key term - Cancellation

Definition

Cancellation is the process of eliminating or simplifying expressions by removing or canceling out common factors between the numerator and denominator of a fraction. This technique is widely used in various mathematical operations, including multiplying and dividing fractions, mixed numbers, and monomials.

5 Must Know Facts For Your Next Test

1. Cancellation is a crucial step in multiplying and dividing fractions, as it helps to reduce the complexity of the expression and make the calculations more manageable.
2. When multiplying fractions, cancellation can be performed by identifying and removing common factors between the numerators and denominators before carrying out the multiplication.
3. In the context of dividing fractions, cancellation is used to simplify the expression by removing common factors between the dividend and divisor.
4. Cancellation is also applicable when working with mixed numbers and complex fractions, as it can help to convert the expressions into simpler, more manageable forms.
5. Cancellation is a fundamental concept in the division of monomials, as it allows for the simplification of the expression by removing common factors between the numerator and denominator.

Review Questions

• Explain how cancellation is used when multiplying fractions.
  • When multiplying fractions, cancellation can be used to simplify the expression by identifying and removing common factors between the numerators and denominators before carrying out the multiplication. This process reduces the complexity of the calculation and often results in a more manageable expression. By canceling out common factors, the fractions can be expressed in their simplest form, making the multiplication more efficient and the final result more easily interpretable.
• Describe the role of cancellation in the division of mixed numbers and complex fractions.
  • Cancellation is a crucial step in the division of mixed numbers and complex fractions. By identifying and removing common factors between the dividend and divisor, the expression can be simplified, making the division process more straightforward. This is particularly important when dealing with mixed numbers, as the cancellation of common factors can help convert the mixed number into an improper fraction or a simpler expression. Similarly, in the case of complex fractions, cancellation can be used to reduce the expression to a more manageable form, facilitating the division operation.
• Analyze the role of cancellation in the division of monomials and explain how it contributes to the simplification of the expression.
  • Cancellation is a fundamental concept in the division of monomials, as it allows for the simplification of the expression by removing common factors between the numerator and denominator. By identifying and canceling out these common factors, the division of monomials becomes more efficient and the resulting expression is in its simplest form. This is particularly important when working with complex monomial expressions, as the cancellation of common factors can significantly reduce the complexity of the division operation, making the final result more easily interpretable and manageable.

Related terms

Common Factor: A number or expression that divides evenly into two or more other numbers or expressions without a remainder.

Simplification:

The process of reducing an expression to its simplest form by performing various operations, such as combining like terms, factoring, or canceling out common factors.

Equivalent Fractions:

Fractions that represent the same numerical value, even though the numerator and denominator may be different.