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Chapter 7: Problem 26

Change the percent to a simplified fraction or mixed number. $$66 \frac{2}{3} \%$$

Short Answer

Expert verified
Simplified fraction is $$ \frac{2}{3}.$$

Step by step solution

01

Convert the Mixed Number to an Improper Fraction

First, convert the mixed number to an improper fraction. We have $$66 \frac{2}{3} \text{ percent}$$. To convert the mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator: $$ 66 \times 3 + 2 = 198 + 2 = 200.$$ So, the improper fraction is $$ \frac{200}{3}.$$
02

Convert Percent to Fraction

To convert a percent to a fraction, place the percent over 100 and simplify. For the improper fraction $$\frac{200}{3} \text{ percent},$$ place it over 100: $$ \frac{\frac{200}{3}}{100} = \frac{200}{3} \times \frac{1}{100} = \frac{200}{300}.$$
03

Simplify the Fraction

Simplify the fraction $$\frac{200}{300}$$ by factoring out the greatest common divisor (GCD). GCD of 200 and 300 is 100: $$ \frac{200 \text{ 梅 100}}{300 \text{ 梅 100}} = \frac{2}{3}.$$

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Key Concepts

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

simplifying fractions
Simplifying fractions is all about making a fraction as simple as possible. When we simplify a fraction, we reduce it to its smallest possible numerator and denominator, without changing its value.
For example, if you have the fraction \(\frac{200}{300}\), you can simplify it to \(\frac{2}{3}\).
To do this, we need to find the Greatest Common Divisor (GCD) of the numerator and the denominator and divide both by this number.
  • First, find the GCD of 200 and 300, which is 100.
  • Then, divide both the numerator and the denominator by 100: \(\frac{200}{300} \rightarrow \frac{200 梅 100}{300 梅 100} = \frac{2}{3}\).
Simplifying makes the fraction easier to understand and work with. Remember, the value of the fraction doesn鈥檛 change when you simplify it.
improper fractions
An improper fraction has a numerator larger than its denominator. For instance, \(\frac{200}{3}\) is an improper fraction.
When converting a mixed number to an improper fraction, follow these steps:
  • Multiply the integer part by the denominator.
  • Add the numerator to this product.
  • Place the result over the original denominator.
So, for \(\text{66}\frac{2}{3}\), we do
  • 66 脳 3 = 198
  • 198 + 2 = 200 (our new numerator)
  • So, the improper fraction is \(\frac{200}{3}\).
Understanding improper fractions helps in working with larger values that can't be easily described with smaller fractions.
mixed numbers
Mixed numbers combine a whole number with a fraction. They are useful for expressing values greater than one in a simpler form.
To convert a mixed number to an improper fraction:
  • Multiply the whole number by the denominator of the fraction.
  • Add the numerator to this product.
  • Place the result over the original denominator.
For \(\text{66}\frac{2}{3}\):
  • 66 (whole number) 脳 3 (denominator) = 198
  • 198 + 2 (numerator) = 200
  • So, \(\text{66}\frac{2}{3}\) becomes \(\frac{200}{3}\) as an improper fraction.
Mixed numbers make it easier to visualize and communicate quantities that are not whole numbers, providing a clear representation of more complex values.

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