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How to Cross Multiply to Solve Ratio Problems with Examples

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Poppy

28/06/2022

Maths

Ratio

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 of proportion
  • Explore techniques for solving changing ratio problems with algebra
  • Practice with examples and worksheets to master these concepts
...

28/06/2022

257

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

View

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.

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Maths

257

28 Jun 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

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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.

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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.

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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

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Best app on earth! no words because it’s too good

Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

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This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

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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

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very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

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

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This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

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