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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0:57 minutes

Problem 171

Textbook Question

Write each percent as a fraction. Give answers in lowest terms. 51%

Verified step by step guidance

Start by understanding that a percent is a way of expressing a number as a fraction of 100. So, 51% means 51 out of 100.

Write 51% as a fraction: \( \frac{51}{100} \).

Check if the fraction \( \frac{51}{100} \) can be simplified by finding the greatest common divisor (GCD) of 51 and 100.

Determine the GCD of 51 and 100. Since 51 is a product of 3 and 17, and 100 is a product of 2 and 5, they have no common factors other than 1.

Since the GCD is 1, the fraction \( \frac{51}{100} \) is already in its simplest form.

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Key Concepts

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

Percentages

A percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol '%'. For example, 51% means 51 out of 100, which can be represented as the fraction 51/100. Understanding percentages is crucial for converting them into fractions.

Fractions

A fraction represents a part of a whole and is expressed as a ratio of two integers, with a numerator (top number) and a denominator (bottom number). To convert a percentage to a fraction, the percentage is placed over 100, and simplification may be necessary to express it in lowest terms.

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.