Year 10 - Maths
Checking and securing understanding of calculating with fractions and decimals
Arithmetic procedures: index laws
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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 learn how to manipulate indices and perform calculations without conversion by understanding index laws.
Lesson Summary
You will learn to evaluate an expression involving decimals and fractions.
Key Notes
- Where a calculation contains a mixture of fractions and decimals, conversion is useful.
- Fluent use of your calculator is useful for both calculating and checking.
- Equivalent fractions can help to reduce the complexity of calculations.
Vocabulary To Learn
- Equivalent fractions: Two fractions are equivalent if they have the same value.
- 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
- The incorrect input of a mixed number is common i.e some pupils press a number then the fraction button. Others inefficiently sum the integer and proper fraction.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Where a calculation contains a mixture of fractions and decimals, conversion is useful. Fluent use of your calculator is useful for both calculating and checking.
2. Use this key word in a maths sentence and explain it clearly. 'Equivalent fractions'
Two fractions are equivalent if they have the same value. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: The incorrect input of a mixed number is common i.e some pupils press a number then the fraction button. Others inefficiently sum the integer and proper fraction. Correction: Reiterating the mixed number button is located above the proper fraction button.
More Lessons In This Unit
- Advanced problem solving with the laws of indices Study Guide
- Checking and securing understanding of calculations involving negative numbers Study Guide
- Checking and securing understanding of converting between fractions and decimals Study Guide
- Checking and securing understanding of LCM and HCF Study Guide
- Checking and securing understanding of prime factorisation Study Guide
- Checking and securing understanding of roots and integer indices Study Guide
- Converting any recurring decimal to a fraction Study Guide
- Problem solving with the laws of indices Study Guide
- The laws of indices - division Study Guide
- The laws of indices - fractional exponents Study Guide
- The laws of indices - multiplication Study Guide
- The laws of indices - negative and zero exponents Study Guide
- The laws of indices - raising a power to a power Study Guide
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