Question

Write the equivalent fraction, the reduced fraction, and the decimal equivalent for 45%. Jenny solved this problem and her work is shown below. What mistake did she make?

45% = StartFraction 45 Over 100 EndFraction = StartFraction 9 Over 20 EndFraction = 4.5

Answer 1

Let's break down Jenny's calculations step by step to identify the mistake.

1. **Finding the equivalent fraction**:
To convert 45% into a fraction, you start with 45% as:
\[
45\% = \frac{45}{100}
\]

2. **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 \(\frac{9}{20}\).

3. **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 \(4.5\).