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Chapter 6: Problem 71

In the following exercises, convert each fraction to a percent. $$6 \frac{4}{5}$$

Short Answer

Expert verified
680%

Step by step solution

01

Convert the Mixed Number to an Improper Fraction

Convert the mixed number to an improper fraction. For the mixed number 6 \( \frac{4}{5} \), multiply the whole number 6 by the denominator 5, and then add the numerator 4. Place the result over the original denominator.\[ 6 \times 5 + 4 = 30 + 4 = 34 \]So, \( 6 \frac{4}{5} \) becomes \( \frac{34}{5} \).
02

Divide the Numerator by the Denominator

Divide the numerator by the denominator to convert the fraction to a decimal.\[ \frac{34}{5} = 6.8 \]
03

Convert the Decimal to a Percent

Multiply the decimal by 100 to convert it to a percent.\[ 6.8 \times 100 = 680 \]So, \( 6 \frac{4}{5} \) is equal to 680%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Improper Fractions
An improper fraction is a fraction where the numerator (the number on top) is larger than or equal to the denominator (the number at the bottom). For instance, in the fraction \(\frac{34}{5}\), 34 is larger than 5, making it an improper fraction. Converting mixed numbers (a whole number and a fraction) into improper fractions is often necessary to perform calculations or conversions. Here's how to do it:
  • Multiply the whole number by the fraction's denominator.
  • Add the result to the numerator of the fraction.
  • Place this sum over the original denominator.
For the mixed number 6 \( \frac{4}{5} \), multiply 6 (whole number) by 5 (denominator), which gives 30. Add 4 (numerator) to get 34. Therefore, 6 \( \frac{4}{5} \) is equivalent to \(\frac{34}{5}\). This form is helpful for the next steps in conversions.
Decimal Conversion
Converting a fraction to a decimal might seem tricky, but it is simply dividing the numerator by the denominator. Once you have an improper fraction, like \( \frac{34}{5} \), the next step is to convert this fraction to a decimal.
In \( \frac{34}{5} \), you divide 34 by 5. This gives you 6.8. Breaking this down:
  • 34 (numerator) divided by 5 (denominator) equals 6.8.
Now, you have converted the improper fraction into a decimal, which is an essential step before converting it to a percent.
Percent Calculation
Once you have the decimal, converting it to a percent is straightforward. You simply multiply the decimal by 100. A percent represents parts out of 100, so multiplying a decimal by 100 converts it directly.
For our decimal 6.8:
  • Multiply 6.8 by 100.
  • This equals 680.
So, 6.8 converted to a percent is 680%. To summarize, converting a mixed number to a percent involves converting the mixed number to an improper fraction, then to a decimal, and finally multiplying the decimal by 100 to get the percent.

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