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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1:09 minutes

Problem 172

Textbook Question

Write each percent as a fraction. Give answers in lowest terms. 47%

Verified step by step guidance

Start by understanding that a percent is a way of expressing a number as a fraction of 100. So, 47% can be written as \( \frac{47}{100} \).

Next, check if the fraction \( \frac{47}{100} \) can be simplified. To do this, find the greatest common divisor (GCD) of the numerator (47) and the denominator (100).

Since 47 is a prime number, it only has two divisors: 1 and 47. Check if 47 divides 100 evenly.

Since 47 does not divide 100 evenly, the GCD of 47 and 100 is 1.

Therefore, the fraction \( \frac{47}{100} \) 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 represents a part per hundred and is denoted by the symbol '%'. To convert a percentage to a fraction, you place the percentage value over 100. For example, 47% means 47 out of 100, which can be expressed as the fraction 47/100.

Simplifying Fractions

Simplifying a fraction involves reducing it to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD). For instance, if a fraction is 12/16, both numbers can be divided by 4, resulting in the simplified fraction 3/4.

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. For example, the fraction 2/5 is in lowest terms, while 4/10 can be simplified to 2/5, which is its lowest form.