Get started for free

Log In Start studying!

Get started for free Log out

Chapter 6: Problem 19

Write the ratio in lowest terms. \(8 \mathrm{m}\) to \(2 \mathrm{m}\)

### Short Answer

Expert verified

4:1

## Step by step solution

01

## Write the ratio as a fraction

Express the given ratio in fraction form. Here, the ratio of 8 \text{m} to 2 \text{m} can be written as \( \dfrac{8 \text{m}}{2 \text{m}} \).

02

## Cancel out the common units

The units 'm' (meters) in both the numerator and the denominator can be canceled out, simplifying the expression to \( \dfrac{8}{2} \).

03

## Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor (GCD). For 8 and 2, the GCD is 2. So, \( \dfrac{8 \div 2}{2 \div 2} = \dfrac{4}{1} \).

04

## Write the simplified ratio

The simplified ratio is then 4 to 1.

## Key Concepts

These are the key concepts you need to understand to accurately answer the question.

###### Ratios

A ratio compares two quantities to show the relative size of one quantity to the other. Ratios can be written in three main forms: as a fraction, with a colon (e.g., 8:2), or using the word 'to' (e.g., 8 to 2). Ratios help us understand the relationship between different quantities. For example, in the exercise, the ratio 8 meters to 2 meters represents how much larger 8 meters is compared to 2 meters. To make ratios more understandable and easier to work with, we often simplify them.

###### Fractions

Fractions are a way to represent parts of a whole. They consist of a numerator (the top part) and a denominator (the bottom part). In our problem, we turned the ratio 8 meters to 2 meters into a fraction, giving us \(\frac{8 \text{m}}{2 \text{m}}\). Fractions help to visualize the division of quantities. When simplifying a ratio, converting it to a fraction allows us to perform easier arithmetic operations such as division. This conversion is the first step to simplification.

###### Greatest Common Divisor (GCD)

The Greatest Common Divisor (GCD) is the largest number that evenly divides both the numerator and the denominator of a fraction. Finding the GCD is crucial in simplifying fractions because it helps reduce the fraction to its simplest form. In our example, the GCD of 8 and 2 is 2. Thus, we divide both 8 and 2 by 2, which simplifies \(\frac{8}{2}\) to \(\frac{4}{1}\). Calculating the GCD makes the numbers easier to work with and can reveal the simplest ratio between two quantities.

###### Unit Cancellation

Unit cancellation involves removing units that appear in both the numerator and the denominator of a fraction. This step simplifies the arithmetic in problems involving ratios with units. In our example, the units 'meters' appeared in both parts of the ratio 8 meters to 2 meters. By canceling out the 'meters,' we turned \(\frac{8 \text{m}}{2 \text{m}}\) into \(\frac{8}{2}\). Removing the units makes the mathematical process cleaner and focuses purely on the numerical relationship.

### 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

## Recommended explanations on Math Textbooks

### Decision Maths

Read Explanation### Applied Mathematics

Read Explanation### Mechanics Maths

Read Explanation### Pure Maths

Read Explanation### Probability and Statistics

Read Explanation### Statistics

Read ExplanationWhat do you think about this solution?

We value your feedback to improve our textbook solutions.

## Study anywhere. Anytime. Across all devices.

Sign-up for free

This website uses cookies to improve your experience. We'll assume you're ok with this, but you can opt-out if you wish. Accept

Privacy & Cookies Policy

#### Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.

Always Enabled

Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.

Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.