Let's break down Jenny's calculations step by step to identify the mistake.
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Finding the equivalent fraction: To convert 45% into a fraction, you start with 45% as: \[ 45% = \frac{45}{100} \]
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Reducing the fraction: To reduce \(\frac{45}{100}\), you need to find the greatest common divisor (GCD) of 45 and 100. The GCD is 5. \[ \frac{45 \div 5}{100 \div 5} = \frac{9}{20} \] So, the reduced fraction is \(\frac{9}{20}\).
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Finding the decimal equivalent: To convert a fraction to a decimal, you divide the numerator by the denominator: \[ \frac{9}{20} = 0.45 \]
Now, let's summarize:
- The equivalent fraction is \(\frac{45}{100}\).
- The reduced fraction is \(\frac{9}{20}\).
- The decimal equivalent is \(0.45\).
Identifying the mistake: The crucial error in Jenny's work is in the decimal conversion. She incorrectly stated that \(\frac{9}{20} = 4.5\). This is incorrect.
The correct decimal equivalent of \(\frac{9}{20}\) is: \[ \frac{9}{20} = 0.45 \]
Thus, the complete and correct summary is:
- The equivalent fraction: \(\frac{45}{100}\)
- The reduced fraction: \(\frac{9}{20}\)
- The decimal equivalent: \(0.45\)
Jenny's mistake was in calculating the decimal equivalent; the correct decimal for \(\frac{9}{20}\) is \(0.45\), not \(4.5\).
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