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Answer
\( 7 \frac{1}{4} \% \) of 480 is 34.8.
Solution
To calculate \( 7 \frac{1}{4} \% \) of 480, follow these steps:
1. **Convert the Percentage to a Decimal:**
\( 7 \frac{1}{4} \% \) can be converted to a decimal by first converting the mixed number to an improper fraction and then dividing by 100.
\[
7 \frac{1}{4} = \frac{29}{4}
\]
\[
7 \frac{1}{4} \% = \frac{29}{4} \times \frac{1}{100} = \frac{29}{400} = 0.0725
\]
2. **Multiply by the Given Number:**
Now, multiply the decimal form of the percentage by 480.
\[
0.0725 \times 480 = 34.8
\]
**Alternatively**, you can perform the multiplication step-by-step:
- \( 0.07 \times 480 = 33.6 \)
- \( 0.0025 \times 480 = 1.2 \)
Adding these together:
\[
33.6 + 1.2 = 34.8
\]
3. **Final Answer:**
\( 7 \frac{1}{4} \% \) of 480 is **34.8**.
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Simplify this solution Beyond the Answer
To find \( 7 \frac{1}{4} \% \) of 480, first convert the mixed number into a decimal. \( 7 \frac{1}{4} \% \) equals \( 7.25\% \), which can be expressed as \( \frac{7.25}{100} \) or \( 0.0725 \). Now, multiply this by 480: \( 0.0725 \times 480 = 34.8 \). So, \( 7 \frac{1}{4} \% \) of 480 is 34.8. To clarify further, using percentages in calculations can often feel cumbersome, but it's just multiplication by a decimal! A common mistake is forgetting to convert the percentage into decimal form before performing the calculation. Just remember—divide by 100! This small step saves you from a big headache later!
