key term - Multiplication of Fractions

Definition

Multiplication of fractions is the process of multiplying two or more fractions together to find a single, simplified fraction as the result. This operation is a fundamental concept in the study of fractions and is essential for simplifying complex rational expressions.

5 Must Know Facts For Your Next Test

1. To multiply fractions, you multiply the numerators together and then multiply the denominators together, resulting in a new fraction.
2. The order of the factors does not affect the product when multiplying fractions, as multiplication is commutative.
3. Multiplying a fraction by 1 does not change the value of the fraction, as 1 is the multiplicative identity.
4. Simplifying the resulting fraction by canceling common factors in the numerator and denominator is an important step in multiplying fractions.
5. Multiplication of fractions is a key skill in simplifying complex rational expressions, as it allows for the reduction of the numerator and denominator.

Review Questions

• Explain the process of multiplying two fractions and how the resulting fraction can be simplified.
  • To multiply two fractions, you multiply the numerators together and then multiply the denominators together, resulting in a new fraction. For example, to multiply $\frac{1}{2}$ and $\frac{3}{4}$, you would multiply the numerators (1 × 3 = 3) and the denominators (2 × 4 = 8), giving you the resulting fraction $\frac{3}{8}$. The resulting fraction can then be simplified by canceling any common factors in the numerator and denominator, such as dividing both the numerator and denominator by 1 to get the simplified fraction $\frac{3}{8}$.
• Describe how the multiplication of fractions is used in the simplification of complex rational expressions.
  • The multiplication of fractions is a crucial skill in simplifying complex rational expressions, as it allows for the reduction of the numerator and denominator. By multiplying fractions together, you can cancel out common factors in the numerator and denominator, resulting in a simpler, more manageable rational expression. This process of simplification is essential for evaluating and manipulating complex rational expressions, which often involve the multiplication of multiple fractions.
• Analyze the relationship between the multiplication of fractions and the concept of equivalent fractions, and explain how this relationship can be used to simplify complex expressions.
  • The multiplication of fractions is closely related to the concept of equivalent fractions, as multiplying a fraction by 1 (in the form of a fraction) does not change the value of the original fraction. This property can be leveraged to simplify complex expressions involving fractions. By identifying common factors in the numerator and denominator of a fraction and multiplying the fraction by an equivalent form (a fraction equal to 1), you can cancel out those common factors and arrive at a simpler, more manageable expression. This process of simplification, which relies on the multiplication of fractions, is essential for working with and manipulating complex rational expressions.

Related terms

Fraction:

A fraction is a numerical quantity that represents a part of a whole, expressed as a ratio of two integers - the numerator and the denominator.

Simplification:

Simplification is the process of reducing a fraction or complex expression to its most basic form by performing operations such as canceling out common factors in the numerator and denominator.

Rational Expression:

A rational expression is a quotient of two polynomial expressions, where the denominator is not equal to zero.