Table of contents

0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

0:57 minutes

Problem 8b

Textbook Question

Write each fraction in lowest terms. 4/12

Verified step by step guidance

Identify the greatest common divisor (GCD) of the numerator and the denominator. In this case, find the GCD of 4 and 12.

Divide both the numerator and the denominator by their GCD.

Rewrite the fraction using the results from the division.

Verify that the fraction is in its simplest form by checking that the numerator and the denominator have no common factors other than 1.

Express the simplified fraction as the final answer.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Lowest Terms

A fraction is in lowest terms when the numerator and denominator have no common factors other than 1. This means that the fraction cannot be simplified any further. To express a fraction in lowest terms, you divide both the numerator and the denominator by their greatest common divisor (GCD). For example, in the fraction 4/12, both 4 and 12 can be divided by 4, resulting in 1/3.

Numerator and Denominator

In a fraction, the numerator is the top part that represents how many parts we have, while the denominator is the bottom part that indicates the total number of equal parts the whole is divided into. Understanding the roles of the numerator and denominator is essential for simplifying fractions and performing operations with them. For instance, in the fraction 4/12, 4 is the numerator and 12 is the denominator.

Greatest Common Divisor (GCD)

The greatest common divisor (GCD) of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder. Finding the GCD is crucial for simplifying fractions to their lowest terms. For example, the GCD of 4 and 12 is 4, which is used to simplify the fraction 4/12 to 1/3 by dividing both the numerator and denominator by 4.