Year 7 - Maths
Expressing one number as a fraction of another
Understanding multiplicative relationships: fractions and 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
This unit introduces the concept of multiplicative relationsihps, and connects fractions to the idea of ratios. Ratios are then explored in depth and used to solve contextual problems such as those involving exchange rates and general conversions.
Lesson Summary
You will learn to express one number as a fraction of another.
Key Notes
- There exists a multiplier for any pair of values.
- The multiplier is more than just a scaling factor.
- The multiplier also expresses one number as a fraction of the other.
Vocabulary To Learn
- Reciprocal: The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.
- Terminating decimal: A terminating decimal is one that has a finite number of digits after the decimal point.. E.g. 92.2, 193.3894, non-example: $$1.\\dot9$$.
Common Mistakes To Avoid
- Only see the amount, not proportion. E.g £30 from £100 is no different to £30 from £60.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There exists a multiplier for any pair of values. The multiplier is more than just a scaling factor.
2. Use this key word in a maths sentence and explain it clearly. 'Reciprocal'
The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Only see the amount, not proportion. E.g £30 from £100 is no different to £30 from £60. Correction: Referring to the whole using bar models or fractions can emphasise the amount with respect to the whole.
More Lessons In This Unit
- Checking and securing finding a fraction of a given amount Study Guide
- Checking understanding of multiplicative relationships Study Guide
- Deepening understanding with fractions of a given amount Study Guide
- Describing exchange rates with ratio Study Guide
- Describing more conversions with ratio Study Guide
- Determining the part Study Guide
- Determining the whole Study Guide
- Dividing a quantity into a given ratio Study Guide
- Equivalent multiplicative relationships Study Guide
- Expressing multiplicative relationships as ratios and fractions Study Guide
- Multiplicative relationships Study Guide
- Multiplicative relationships in context Study Guide
- Problem solving with fractions and ratios Study Guide
- Ratio language and notation Study Guide
- Representing a multiplicative relationship Study Guide
- Securing understanding of ratio as a multiplicative relationship Study Guide
Browse all guides in the Year 7 Maths guide library.