Year 7 - Maths
Dividing a fraction by a fraction
Arithmetic procedures with fractions
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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 revisits and secures fraction operations and extends pupil understanding to division of whole numbers by fractions and division of fractions by fractions.
Lesson Summary
You will learn to use the mathematical structures that underpin the division of fractions to divide a fraction by a fraction.
Key Notes
- A diagram can help to show the underlying structure.
- Another method is the use the reciprocal of the dividing fraction.
- The reciprocal is the multiplicative inverse.
- The product of a number and its reciprocal is one.
Vocabulary To Learn
- Reciprocal: A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1
Common Mistakes To Avoid
- Numerators are divided and denominators are divided.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A diagram can help to show the underlying structure. Another method is the use the reciprocal of the dividing fraction.
2. Use this key word in a maths sentence and explain it clearly. 'Reciprocal'
A 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: Numerators are divided and denominators are divided. Correction: Emphasize the definition of division. "How many times does.... fit into it?".
More Lessons In This Unit
- Checking and securing dividing a fraction by a whole number Study Guide
- Checking understanding of addition and subtraction with fractions Study Guide
- Checking understanding of multiplication with fractions Study Guide
- Deepening understanding of multiplication with fractions Study Guide
- Dividing a whole number by a fraction Study Guide
- Priority of operations with positive and negative integers, decimals and fractions Study Guide
- Problem solving with arithmetic procedures involving fractions Study Guide
- Securing understanding of addition and subtraction with fractions Study Guide
- Securing understanding of multiplication with fractions Study Guide
Browse all guides in the Year 7 Maths guide library.