversely, when multiplying or dividing two numbers with different signs, the result will be negative. For instance, $+4 \times (-7) = -28$ and $(-15) \div (+3) = -5$.
• Analyze the sign of a number raised to an even or odd power in the context of integers.
  • The sign rules for exponents state that the sign of a number raised to an even power will always be positive, regardless of the sign of the base number. For example, $(-3)^2 = +9$ and $(-5)^4 = +625$. However, the sign of a number raised to an odd power will be the same as the sign of the base number. In other words, $(-2)^3 = -8$ and $(-6)^5 = -7,776$. This is an important concept to understand when working with integers and their operations.

Related terms

Integers:

Integers are whole numbers, both positive and negative, including zero.

Positive Numbers: Positive numbers are numbers greater than zero, represented with a positive sign (e.g., +3, 7).

Negative Numbers: Negative numbers are numbers less than zero, represented with a negative sign (e.g., -5, -12).