Year 10 - Maths
Combining ratios
Ratio
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will learn how to combine ratios, interpret algebraic ratios, and investigate quantity changes and their effect on ratios.
Lesson Summary
You will learn to combine ratios.
Key Notes
- There may be a relationship between quantities A and B and a relationship between quantities B and C
- Therefore there is a relationship between A and C
- If A : B and B : C then A : B : C and A : C
- When the common quantity is not the same in each ratio, equivalent ratios can be used
- For example, if A:B and 2B:5C then 2A:2B:5C and 2A:5C
Vocabulary To Learn
- Proportion: A part to whole (sometimes part to part) comparison. If two things are proportional then the ratio of part to whole is maintained and the multiplicative relationship between parts is also maintained.
- Ratio: A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.
- LCM: LCM is an abbreviation for lowest common multiple.
- Lowest common multiple: The lowest common multiple is the lowest number that is a multiple of two or more numbers.
Common Mistakes To Avoid
- Combining ratios without using equivalent ratios to equate the common part.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There may be a relationship between quantities A and B and a relationship between quantities B and C. Therefore there is a relationship between A and C.
2. Use this key word in a maths sentence and explain it clearly. 'Proportion'
A part to whole (sometimes part to part) comparison. If two things are proportional then the ratio of part to whole is maintained and the multiplicative relationship between parts is also maintained. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Combining ratios without using equivalent ratios to equate the common part. Correction: Pupils may need to spend extra time finding equivalent ratios and looking at when it is ok to combine ratios or not.
More Lessons In This Unit
- Algebraic ratios Study Guide
- Changing ratios Study Guide
- Checking and securing understanding of converting between ratios, percentages and fractions Study Guide
- Checking and securing understanding of equivalent ratios Study Guide
- Checking and securing understanding of real world ratios Study Guide
- Checking and securing understanding of sharing in a ratio Study Guide
- Checking and securing understanding of simplifying and unitising ratios Study Guide
- Problem solving with algebraic ratios Study Guide
- Problem solving with ratios Study Guide
- Writing equations from ratios Study Guide
Browse all guides in the Year 10 Maths guide library.