÷

Definition

The division symbol, also known as the obelus, is a mathematical operation that represents the division of one number by another. It is used to indicate that one quantity is to be divided by another, resulting in a quotient.

5 Must Know Facts For Your Next Test

1. The division symbol (÷) is used to indicate that the number or expression to the left of the symbol is to be divided by the number or expression to the right of the symbol.
2. When dividing rational expressions, the numerator of the first expression is multiplied by the reciprocal of the second expression.
3. Dividing a rational expression by a constant is equivalent to multiplying the rational expression by the reciprocal of the constant.
4. Simplifying a rational expression often involves canceling common factors in the numerator and denominator to obtain the lowest possible terms.
5. The properties of division, such as the inverse relationship between multiplication and division, apply to the division of rational expressions.

Review Questions

• Explain the process of dividing two rational expressions.
  • To divide two rational expressions, you first need to find the reciprocal of the second expression. Then, you multiply the first expression by the reciprocal of the second expression. This is because division is the inverse operation of multiplication, and dividing by a number is the same as multiplying by its reciprocal. After performing the multiplication, you can simplify the resulting rational expression by canceling any common factors in the numerator and denominator.
• Describe the relationship between division and reciprocals in the context of rational expressions.
  • In the context of rational expressions, the relationship between division and reciprocals is crucial. When dividing one rational expression by another, you can rewrite the division as multiplication by the reciprocal of the second expression. This is because the reciprocal of a number or expression is the value obtained by inverting the fraction, which effectively reverses the division operation. By multiplying the first rational expression by the reciprocal of the second, you can perform the division and simplify the resulting expression.
• Analyze the role of simplification in the division of rational expressions.
  • Simplifying rational expressions is an essential step when dividing them. After performing the division operation, the resulting expression may contain common factors in the numerator and denominator. Canceling these common factors through simplification is crucial because it reduces the expression to its lowest terms, making it easier to work with and understand. Simplification also helps to minimize the complexity of the expression, making it more manageable for further calculations or algebraic manipulations. The ability to effectively simplify rational expressions is a key skill in the context of dividing them.

Related terms

Rational Expression: A rational expression is a mathematical expression that can be written as the quotient of two polynomials.

Reciprocal: The reciprocal of a number is the value obtained by dividing 1 by that number, which is equivalent to inverting the fraction.

Simplify: Simplifying a rational expression involves reducing the expression to its lowest terms by canceling common factors in the numerator and denominator.