Table of contents

0. Review of Algebra4h 18m
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 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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2:14 minutes

Problem 14

Textbook Question

Write each fraction in lowest terms. 16/64

Verified step by step guidance

Identify the greatest common divisor (GCD) of the numerator and the denominator. In this case, find the GCD of 16 and 64.

Divide both the numerator and the denominator by their GCD to simplify the fraction.

Rewrite the fraction using the results from the division in the previous step.

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

If needed, express the simplified fraction in different forms, such as a decimal or a percentage, to understand its value better.

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Key Concepts

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

Fractions

A fraction represents a part of a whole and is expressed as a ratio of two integers, where the numerator indicates how many parts are taken, and the denominator indicates the total number of equal parts. Understanding fractions is essential for performing operations such as simplification, addition, and subtraction.

Lowest Terms

A fraction is in lowest terms when the numerator and denominator have no common factors other than 1. To simplify a fraction, one must divide both the numerator and denominator by their greatest common divisor (GCD). This process ensures that the fraction is expressed in its simplest form, making it easier to understand and work with.

Greatest Common Divisor (GCD)

The greatest common divisor is the largest positive integer that divides two or more integers without leaving a remainder. Finding the GCD is crucial for simplifying fractions, as it allows one to reduce the fraction to its lowest terms by dividing both the numerator and denominator by this value.