Multiplication of Integers

Definition

Multiplication of integers is a mathematical operation that involves the repeated addition of a number to itself a certain number of times. It is a fundamental operation in the context of integers, which are positive and negative whole numbers, including zero.

5 Must Know Facts For Your Next Test

1. The product of two positive integers is always a positive integer.
2. The product of a positive integer and a negative integer is always a negative integer.
3. The product of two negative integers is always a positive integer.
4. Multiplying an integer by zero always results in a product of zero.
5. The commutative property of multiplication holds for integers, meaning $a \times b = b \times a$.

Review Questions

• Explain the rules for multiplying positive and negative integers.
  • The rules for multiplying positive and negative integers are as follows: 1) The product of two positive integers is always positive. 2) The product of a positive integer and a negative integer is always negative. 3) The product of two negative integers is always positive. These rules are based on the properties of integers and the commutative property of multiplication, which states that the order of the factors does not change the product.
• Describe the relationship between multiplication and repeated addition for integers.
  • Multiplication of integers is closely related to the concept of repeated addition. For example, $3 \times 4$ can be interpreted as adding the number 3 to itself 4 times, which results in 12. Similarly, $-2 \times 5$ can be interpreted as adding the number -2 to itself 5 times, which results in -10. This connection between multiplication and repeated addition is a fundamental property of integers and is essential for understanding the rules and applications of integer multiplication.
• Analyze the effect of multiplying an integer by zero and explain the significance of this property.
  • Multiplying any integer, whether positive, negative, or zero, by the number zero always results in a product of zero. This property is known as the zero property of multiplication and is a crucial aspect of working with integers. The significance of this property is that it allows for simplification of mathematical expressions and ensures consistency in the behavior of integers under multiplication. Understanding this property is essential for performing accurate calculations and manipulations involving integers.

Related terms

Integer: An integer is a whole number, which can be positive, negative, or zero. Integers do not include fractions or decimal numbers.

Positive Integer: A positive integer is a whole number greater than zero, such as 1, 2, 3, 4, and so on.

Negative Integer: A negative integer is a whole number less than zero, such as -1, -2, -3, -4, and so on.