Remainder

Definition

The remainder is the amount left over after dividing one number by another. It represents the part of the dividend that cannot be evenly divided by the divisor, leaving a non-zero value behind.

5 Must Know Facts For Your Next Test

1. The remainder is always less than the divisor and has the same sign as the dividend.
2. If the remainder is 0, then the dividend is evenly divisible by the divisor.
3. The remainder can be used to determine if a number is divisible by another number.
4. The remainder is an important concept in understanding the relationship between division and multiplication.
5. Remainders are often used in real-world applications, such as in calculating change or determining the number of complete sets that can be made from a collection of items.

Review Questions

• Explain how the remainder relates to the concept of dividing whole numbers.
  • The remainder is a crucial component of dividing whole numbers. When dividing one number by another, the remainder represents the part of the dividend that cannot be evenly divided by the divisor. It is the amount left over after the division process, and it is always less than the divisor. The presence of a non-zero remainder indicates that the dividend is not evenly divisible by the divisor, while a remainder of 0 means the dividend can be divided without a leftover amount.
• Describe the relationship between the remainder, dividend, and divisor in a division problem.
  • In a division problem, the remainder is directly related to the dividend and divisor. The remainder is the amount left over after the dividend has been divided by the divisor. The remainder will always be less than the divisor and will have the same sign as the dividend. The relationship can be expressed as: Dividend = Divisor × Quotient + Remainder. This equation highlights how the remainder is the part of the dividend that cannot be evenly divided by the divisor, leaving a non-zero value behind.
• Analyze how the remainder can be used to determine if a number is divisible by another number.
  • The remainder can be used to determine if a number is divisible by another number. If the remainder is 0 when dividing one number by another, it means the dividend is evenly divisible by the divisor, and the two numbers are said to be divisible. Conversely, if the remainder is non-zero, it indicates that the dividend is not evenly divisible by the divisor. This property of the remainder is particularly useful in various mathematical and real-world applications, such as checking for factors, prime numbers, or determining the number of complete sets that can be made from a collection of items.

Related terms

Dividend: The number being divided in a division problem.

Divisor: The number by which the dividend is being divided.

Quotient: The result of dividing the dividend by the divisor.