Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
Lowest terms refers to the simplest form of a fraction, where the numerator and denominator have no common factors other than 1. In this form, the fraction cannot be reduced any further.
5 Must Know Facts For Your Next Test
Fractions in lowest terms have the smallest possible whole number values for the numerator and denominator.
To express a fraction in lowest terms, you must find the greatest common factor (GCF) of the numerator and denominator, and then divide both the numerator and denominator by the GCF.
Fractions in lowest terms cannot be further simplified without changing the value of the fraction.
Expressing a fraction in lowest terms is important for performing operations with fractions, such as addition, subtraction, multiplication, and division.
Fractions in lowest terms are often used in mathematical proofs and problem-solving to simplify expressions and make calculations more efficient.
Review Questions
Explain the process of reducing a fraction to its lowest terms.
To reduce a fraction to its lowest terms, you need to find the greatest common factor (GCF) of the numerator and denominator. Once you have identified the GCF, you divide both the numerator and denominator by the GCF. This will result in a fraction with the smallest possible whole number values for the numerator and denominator, and the fraction cannot be reduced any further without changing its value.
Describe the importance of expressing fractions in lowest terms in the context of fraction operations.
Expressing fractions in lowest terms is crucial when performing operations with fractions, such as addition, subtraction, multiplication, and division. Fractions in lowest terms have the smallest possible whole number values for the numerator and denominator, which can simplify the calculations and make the operations more efficient. Additionally, working with fractions in lowest terms can help ensure the accuracy of the results and prevent unnecessary rounding errors.
Analyze the relationship between fractions in lowest terms and mathematical proofs or problem-solving.
Fractions in lowest terms are often used in mathematical proofs and problem-solving because they provide the simplest representation of a fractional quantity. By expressing fractions in lowest terms, mathematicians can streamline their work, make calculations more efficient, and ensure the validity of their arguments or solutions. Fractions in lowest terms also help to maintain the integrity of mathematical concepts and relationships, which is crucial in the context of rigorous mathematical reasoning and problem-solving.