Year 10 - Maths
Checking and securing understanding of simplifying and unitising 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 simplify a ratio, including expressing a ratio in unitary form.
Key Notes
- There are infinitely many equivalent ratios.
- A ratio is in its simplest form if the HCF of all the parts is one and all parts are integers.
- A ratio is in unitary form if one of the parts is equal to one.
- A ratio in unitary form may not be a simplified ratio.
Vocabulary To Learn
- Unitary ratio: A unitary ratio is any ratio where one part of the ratio is 1
Common Mistakes To Avoid
- Not simplifying the ratio completely or over-simplifying a three part ratio when two of the parts share a further common factor
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There are infinitely many equivalent ratios. A ratio is in its simplest form if the HCF of all the parts is one and all parts are integers.
2. Use this key word in a maths sentence and explain it clearly. 'Unitary ratio'
A unitary ratio is any ratio where one part of the ratio is 1. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Not simplifying the ratio completely or over-simplifying a three part ratio when two of the parts share a further common factor. Correction: Link two part ratios back to simplifying fractions and remind pupils to consider if either number is a multiple of 3 as this is often missed. Remind pupils that to simplify a ratio, every part must share the common factor you are dividing by.
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
- Combining 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.