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Easy Guide: Simplifying Ratios with Decimals, Fractions & Whole Numbers for Kids

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Zuzanna <3

2/26/2023

Maths

Ratios

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Maths

Ratio, proportion and rates of exchange

Ratio in context

287

•

Feb 26, 2023

•

3 pages

Easy Guide: Simplifying Ratios with Decimals, Fractions & Whole Numbers for Kids

user profile picture

Zuzanna <3

@zuzanna_018

Hey there! Ready to master simplifying ratios with decimals and whole numbers? This guide makes it super simple with examples and worksheets. Learn how to simplify ratios with fractions, use calculators, and even convert decimals to ratios in Excel. Perfect for solving ratio word problems and finding unknown ratios step by step. Dive in to make math fun and easy!

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X÷ Ratios Ratios are proportional representations of certain data. They are an ordered pair of numbers a and b written as a:b ↓ Example 1) s

Advanced Ratio Concepts and Applications

This page delves into more complex aspects of ratios, including expressing ratios as fractions, sharing quantities in given ratios, and finding unknown ratios in word problems.

Expressing ratios as fractions is a useful skill that allows for a different perspective on proportional relationships. To do this, add the parts of the ratio to find the total, then express each part as a fraction of this total.

Example: For a room painted blue and green in the ratio 2:3, the total parts are 2 + 3 = 5. The fraction painted blue is 2/5, and the fraction painted green is 3/5.

Sharing in a given ratio is a common application of ratio concepts. This involves dividing a total quantity according to the proportions specified by a ratio.

Example: To share £25 in the ratio 2:3, first find the total parts (2 + 3 = 5), then divide the total amount by this (£25 ÷ 5 = £5 per part). Finally, multiply each ratio part by this amount (2 × £5 = £10 and 3 × £5 = £15).

Finding unknown ratios in word problems requires careful analysis and step-by-step problem-solving. This often involves working backwards from known quantities to determine unknown parts of a ratio.

Example: In a sports team with a girl-to-boy ratio of 4:5 and 12 girls, we first calculate that 1 part of the ratio equals 3 people (12 ÷ 4). Then, we multiply this by the boys' part of the ratio (3 × 5 = 15) to find that there are 15 boys in the team.

These techniques are essential for solving ratio word problems and demonstrate the practical applications of ratio concepts in real-world scenarios.

X÷ Ratios Ratios are proportional representations of certain data. They are an ordered pair of numbers a and b written as a:b ↓ Example 1) s

Advanced Applications of Ratios

This page explores more sophisticated applications of ratios, including scale factors and combining multiple ratios into a single expression.

Scale factors are a practical application of ratios, commonly used in map-making and model construction. They represent the relationship between actual sizes and their representations.

Example: For a map with a scale of 2cm : 3.5km, to find the map distance for an actual distance of 8.5km, we calculate (2 ÷ 3.5) × 8.5 = 4.9cm (to 1 decimal place).

Combining multiple ratios into a single expression is a more advanced technique that requires identifying common factors and using the concept of lowest common multiples (LCM).

Example: To combine the ratios a:b = 3:8 and b:c = 6:11 into a single ratio a:b:c, we first identify b as the common factor. We then find the LCM of the b values (24) and adjust the other parts of the ratios accordingly, resulting in the combined ratio of 9:24:44.

These advanced applications demonstrate the versatility of ratio concepts in solving complex problems and representing relationships between multiple quantities. They are particularly useful in fields such as engineering, architecture, and data analysis.

Highlight: Understanding these advanced ratio techniques enhances problem-solving skills and provides a foundation for more complex mathematical concepts.

X÷ Ratios Ratios are proportional representations of certain data. They are an ordered pair of numbers a and b written as a:b ↓ Example 1) s

Understanding Ratios and Their Simplification

Ratios are an essential concept in mathematics, representing proportional relationships between quantities. This page introduces the basics of ratios and demonstrates how to simplify them using whole numbers and decimals.

Definition: A ratio is an ordered pair of numbers a and b, written as a:b, that represents a proportional relationship between two quantities.

The process of simplifying ratios involves finding the highest common factor (HCF) of the numbers in the ratio and dividing both sides by this factor. This technique is applicable to ratios with whole numbers, decimals, and fractions.

Example: To simplify a ratio of 6 boys to 8 girls (6:8), we identify the HCF as 2. Dividing both sides by 2 results in the simplified ratio of 3:4.

When dealing with ratios with decimals, the first step is to convert the decimals to whole numbers by multiplying both sides of the ratio by an appropriate factor. Then, the simplification process can proceed as usual.

Example: To simplify the ratio 6:1.5, multiply both sides by 2 to get 12:3. The HCF of 12 and 3 is 3, so dividing both sides by 3 gives the simplified ratio of 4:1.

For ratios with fractions, the approach involves converting the fractions to a common denominator, multiplying both sides by this denominator to obtain whole numbers, and then simplifying as before.

Highlight: When simplifying ratios with different units, always convert to the smaller unit before proceeding with the simplification process.



We thought you’d never ask...

What is the Knowunity AI companion?

Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.

Where can I download the Knowunity app?

You can download the app in the Google Play Store and in the Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

Subjects

Maths

Ratio, proportion and rates of exchange

Ratio in context

 

Maths

•

287

•

Feb 26, 2023

•

3 pages

Easy Guide: Simplifying Ratios with Decimals, Fractions & Whole Numbers for Kids

user profile picture

Zuzanna <3

@zuzanna_018

Hey there! Ready to master simplifying ratios with decimals and whole numbers? This guide makes it super simple with examples and worksheets. Learn how to simplify ratios with fractions, use calculators, and even convert decimals to ratios in Excel. Perfect for solving ratio word problems and finding unknown ratios step by step. Dive in to make math fun and easy!

X÷ Ratios Ratios are proportional representations of certain data. They are an ordered pair of numbers a and b written as a:b ↓ Example 1) s

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Advanced Ratio Concepts and Applications

This page delves into more complex aspects of ratios, including expressing ratios as fractions, sharing quantities in given ratios, and finding unknown ratios in word problems.

Expressing ratios as fractions is a useful skill that allows for a different perspective on proportional relationships. To do this, add the parts of the ratio to find the total, then express each part as a fraction of this total.

Example: For a room painted blue and green in the ratio 2:3, the total parts are 2 + 3 = 5. The fraction painted blue is 2/5, and the fraction painted green is 3/5.

Sharing in a given ratio is a common application of ratio concepts. This involves dividing a total quantity according to the proportions specified by a ratio.

Example: To share £25 in the ratio 2:3, first find the total parts (2 + 3 = 5), then divide the total amount by this (£25 ÷ 5 = £5 per part). Finally, multiply each ratio part by this amount (2 × £5 = £10 and 3 × £5 = £15).

Finding unknown ratios in word problems requires careful analysis and step-by-step problem-solving. This often involves working backwards from known quantities to determine unknown parts of a ratio.

Example: In a sports team with a girl-to-boy ratio of 4:5 and 12 girls, we first calculate that 1 part of the ratio equals 3 people (12 ÷ 4). Then, we multiply this by the boys' part of the ratio (3 × 5 = 15) to find that there are 15 boys in the team.

These techniques are essential for solving ratio word problems and demonstrate the practical applications of ratio concepts in real-world scenarios.

X÷ Ratios Ratios are proportional representations of certain data. They are an ordered pair of numbers a and b written as a:b ↓ Example 1) s

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Advanced Applications of Ratios

This page explores more sophisticated applications of ratios, including scale factors and combining multiple ratios into a single expression.

Scale factors are a practical application of ratios, commonly used in map-making and model construction. They represent the relationship between actual sizes and their representations.

Example: For a map with a scale of 2cm : 3.5km, to find the map distance for an actual distance of 8.5km, we calculate (2 ÷ 3.5) × 8.5 = 4.9cm (to 1 decimal place).

Combining multiple ratios into a single expression is a more advanced technique that requires identifying common factors and using the concept of lowest common multiples (LCM).

Example: To combine the ratios a:b = 3:8 and b:c = 6:11 into a single ratio a:b:c, we first identify b as the common factor. We then find the LCM of the b values (24) and adjust the other parts of the ratios accordingly, resulting in the combined ratio of 9:24:44.

These advanced applications demonstrate the versatility of ratio concepts in solving complex problems and representing relationships between multiple quantities. They are particularly useful in fields such as engineering, architecture, and data analysis.

Highlight: Understanding these advanced ratio techniques enhances problem-solving skills and provides a foundation for more complex mathematical concepts.

X÷ Ratios Ratios are proportional representations of certain data. They are an ordered pair of numbers a and b written as a:b ↓ Example 1) s

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Understanding Ratios and Their Simplification

Ratios are an essential concept in mathematics, representing proportional relationships between quantities. This page introduces the basics of ratios and demonstrates how to simplify them using whole numbers and decimals.

Definition: A ratio is an ordered pair of numbers a and b, written as a:b, that represents a proportional relationship between two quantities.

The process of simplifying ratios involves finding the highest common factor (HCF) of the numbers in the ratio and dividing both sides by this factor. This technique is applicable to ratios with whole numbers, decimals, and fractions.

Example: To simplify a ratio of 6 boys to 8 girls (6:8), we identify the HCF as 2. Dividing both sides by 2 results in the simplified ratio of 3:4.

When dealing with ratios with decimals, the first step is to convert the decimals to whole numbers by multiplying both sides of the ratio by an appropriate factor. Then, the simplification process can proceed as usual.

Example: To simplify the ratio 6:1.5, multiply both sides by 2 to get 12:3. The HCF of 12 and 3 is 3, so dividing both sides by 3 gives the simplified ratio of 4:1.

For ratios with fractions, the approach involves converting the fractions to a common denominator, multiplying both sides by this denominator to obtain whole numbers, and then simplifying as before.

Highlight: When simplifying ratios with different units, always convert to the smaller unit before proceeding with the simplification process.

We thought you’d never ask...

What is the Knowunity AI companion?

Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.

Where can I download the Knowunity app?

You can download the app in the Google Play Store and in the Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

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4.9/5

App Store

4.8/5

Google Play

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user