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Chapter 7: Problem 33

Write each percent as a fraction or mixed number in simplest form. $$ 10 \frac{1}{3} \% $$

Short Answer

Expert verified
The percent \(10 \frac{1}{3}\%\) is \(\frac{31}{300}\) in simplest form.

Step by step solution

01

Convert Mixed Number to Improper Fraction

First, convert the mixed number percentage to an improper fraction. The mixed number is \( 10 \frac{1}{3} \). To convert it, multiply the denominator (3) by the whole number (10) and add the numerator (1): \( 3 \times 10 + 1 = 31 \). So, \( 10 \frac{1}{3} \) becomes \( \frac{31}{3} \).
02

Convert Percent to Fraction

To change the percentage to a fraction, divide by 100 since percent means per 100. So, \( \frac{31}{3} \% \) becomes \( \frac{31}{3} \times \frac{1}{100} = \frac{31}{300} \).
03

Simplify the Fraction

Check if \( \frac{31}{300} \) can be simplified. Since 31 is a prime number and does not divide 300 evenly, \( \frac{31}{300} \) is already in simplest form.

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Key Concepts

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

Mixed Numbers
Mixed numbers combine a whole number with a fraction. For example, in the mixed number \(10 \frac{1}{3}\), "10" is the whole number and "\(\frac{1}{3}\)" is the fraction.
The mixed number can represent quantities larger than a simple fraction. It's often used when dealing with measurements in everyday life, such as heights or recipes.
  • To convert a mixed number into an improper fraction, you must multiply the whole number by the fraction鈥檚 denominator and add the numerator.
  • This gives you the new numerator over the original denominator.
Converting \(10 \frac{1}{3}\) into an improper fraction involves the following calculation:
Multiply the whole number "10" by the denominator "3" which equals 30. Then add the numerator "1" to make 31. Hence, \(10 \frac{1}{3} = \frac{31}{3}\) as an improper fraction.
Improper Fractions
An improper fraction has a numerator larger than or equal to its denominator. These are crucial in mathematical operations as they simplify calculations and equations.
For example, \(\frac{31}{3}\) is an improper fraction because "31" (numerator) is greater than "3" (denominator).
  • Improper fractions can be useful in particular mathematical contexts, such as algebraic equations where they simplify solutions.
  • To convert an improper fraction into a mixed number, divide the numerator by the denominator.
  • The quotient becomes the whole number, and the remainder over the denominator forms the fractional part.
Understanding improper fractions helps in learning how to handle larger numbers and quantities efficiently by maintaining simplicity during complex math equations.
Simplification of Fractions
Simplifying fractions means reducing a fraction to its simplest form where the numerator and the denominator have no common factors other than 1.
The simplified form makes a fraction easier to work with.
  • To simplify, you find the greatest common divisor (GCD) of the numerator and the denominator.
  • Then divide both by this GCD.
  • The fraction is in simplest form when it cannot be reduced further.
For the fraction \(\frac{31}{300}\), 31 is a prime number, which means it can only be divided by 1 and itself.
No simplification is possible if none of these divides 300 without a remainder.
Therefore, \(\frac{31}{300}\) is already in its simplest form and ready for any further operations or interpretations.

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Most popular questions from this chapter

Perform the indicated operations. \(\frac{3}{11} \div \frac{9}{22} \cdot \frac{1}{3}\)

In your own words, explain how to write a decimal as a percent.

Perform the indicated operations. $$ 6 \frac{2}{3}-4 \frac{5}{6} $$

Write each fraction as a decimal and then write each decimal as a percent. Round the decimal to three decimal places (nearest thousandth) and the percent to the nearest tenth percent. $$ \frac{21}{79} $$

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