/*! 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 24 Express each ratio as a fraction... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 24

Express each ratio as a fraction in simplest form. 68 meters in 15 seconds

Short Answer

Expert verified
The ratio 68 meters in 15 seconds expressed as a fraction in simplest form is \( \frac{68}{15} \).

Step by step solution

01

Understand the Ratio

The given problem asks you to express the ratio of 68 meters to 15 seconds as a fraction. A ratio is a comparison of two quantities, in this case, the distance in meters to the time in seconds.
02

Write the Ratio as a Fraction

To express a ratio as a fraction, write the first quantity as the numerator and the second quantity as the denominator. Therefore, the ratio of 68 meters to 15 seconds can be written as the fraction \( \frac{68}{15} \).
03

Simplify the Fraction

To simplify the fraction, find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 68 and 15 is 1 since they have no common factors other than 1, which means the fraction is already in its simplest form.

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. At their core, fractions express how many parts of something exist if it was divided into equal pieces. A fraction consists of two main parts: the numerator and the denominator.
  • The numerator is the number on top, indicating how many parts we are considering.
  • The denominator, at the bottom, shows how many equal parts the whole is divided into.
In our exercise, the fraction \( \frac{68}{15} \) is derived from a ratio, reflecting 68 meters per 15 seconds. This is key in translating real-world data into a manageable form to perform further mathematical operations. Fractions help us compare, measure, and understand relationships between quantities.
Simplifying Fractions
Simplifying fractions is an essential skill in mathematics that involves expressing a fraction in a way that is easiest to understand. The goal is to reduce the fraction to its simplest form while maintaining the same value.
  • Identify any common factors shared by the numerator and the denominator.
  • Divide both parts of the fraction by their greatest common factor.
For instance, with the fraction \( \frac{68}{15} \), checking for common factors is crucial to know if the fraction can be simplified further. Simplification makes fractions easier to read and use, especially in subsequent calculations or comparisons, allowing clearer insights into the data.
Greatest Common Divisor
The Greatest Common Divisor (GCD) is the largest number that can evenly divide two numbers. Finding the GCD helps us simplify fractions because it shows us the greatest factor by which the numerator and denominator can both be divided.
Here's how you can find the GCD:
  • List the factors of each number.
  • Identify the largest factor that both numbers share.
  • Divide the numerator and the denominator by this factor.
In the case of the fraction \( \frac{68}{15} \), since 68 and 15 share no common factors other than 1, their GCD is 1. This tells us that \( \frac{68}{15} \) is already in its simplest form. Understanding the GCD isn't just about simplifying fractions鈥攊t's a useful skill when comparing ratios and understanding portions in contexts like data analysis, cooking, and beyond.

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 each sum or difference. Write in simplest form. $$ 8 \frac{1}{6}+14 \frac{5}{6} $$

Find a fraction that satisfies all of the conditions below. Then write a sentence explaining why you think your fraction is or is not the only solution that satisfies the conditions. \(\cdot\) The fraction can be written as a percent greater than \(1 \%\) \(\cdot\) The fraction can be written as a percent less than \(50 \%\) \(\cdot\) The decimal equivalent of the fraction is a terminating decimal. \- The value of the denominator minus the value of the numerator is 3 .

Solve each proportion. $$\frac{75}{8}=\frac{n}{100}$$

The amount of sales tax paid on a purchase is proportional to the price of the item. If the sales tax rate is \(6.25 \%\), find the equation if \(p\) is the price of the item and \(t\) is the sales tax. \(\mathbf{F} \quad p=0.0625 t\) \(\mathbf{H} t=6.25 p\) \(\mathbf{G} p=6.25 t\) \(\mathbf{J} \quad t=0.0625 p\)

Simplify each fraction. $$\frac{25}{100}$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Logic and Functions

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.