Sign Rules

Definition

Sign rules are a set of guidelines that govern the operations of addition, subtraction, multiplication, and division with positive and negative integers. These rules determine the resulting sign of the output based on the signs of the input numbers.

5 Must Know Facts For Your Next Test

1. The product of two positive integers or two negative integers is always positive.
2. The product of a positive integer and a negative integer is always negative.
3. The quotient of a positive integer divided by a positive integer is always positive.
4. The quotient of a negative integer divided by a negative integer is always positive.
5. The quotient of a positive integer divided by a negative integer is always negative.

Review Questions

• Explain the sign rules for multiplying integers.
  • The sign rules for multiplying integers state that the product of two positive integers or two negative integers is always positive, while the product of a positive integer and a negative integer is always negative. For example, $+3 \times +5 = +15$, $-4 \times -7 = +28$, and $+2 \times -6 = -12$. These rules are important for understanding the behavior of integers during multiplication operations.
• Describe the sign rules for dividing integers.
  • The sign rules for dividing integers state that the quotient of a positive integer divided by a positive integer or a negative integer divided by a negative integer is always positive, while the quotient of a positive integer divided by a negative integer is always negative. For example, $+20 \div +4 = +5$, $-18 \div -3 = +6$, and $+15 \div -3 = -5$. These sign rules help determine the correct sign of the result when dividing integers.
• Analyze the relationship between the signs of the input numbers and the sign of the result in integer operations.
  • The sign rules for integer operations, including addition, subtraction, multiplication, and division, are based on the relationship between the signs of the input numbers and the sign of the result. Specifically, the sign of the result depends on the combination of positive and negative signs in the input numbers. Understanding these sign rules is crucial for accurately performing operations with integers and interpreting the meaning of the results in the context of the 3.4 Multiply and Divide Integers topic.

Related terms

Positive Integer: A positive integer is a whole number greater than zero, such as 1, 2, 3, and so on.

Negative Integer: A negative integer is a whole number less than zero, such as -1, -2, -3, and so on.

Absolute Value: The absolute value of a number is the distance of that number from zero on the number line, regardless of its sign.