/*! 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 65 Convert the given fraction to a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 65

Convert the given fraction to a percent. $$ \frac{6}{5} $$

Short Answer

Expert verified
120%

Step by step solution

01

Understand the Fraction-to-Percent Conversion

To convert a fraction to a percentage, we need to multiply the fraction by 100. This is because 'percent' means 'per hundred'. So, the fraction will be expressed as a number out of 100.
02

Multiply the Fraction by 100

Start by multiplying the fraction \( \frac{6}{5} \) by 100. This can be written as \( \frac{6}{5} \times 100 \).
03

Perform the Multiplication

Carry out the multiplication: \( \frac{6}{5} \times 100 = \frac{600}{5} \).
04

Simplify the Result

Now, divide 600 by 5 to simplify the fraction: \( \frac{600}{5} = 120 \). So, \( 120 \) is the percentage value.

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.

Fraction Multiplication
When multiplying fractions, you multiply the numerators together and the denominators together. However, remember in the given exercise we're multiplying a fraction by a whole number. In this case, think of the whole number as a fraction with a denominator of 1. For example, multiplying \(\frac{6}{5}\) by 100 is like multiplying \(\frac{6}{5}\) by \(\frac{100}{1}\).

This gives:
  • The new numerator is \(6 \times 100 = 600\)
  • The new denominator is \(5 \times 1 = 5\)
So, you end up with \(\frac{600}{5}\). It鈥檚 important to keep track of both parts of the fraction as you multiply, ensuring you apply the operation correctly to both the top and the bottom.
Simplifying Fractions
Simplifying fractions means reducing them to their simplest form where the numerator and the denominator have no common factors other than 1.

In our example, after multiplying, we got \(\frac{600}{5}\). To simplify this, check the numbers 600 and 5 for any common factors:
  • Divide both the numerator and the denominator by 5, the greatest common factor.
  • The division process is simple: \(\frac{600}{5} = 120\).
Now the fraction is simplified to a whole number 120. The process of simplifying ensures that the fraction is as reduced as possible, making it easier to interpret and use, especially when converting to percentages.
Understanding Percentages
Percentages are a way of expressing ratios as fractions of 100, which makes them easy to understand and compare. The term 'percent' originates from Latin, meaning 'per hundred'.

Whenever you convert a fraction to a percentage, you essentially find out how much that fraction would be when `set` against 100. As shown in the original problem, \(\frac{6}{5}\) becomes 120 when converted to a percent. Here's why:
  • Multiplying a fraction by 100 changes its scale to a comparison against a whole of 100 units.
  • It answers the question of how much part of the whole the fraction represents in a straightforward manner.
Converting fractions to percentages helps in various applications, such as calculating discounts, determining grades, or understanding data statistics with ease.

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

A business owner borrows $$\$ 3,200$$ for 6 months. At the end of the 6 -month loan period, the interest owed is $$\$ 96$$. What was the simple yearly interest rate (as a percent)?

The balance on a 8-year loan is $$\$ 4,422$$. If the principal borrowed was $$\$ 3,300$$, what was the simple interest rate (as a percent)?

Suppose that $5,200 is invested at 3.5% simple interest per year. What will the balance be after 2 years?

In an election for class president, the vote distribution among three candidates is shown in the following table. $$ \begin{array}{c|c} \text { Candidate } & \text { Votes } \\ \hline \text { Bernardo } & 38 \\ \text { Fernando } & 49 \\ \text { Aisha } & 44 \\ \hline \end{array} $$ Use a protractor to help create a pie chart showing the distribution of votes.

A business owner borrows $2,400 for 4 months at a 8.25% per year simple interest rate. At the end of the 4-month loan period, how much interest is owed?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Pure 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.