/*! 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 100 Explain the difference between \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 100

Explain the difference between \(\frac{3}{4}\) and \(\frac{3}{4} \%\)

Short Answer

Expert verified
\( \frac{3}{4} \) is much larger than \( \frac{3}{4} \% = \frac{3}{400} \).

Step by step solution

01

- Understand Fractions

A fraction, such as \(\frac{3}{4}\), represents a part of a whole. Here, it means 3 parts out of 4.
02

- Understand Percentages

A percentage is a fraction of 100. For example, \(x \%\) is equivalent to \(\frac{x}{100}\).
03

- Convert Percentage to Fraction

To convert \(\frac{3}{4} \%\) to a fraction, divide it by 100: \(\frac{3}{4 \times 100} = \frac{3}{400}\).
04

- Compare the Two Values

Now compare \(\frac{3}{4}\) and \(\frac{3}{400}\). The fraction \(\frac{3}{4}\) is much larger than \(\frac{3}{400}\).

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.

Fractions
Fractions are a way to represent parts of a whole. When you see something like \(\frac{3}{4}\), it means 3 parts out of 4 total parts.
  • The top number is called the 'numerator'.
  • The bottom number is the 'denominator'.

Fractions can describe sizes, portions, and relationships between quantities. If you divide an item into 4 equal parts and take 3 of those parts, you have \(\frac{3}{4}\) of the item.
Percentages
Percentages are a way to express fractions out of 100. The term comes from Latin 'per centum', meaning 'by the hundred'.
  • Think of percentages as fractions with a denominator of 100.
  • For example, 50% is the same as saying \(\frac{50}{100}\).

When you see a percentage, it's an indication of how many parts out of a whole made up of 100 parts something represents. For instance, 75% means 75 parts out of 100.
Fraction to Percentage Conversion
Converting fractions to percentages is straightforward. You simply multiply the fraction by 100.
  • For example, to convert \(\frac{3}{4}\) to a percentage: \(\frac{3}{4} \times 100 = 75\)%.
  • To convert \(\frac{1}{2}\) to a percentage: \(\frac{1}{2} \times 100 = 50\)%.

Converting a percentage to a fraction involves dividing by 100. For instance, 25% becomes \(\frac{25}{100} = \frac{1}{4}\).
Comparison of Fractions and Percentages
Comparing fractions and percentages may initially seem tricky because they are different formats. However, with conversions, they become easier to understand.
  • For instance, \(\frac{3}{4}\) expressed as a fraction is \(\frac{3}{4} = 75\text{%}\).
  • Meanwhile, \(\frac{3}{4}\)\text{%} can be converted to a fraction by dividing it by 100, giving \(\frac{3}{400}\).

Clearly, \(\frac{3}{4}\) is much larger than \(\frac{3}{400}\). This showcases why understanding and accurately converting between the two is essential.

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

Find the total amount in an account for an investment subject to the following conditions. Principal \$ 4,000 Annual Interest Rate $$3 \%$$ Time, Years $$3$$ Compounded Semiannually Total Amount __________

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{13}{15}$$

Find the total amount in an account for an investment subject to the following conditions. Principal $$\$ 14,000$$ Annual Interest Rate $$4.5 \%$$ Time, Years $$3$$ Compounded Monthly Total Amount __________

Explain the difference between \(10 \%\) and \(0.10 \%\)

Explain the difference between \(25 \%\) and \(0.25 \%\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

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.