/*! 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 18 Change each of the following per... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 18

Change each of the following percentages to a ratio, and reduce to lowest terms. \(16 \%\)

Short Answer

Expert verified
The ratio is 4:25.

Step by step solution

01

Understand the Percentage

A percentage is a way of expressing a number as a fraction of 100. The percentage given here is 16%.
02

Convert Percentage to Fraction

Since 16% means 16 out of every 100, we convert this to a fraction as \( \frac{16}{100} \).
03

Simplify the Fraction

Find the greatest common divisor (GCD) of 16 and 100, which is 4. Then divide both the numerator and the denominator by 4. \[ \frac{16 \div 4}{100 \div 4} = \frac{4}{25} \]
04

Write the Fraction as a Ratio

A ratio compares two quantities. Write the simplified fraction as a ratio: 4:25.

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.

Simplifying Fractions
Simplifying fractions is a key mathematical skill that allows us to reduce fractions to their simplest form, making them easier to work with. When you simplify a fraction, you find a smaller equivalent fraction that retains the same value.
Start by determining the greatest common divisor (GCD) of both the numerator and the denominator. The GCD is the largest number that can evenly divide both numbers. For the fraction \( \frac{16}{100} \), the GCD is 4.
Next, divide both the numerator and the denominator by the GCD.
  • Numerator: \( 16 \div 4 = 4 \)
  • Denominator: \( 100 \div 4 = 25 \)
So, \( \frac{16}{100} \) simplifies to \( \frac{4}{25} \). Simplifying fractions makes calculations easier and keeps numbers manageable.
Understanding Percentages
Percentages are a way of expressing numbers as parts per hundred. This means any percentage expresses a proportion relative to a total of 100.
For example, when you see 16%, it represents 16 parts out of 100. Understanding percentages helps in making sense of proportions and scaling.
  • Convert percentages to fractions by placing the percentage number over 100. So, 16% becomes \( \frac{16}{100} \).
  • Recognize that converting percentages to fractions makes it easier to perform many mathematical operations, such as simplifying fractions or comparing ratios.
Learning to convert and interpret percentages is useful in everyday contexts, like calculating discounts or understanding statistics.
Mathematical Ratios
Ratios are a fundamental concept used to compare quantities. A ratio tells you how much of one thing there is compared to another.
To form a ratio from a fraction, consider each part of the fraction as a separate quantity. For the fraction \( \frac{4}{25} \), the ratio becomes 4:25. This means for every 4 units of one quantity, there are 25 units of another.
  • Ratios provide a simple way to communicate relationships between numbers.
  • They are useful for solving problems in fields ranging from culinary recipes to engineering and business analytics.
Understanding how to express a fractional quantity as a ratio simplifies interpreting part-to-whole and part-to-part comparisons, making ratios a versatile tool in both academia and real-world applications.

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 client's weight increased from \(120 \mathrm{lb}\) to \(132 \mathrm{lb}\). What was the percent of increase in body weight?

Convert the following percents to decimals. \(4.4 \%\)

Perform the indicated operations. 100 is what percentage of \(750 ?\)

A client is on a \(1,000 \mathrm{~mL}\) fluid restriction per 24 hours. At breakfast and lunch the client consumed \(40 \%\) of the fluid allowance. How many milliliters did the client consume?

In a portion of turkey that is \(100 \mathrm{~g}\) (grams), there are \(23 \mathrm{~g}\) of protein and \(4 \mathrm{~g}\) of fat. What percentage of the portion is protein? What percentage is fat?
See all solutions

Recommended explanations on Biology Textbooks

Ecology

Read Explanation

Ecosystems

Read Explanation

Organ Systems

Read Explanation

Heredity

Read Explanation

Astrobiological Science

Read Explanation

Chemistry of Life

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.