Multiple

Definition

In mathematics, a multiple is a number that can be expressed as the product of an integer and another integer. This concept is foundational in understanding various mathematical operations and helps in recognizing patterns in numbers, such as those related to multiplication, division, and factors.

5 Must Know Facts For Your Next Test

1. Multiples of a number are generated by multiplying that number by the integers (e.g., multiples of 3 are 3, 6, 9, 12...).
2. The smallest multiple of any non-zero integer is the integer itself.
3. Multiples can be used to find common denominators when adding or subtracting fractions.
4. Understanding multiples is crucial for solving problems involving ratios and proportions.
5. The concept of least common multiple (LCM) is vital for finding the smallest multiple shared by two or more numbers.

Review Questions

• How does understanding multiples contribute to solving problems with fractions?
  • Understanding multiples helps in finding common denominators when adding or subtracting fractions. By identifying the multiples of the denominators involved, one can determine the least common multiple (LCM), which allows for the conversion of each fraction to an equivalent fraction with a common denominator. This process makes it easier to perform addition or subtraction accurately.
• Explain how multiples relate to factors and why this relationship is important in mathematics.
  • Multiples and factors are closely related concepts; a multiple of a number contains that number as a factor. For example, since 12 is a multiple of 4, it means that 4 is also a factor of 12. This relationship is crucial because it allows for simplification of problems involving division and helps in identifying relationships between numbers, such as in factorization and finding greatest common divisors.
• Analyze the significance of least common multiples in real-world applications such as scheduling and resource management.
  • The least common multiple (LCM) plays a vital role in real-world applications like scheduling events or managing resources. For instance, if two events occur every 3 days and every 5 days respectively, the LCM helps determine when both events will coincide again, which is after 15 days. This concept helps in planning effectively and ensuring optimal use of resources while avoiding conflicts in scheduling.

Related terms

Factor:

A factor is a whole number that divides another number without leaving a remainder.

Integer:

An integer is a whole number that can be positive, negative, or zero, and does not include fractions or decimals.

Divisible: A number is said to be divisible by another if it can be divided by that number without leaving a remainder.