/*! 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 21 Write the ratio in lowest terms.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 21

Write the ratio in lowest terms. \(33 \mathrm{cm}\) to \(15 \mathrm{cm}\)

Short Answer

Expert verified
11:5

Step by step solution

01

- Write the ratio as a fraction

Express the given ratio as a fraction: \(\frac{33 \text{ cm}}{15 \text{ cm}}\).
02

- Simplify the fraction

To simplify the fraction, find the greatest common divisor (GCD) of 33 and 15. The GCD of 33 and 15 is 3.
03

- Divide both the numerator and the denominator by the GCD

Divide both the numerator and the denominator of the fraction by the GCD (3): \(\frac{33 \text{ cm} \/ 3}{15 \text{ cm} \/ 3} = \frac{11}{5}\).
04

- Write the simplified ratio

Now, write the simplified fraction as a ratio: 11:5

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. A fraction consists of two parts: the numerator and the denominator. The numerator (top part) indicates how many equal parts are being considered, while the denominator (bottom part) shows the total number of equal parts in the whole. When simplifying or comparing ratios, we often convert them into fractions.
For example, in our exercise, the ratio 33 cm to 15 cm is written as the fraction \(\frac{33 \text{ cm}}{15 \text{ cm}}\).
greatest common divisor (GCD)
The Greatest Common Divisor (GCD), also known as the Greatest Common Factor (GCF), is the largest number that can exactly divide two or more numbers without leaving a remainder. To simplify fractions, we use the GCD to reduce the numerator and denominator. Finding the GCD involves listing the factors of each number and identifying the largest factor they share.
In the case of 33 and 15, the common divisors are found, and the greatest one is 3. So, the GCD of 33 and 15 is 3.
numerator and denominator
The terms numerator and denominator are essential in understanding fractions. The numerator is the top number in a fraction and signifies the number of parts considered. The denominator is the bottom number and shows the total number of equal parts in the whole.
In our fraction \(\frac{33}{15}\), 33 is the numerator, and 15 is the denominator. To simplify this fraction, we divide both these numbers by their GCD, which in this instance is 3. This yields \(\frac{11}{5}\), where 11 is the new numerator and 5 is the new denominator.
lowest terms
When a fraction is in its lowest terms, it means it cannot be simplified further. To reduce a fraction to its lowest terms, you divide both the numerator and the denominator by their Greatest Common Divisor (GCD).
In our example, we started with the fraction \(\frac{33}{15}\). We found the GCD to be 3. By dividing the numerator (33) and the denominator (15) by 3, we reduced the fraction to \(\frac{11}{5}\), which is in its lowest terms because 11 and 5 have no common divisor besides 1.

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

Evelyn won an election by a ratio of 6 to \(5 .\) If she received 7230 votes, how many votes did her opponent receive?

Mayonnaise comes in 32 - 16 - and 8 -oz jars. They are priced at \(\$ 5.59, \$ 3.79\), and \(\$ 2.59\), respectively. Find the unit cost of each size jar to find the best buy. (Round to three decimal places.)

Erik bought \(\$ 624\) Canadian with \(\$ 600\) American. At this rate, how many Canadian dollars can he buy with \(\$ 250\) American?

Refer to the table showing Alex Rodriguez's salary (rounded to the nearest \(\$ 100,000\) ) for selected years during his career. Write each ratio in lowest terms. \begin{array}{l|l|l|l} \hline \text { Year } & \text { Team } & \text { Salary } & \text { Position } \\ \hline 2007 & \text { New York Yankees } & \$ 22,700,000 & \text { Third baseman } \\ \hline 2004 & \text { New York Yankees } & \$ 22,000,000 & \text { Third baseman } \\ \hline 2000 & \text { Seattle Mariners } & \$ 4,400,000 & \text { Shortstop } \\ \hline 1996 & \text { Seattle Mariners } & \$ 400,000 & \text { Shortstop } \\ \hline \end{array} Write a ratio of Alex's salary for the year 2004 to the year 1996.

Solve the proportion. $$\frac{-2.4}{3}=\frac{m}{5}$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.