key term - Division

Definition

Division is a mathematical operation that involves the partitioning of a quantity into equal parts or the determination of how many times one number is contained within another. It is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication.

5 Must Know Facts For Your Next Test

1. Division is the inverse operation of multiplication, and it is used to find how many times one number is contained in another.
2. The division symbol (÷) represents the act of dividing one number by another, with the dividend being the number being divided and the divisor being the number it is divided by.
3. When solving equations with variables and constants on both sides, division is used to isolate the variable by dividing both sides of the equation by the same number.
4. In the context of rational expressions, division is used to simplify complex fractions by dividing the numerator and denominator by a common factor.
5. The properties of division, such as the commutative and associative properties, can be used to simplify and manipulate division expressions.

Review Questions

• Explain how division is used to multiply and divide integers.
  • Division is the inverse operation of multiplication, and it is used to determine how many times one integer is contained within another. For example, to divide 24 by 6, we are asking how many times 6 goes into 24. The answer, 4, is the quotient. Division of integers follows the same rules as multiplication, where a negative divided by a negative results in a positive, and a negative divided by a positive results in a negative.
• Describe how division is used to solve equations with variables and constants on both sides.
  • When solving equations with variables and constants on both sides, division is used to isolate the variable by dividing both sides of the equation by the same number. This allows the variable to be on one side of the equation, with the constant terms on the other side. For example, to solve the equation $2x + 4 = 10$, we would divide both sides by 2 to get $x + 2 = 5$, and then further simplify to find the value of $x$.
• Analyze how division is used to multiply and divide rational expressions.
  • In the context of rational expressions, division is used to simplify complex fractions by dividing the numerator and denominator by a common factor. This process, known as factoring, allows for the cancellation of common factors in the numerator and denominator, resulting in a simpler, equivalent rational expression. Additionally, division of rational expressions follows the same rules as division of integers, where a negative divided by a negative results in a positive, and a negative divided by a positive results in a negative.

Related terms

Dividend:

The number that is being divided in a division operation.

Divisor:

The number by which the dividend is being divided.

Quotient:

The result of a division operation, representing how many times the divisor goes into the dividend.