key term - Lowest Terms

Definition

Lowest terms refers to the simplest form of a fraction, where the numerator and denominator have no common factors other than 1. This concept is crucial in the context of visualizing fractions, simplifying rational expressions, and performing operations on rational expressions.

5 Must Know Facts For Your Next Test

1. A fraction is in lowest terms when the numerator and denominator have no common factors other than 1.
2. To simplify a fraction to its lowest terms, you need to divide both the numerator and denominator by their greatest common factor (GCF).
3. Fractions in lowest terms provide the most concise and efficient way to represent a fractional value.
4. Simplifying rational expressions to their lowest terms is a crucial step in manipulating and evaluating them.
5. Multiplying and dividing rational expressions often requires first simplifying them to their lowest terms.

Review Questions

• Explain the importance of expressing fractions in their lowest terms.
  • Expressing fractions in their lowest terms is important because it provides the most concise and efficient representation of the fractional value. Fractions in lowest terms have no common factors between the numerator and denominator, other than 1. This simplification makes it easier to perform operations, compare values, and understand the true magnitude of the fraction. Fractions in lowest terms are the standard form for representing fractional quantities, as they convey the information with the least amount of redundancy.
• Describe the process of simplifying a fraction to its lowest terms.
  • To simplify a fraction to its lowest terms, you need to find the greatest common factor (GCF) between the numerator and denominator, and then divide both the numerator and denominator by the GCF. This effectively cancels out any common factors, leaving the fraction in its simplest form. For example, to simplify the fraction $\frac{12}{18}$, you would first find the GCF of 12 and 18, which is 6. Then, you would divide both the numerator and denominator by 6, resulting in the fraction $\frac{2}{3}$, which is in lowest terms.
• Explain how the concept of lowest terms is applied in the context of simplifying rational expressions and performing operations on them.
  • When working with rational expressions, it is crucial to simplify them to their lowest terms. This ensures that the expression is in its most concise and manageable form, making it easier to perform operations such as multiplication, division, addition, and subtraction. Simplifying a rational expression to its lowest terms involves factoring the numerator and denominator, and then cancelling out any common factors. This process is essential for accurately evaluating and manipulating rational expressions, as it eliminates redundant information and provides a clear representation of the underlying mathematical relationships.

Related terms

Simplify: To reduce an expression to its simplest form by performing operations and eliminating unnecessary elements.

Equivalent Fractions:

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

Greatest Common Factor (GCF):

The largest positive integer that divides both the numerator and denominator of a fraction without a remainder.