Year 10 - Maths
Algebraic 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 form equations from algebraic ratios and solve to find an unknown.
Key Notes
- Equivalent ratios have a scalar multiplier.
- Two equations can be written which are simultaneous.
- This can be set equal to each other and then solved.
Vocabulary To Learn
- Proportionality: Proportionality means when variables are in proportion if they have a constant multiplicative relationship.
- 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.
- Factorise: A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.
Common Mistakes To Avoid
- When $$x : y$$ are in the ratio 1 : 2 pupils write the equation as $$x = 2y$$
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Equivalent ratios have a scalar multiplier. Two equations can be written which are simultaneous.
2. Use this key word in a maths sentence and explain it clearly. 'Proportionality'
Proportionality means when variables are in proportion if they have a constant multiplicative relationship. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When $$x : y$$ are in the ratio 1 : 2 pupils write the equation as $$x = 2y$$. Correction: Show that the equation $$x = 2y$$ in a ratio table would mean the multiplier from $$y$$ to $$x$$ would be times by 2, this would mean when $$y=1 x=2$$ which is 2 : 1 not 1 : 2.
More Lessons In This Unit
- 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
- Combining ratios Study Guide
- Problem solving with algebraic ratios Study Guide
- Problem solving with ratios Study Guide
- Writing equations from ratios Study Guide
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