QQuestionMathematics
QuestionMathematics
"Fiona has to work out the exact value of 48 ÷ 1 / 2.
48 ÷ 1 / 2 = 24
Fiona's reason:
There are 2 halves in 1, so there will be 24 halves in 48.
Explain what is wrong with Fiona's reason."
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand Fiona's Calculation
Fiona calculated $$48 \div \frac{1}{2} = 24
Step 3:: Identify the Error in Reasoning
Fiona's reasoning that "there are 2 halves in 1, so there will be 24 halves in 48" is incorrect.
Step 4:: Demonstrate the Correct Calculation
48 \div \frac{1}{2} = 48 \times 2 = 96
When dividing by a fraction, we actually multiply by its reciprocal:
Step 5:: Explain Why the Reasoning is Wrong
- The correct operation is: $$48 \div \frac{1}{2} = 48 \times \frac{2}{1} = 96
- Dividing by a fraction is not the same as counting "halves" - This means multiplying 48 by 2, not dividing by 2
Final Answer
The correct calculation of 48 \div \frac{1}{2} is 96, not 24, because dividing by a fraction means multiplying by its reciprocal.
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