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257

Jun 28, 2022

2 pages

How to Cross Multiply to Solve Ratio Problems with Examples

Cross multiplication is a powerful method for solving proportions with... Show more

Ratio eg. Two brothers, Rich and Andrew, shave a
sum of money in the vatio 2:7. Andrew gets
£30 more than Rich. Calculate how much the
broth

Changing Ratios and Algebraic Solutions

This page focuses on solving changing ratio problems with algebra, providing a comprehensive example and step-by-step solution process.

The example problem involves Jan and Kim's marbles, initially in a ratio of 5:6. After Jan gains 2 marbles, the new ratio becomes 7:8. The goal is to determine how many marbles each owned initially.

Example: Jan and Kim own numbers of marbles that are in the ratio 5:6. Jan gains 2 more marbles and the ratio is now 7:8. How many marbles do each own initially?

The solution process involves:

  1. Writing the initial ratio in algebraic form 5x:6x5x : 6x
  2. Expressing the new ratio after the change 5x+2:6x5x+2 : 6x
  3. Setting up an equation based on the new ratio 5x+2:6x=7:85x+2 : 6x = 7 : 8
  4. Using cross multiplication to solve for x
  5. Substituting the value of x to find the original numbers of marbles

Highlight: This problem demonstrates how to apply algebraic techniques to solve complex ratio problems involving changes in quantities.

The solution reveals that initially, Jan owned 40 marbles and Kim owned 48 marbles.

Vocabulary: Changing ratios refer to situations where the ratio between quantities changes due to an increase or decrease in one or more of the quantities involved.

This example illustrates the power of algebra in solving ratio problems, especially when dealing with changing ratios. It combines the concepts of cross multiplication, algebraic manipulation, and ratio analysis to arrive at a precise solution.

Quote: "Initially Jan owned 40, Kim owned 48"

This page provides valuable practice for students preparing for exams like GCSE, where changing ratio questions and algebraic ratio GCSE questions are common.

Ratio eg. Two brothers, Rich and Andrew, shave a
sum of money in the vatio 2:7. Andrew gets
£30 more than Rich. Calculate how much the
broth

Solving Ratio Problems with Cross Multiplication

This page introduces the concept of using cross multiplication to solve ratio problems with variables. It provides a step-by-step example of how to apply this method effectively.

The example problem involves two brothers, Rich and Andrew, sharing money in a ratio of 2:7, with Andrew receiving £30 more than Rich. The solution demonstrates how to use blocks to represent the ratio and solve for the total amount shared.

Example: Two brothers, Rich and Andrew, share a sum of money in the ratio 2:7. Andrew gets £30 more than Rich. Calculate how much the brothers share.

The solution process involves:

  1. Representing the difference between the ratio parts 72=57 - 2 = 5
  2. Assigning a value to the difference 5blocks=£305 blocks = £30
  3. Calculating the value of one block £6£6
  4. Determining the total amount shared 6×(7+26 × (7 + 2 = £54)

Highlight: This method of using blocks to represent ratio parts is particularly useful for visualizing and solving ratio problems.

The page also covers finding the value of n in a ratio, using the example n+3n+3 : 2n = 3 : 5. This introduces the concept of cross multiplication for solving proportions with variables.

Vocabulary: Cross multiplication is a technique used to solve proportions by multiplying the numerator of each fraction by the denominator of the other fraction.

The solution process for finding n involves:

  1. Cross multiplying the ratios
  2. Simplifying the resulting equation
  3. Solving for n

Definition: The cross multiplication property of proportion states that if a:b = c:d, then ad = bc.



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

 

Maths

257

Jun 28, 2022

2 pages

How to Cross Multiply to Solve Ratio Problems with Examples

Cross multiplication is a powerful method for solving proportions with variables. This guide explores its application in ratio problems and changing ratios.

  • Learn how to use cross multiplication to solve ratio problems with variables
  • Understand the cross multiplication property... Show more

Ratio eg. Two brothers, Rich and Andrew, shave a
sum of money in the vatio 2:7. Andrew gets
£30 more than Rich. Calculate how much the
broth

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

Changing Ratios and Algebraic Solutions

This page focuses on solving changing ratio problems with algebra, providing a comprehensive example and step-by-step solution process.

The example problem involves Jan and Kim's marbles, initially in a ratio of 5:6. After Jan gains 2 marbles, the new ratio becomes 7:8. The goal is to determine how many marbles each owned initially.

Example: Jan and Kim own numbers of marbles that are in the ratio 5:6. Jan gains 2 more marbles and the ratio is now 7:8. How many marbles do each own initially?

The solution process involves:

  1. Writing the initial ratio in algebraic form 5x:6x5x : 6x
  2. Expressing the new ratio after the change 5x+2:6x5x+2 : 6x
  3. Setting up an equation based on the new ratio 5x+2:6x=7:85x+2 : 6x = 7 : 8
  4. Using cross multiplication to solve for x
  5. Substituting the value of x to find the original numbers of marbles

Highlight: This problem demonstrates how to apply algebraic techniques to solve complex ratio problems involving changes in quantities.

The solution reveals that initially, Jan owned 40 marbles and Kim owned 48 marbles.

Vocabulary: Changing ratios refer to situations where the ratio between quantities changes due to an increase or decrease in one or more of the quantities involved.

This example illustrates the power of algebra in solving ratio problems, especially when dealing with changing ratios. It combines the concepts of cross multiplication, algebraic manipulation, and ratio analysis to arrive at a precise solution.

Quote: "Initially Jan owned 40, Kim owned 48"

This page provides valuable practice for students preparing for exams like GCSE, where changing ratio questions and algebraic ratio GCSE questions are common.

Ratio eg. Two brothers, Rich and Andrew, shave a
sum of money in the vatio 2:7. Andrew gets
£30 more than Rich. Calculate how much the
broth

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

Solving Ratio Problems with Cross Multiplication

This page introduces the concept of using cross multiplication to solve ratio problems with variables. It provides a step-by-step example of how to apply this method effectively.

The example problem involves two brothers, Rich and Andrew, sharing money in a ratio of 2:7, with Andrew receiving £30 more than Rich. The solution demonstrates how to use blocks to represent the ratio and solve for the total amount shared.

Example: Two brothers, Rich and Andrew, share a sum of money in the ratio 2:7. Andrew gets £30 more than Rich. Calculate how much the brothers share.

The solution process involves:

  1. Representing the difference between the ratio parts 72=57 - 2 = 5
  2. Assigning a value to the difference 5blocks=£305 blocks = £30
  3. Calculating the value of one block £6£6
  4. Determining the total amount shared 6×(7+26 × (7 + 2 = £54)

Highlight: This method of using blocks to represent ratio parts is particularly useful for visualizing and solving ratio problems.

The page also covers finding the value of n in a ratio, using the example n+3n+3 : 2n = 3 : 5. This introduces the concept of cross multiplication for solving proportions with variables.

Vocabulary: Cross multiplication is a technique used to solve proportions by multiplying the numerator of each fraction by the denominator of the other fraction.

The solution process for finding n involves:

  1. Cross multiplying the ratios
  2. Simplifying the resulting equation
  3. Solving for n

Definition: The cross multiplication property of proportion states that if a:b = c:d, then ad = bc.

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