What Percent Of 800 Is $3 \frac{1}{3}$?Enter Your Percent As A Fraction In Simplest Form By Filling In The Boxes.$\square$ \%

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Understanding the Problem

To find the percentage of 800 that is $3 \frac{1}{3}$, we need to first convert the mixed number to an improper fraction. A mixed number is a combination of a whole number and a fraction, in this case, $3 \frac{1}{3}$. To convert it to an improper fraction, we multiply the whole number by the denominator and add the numerator, then write the result over the denominator.

Converting Mixed Number to Improper Fraction

313=(3×3)+13=9+13=1033 \frac{1}{3} = \frac{(3 \times 3) + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3}

Finding the Percentage

Now that we have the improper fraction, we can find the percentage by dividing the numerator by the denominator and multiplying by 100.

Calculating the Percentage

103÷800=103×1800=102400=1240\frac{10}{3} \div 800 = \frac{10}{3} \times \frac{1}{800} = \frac{10}{2400} = \frac{1}{240}

Converting to Percentage

To convert the fraction to a percentage, we multiply by 100.

1240×100=100240=2560=512\frac{1}{240} \times 100 = \frac{100}{240} = \frac{25}{60} = \frac{5}{12}

Simplifying the Fraction

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5.

512÷5=112\frac{5}{12} \div 5 = \frac{1}{12}

Conclusion

Therefore, the percentage of 800 that is $3 \frac{1}{3}$ is 112\frac{1}{12}.

Real-World Applications

This problem may seem simple, but it has real-world applications in various fields such as finance, engineering, and science. For example, in finance, understanding percentages is crucial for calculating interest rates, investment returns, and risk management. In engineering, percentages are used to calculate material costs, labor costs, and project timelines. In science, percentages are used to calculate experimental results, data analysis, and statistical modeling.

Tips and Tricks

  • When working with mixed numbers, it's essential to convert them to improper fractions to simplify calculations.
  • When dividing fractions, we can invert the second fraction and multiply instead.
  • When converting fractions to percentages, we multiply by 100.
  • When simplifying fractions, we divide both the numerator and the denominator by their greatest common divisor.

Practice Problems

  1. What percent of 500 is $2 \frac{1}{2}$?
  2. What percent of 1000 is $4 \frac{2}{3}$?
  3. What percent of 200 is $1 \frac{1}{4}$?

Solutions

  1. 510=12\frac{5}{10} = \frac{1}{2}

  2. 1412=76\frac{14}{12} = \frac{7}{6}

  3. 38\frac{3}{8}

Conclusion

In conclusion, finding the percentage of a number is a simple yet essential math concept that has real-world applications in various fields. By understanding how to convert mixed numbers to improper fractions, divide fractions, and simplify fractions, we can solve problems with ease. Practice problems and solutions are provided to help reinforce the concepts learned in this article.