/*! 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 43 Convert each fraction to a perce... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 43

Convert each fraction to a percent. $$6 \frac{4}{5}$$

Short Answer

Expert verified
680%

Step by step solution

01

Convert the Mixed Number to an Improper Fraction

Convert the mixed number \(6 \frac{4}{5}\) into an improper fraction. Recall that a mixed number \(a \frac{b}{c}\) can be converted into \(\frac{a imes c + b}{c}\). Thus,\[6 \frac{4}{5} = \frac{6 imes 5 + 4}{5} = \frac{30 + 4}{5} = \frac{34}{5}.\]
02

Convert the Improper Fraction to Decimal

Convert the improper fraction \(\frac{34}{5}\) to a decimal. This is done by dividing 34 by 5.\[34 \div 5 = 6.8.\]
03

Convert the Decimal to a Percent

To convert a decimal to a percent, multiply by 100 and add the percent symbol. Therefore,\[6.8 \times 100 = 680\%\].
04

Rewrite the Answer

Thus, the mixed number \(6 \frac{4}{5}\) converted to a percent is \(680\%\).

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.

Mixed Numbers
A mixed number combines a whole number with a fraction. For example, in the mixed number \(6 \frac{4}{5}\), the whole number is \(6\) and the fraction is \(\frac{4}{5}\). Understanding mixed numbers is important when performing conversions, especially in mathematical operations like addition, subtraction, and percent conversions.
  • To convert a mixed number to an improper fraction, we use the formula: \( \frac{a \times c + b}{c}\) where \(a\) is the whole number, \(b\) is the numerator, and \(c\) is the denominator of the fractional part.
  • This formula helps in combining the whole number and the fraction into a single fraction.
Converting mixed numbers into improper fractions makes it easier to then convert these numbers into decimals or percentages. It ensures a smooth transition between different numeric forms.
Improper Fractions
Fractions where the numerator is larger than the denominator are called improper fractions. They are crucial in performing various computations, including conversions. When you have a mixed number, the conversion to an improper fraction like \(\frac{34}{5}\) from \(6 \frac{4}{5}\) allows us to simplify or convert further.
  • An improper fraction will represent the same quantity but is easier to manipulate mathematically, especially when performing division or multiplication tasks, such as when converting to decimals.
  • To solve or simplify improper fractions, one can either convert them into a mixed number (if necessary) or proceed to convert them into decimals.
Proper understanding and conversion of these fractions are fundamental to operations such as decimal conversion.
Decimal Conversion
Decimal conversion involves transforming fractions into decimal form. This is a straightforward process where you divide the numerator by the denominator. For instance, transforming \(\frac{34}{5}\) into a decimal means performing the division, resulting in \(6.8\).
  • This conversion is essential when you need to change fractions to percentages, as percentages are based on a decimal system.
  • Once a number is in decimal form, converting it into a percent is as simple as multiplying by 100 and adding the percent symbol. In our example, multiplying \(6.8\) by 100 gives \(680\%\).
Understanding decimal conversion can greatly enhance your ability to move seamlessly between different numerical forms, allowing effective problem-solving and analysis.

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

Perform the division. If no repeating patterns seems to exist, round the quotient to three decimal places: \(22.35 \div 17\).

2.4 is \(24 \%\) of what number?

Convert \(521 \frac{3}{4} \%\) to a fraction.

A sales person makes a commission of \(16 \%\) on each sale he makes. How much is his commission if he makes a sale of $$\$ 8,500 ?$$

Convert each percent to a fraction. $$22 . \overline{2} \%$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

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.