/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 25 Change the percent to a simplifi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 25

Change the percent to a simplified fraction or mixed number. $$5 \frac{1}{6} \%$$

Short Answer

Expert verified
\(\frac{31}{600}\)

Step by step solution

01

Convert Mixed Number to Improper Fraction

First, change the mixed number into an improper fraction. For the percentage \(5 \frac{1}{6}\%\), multiply the whole number part (5) by the denominator (6) and add the numerator (1). The improper fraction is \(\frac{31}{6}\).
02

Convert Percentage to Fraction

Since percentages are out of 100, express the percentage \(\frac{31}{6}\%\) as a fraction: \(\frac{\frac{31}{6}}{100}\).
03

Simplify Fraction

To simplify, multiply by the reciprocal of 100: \(\frac{31}{6} \times \frac{1}{100}\). This results in \(\frac{31}{600}\). Check for any common factors to simplify further.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Improper Fractions
An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). For example, in the step-by-step solution, we converted the mixed number \(5\frac{1}{6}\) into the improper fraction \(\frac{31}{6}\). To do this, multiply the whole number (5) by the denominator (6) and then add the numerator (1). It looks like this: 5 \times 6 + 1 = 31. So, \(5\frac{1}{6}\) becomes \(\frac{31}{6}\). Improper fractions are useful for calculations and can be easier to work with compared to mixed numbers.
Simplifying Fractions
Simplifying fractions means reducing them to their simplest form. This involves finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by that number. For example, if we have the fraction \(\frac{31}{600}\), and there are no common factors other than 1, then this fraction is already in its simplest form. Simplifying helps in making the fraction easier to work with and understand.
Mixed Number Conversion
A mixed number is made up of a whole number and a fractional part. To convert a mixed number to an improper fraction, multiply the whole number by the denominator, then add the numerator. For example, converting \(5\frac{1}{6}\) to an improper fraction gives \(\frac{31}{6}\). Converting mixed numbers to improper fractions can simplify mathematical operations.
Percentages
A percentage represents a part of a whole, expressed out of 100. For instance, 50% means 50 out of 100. In the exercise, we converted a percentage into a fraction. To change \(5\frac{1}{6}\%\) into a fraction, we first converted the mixed number to an improper fraction, giving us \(\frac{31}{6}\). Then, since percentages are out of 100, we expressed it as \(\frac{\frac{31}{6}}{100}\), simplifying this fraction further to \(\frac{31}{600}\). Understanding percentages and how to convert them to fractions is important in various areas of math and everyday life.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Is the number 0.0087 less than or greater than \(1 \% ?\)

Harvard University reported that 232 African American students were admitted to the freshman class in a recent year. If this represents \(11 \%\) of the total freshman class, how many freshmen were admitted?

During a weak economy, milk prices increased during a 1 -year period. The average price in 2008 was \(\$ 3.90 .\) If this value is \(126 \%\) of the price from 2007 , determine the price in 2007 . Round to two decimal places. (Source: U.S. Department of Agriculture)

Solve the problem using a percent equation. \(225 \%\) of what number is \(18 ?\)

Solve the problem using a percent equation. \(350 \%\) of what number is \(2100 ?\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.