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Chapter 6: Problem 339

In the following exercises, convert each percent to a fraction. $$ 8 \frac{1}{4} \% $$

Short Answer

Expert verified
8 1/4% = 33/400

Step by step solution

01

Convert Mixed Number to Improper Fraction

First, convert the mixed number into an improper fraction. For the given percent, convert 8 1/4 to a fraction.Multiply the whole number part by the denominator of the fractional part and add the numerator:8 脳 4 + 1 = 32 + 1 = 33So, 8 1/4 = 33/4.
02

Convert Percent to Fraction

Since percentages are out of 100, convert the fraction (33/4) to a fraction out of 100:(33/4) 梅 100 = (33/4) 脳 (1/100) = 33/400.
03

Simplify Fraction

Simplify the fraction if possible. In this case, 33/400 is already in its simplest form, as 33 and 400 do not share any common factors other than 1.

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Key Concepts

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

Percent to Fraction
Converting a percent to a fraction is a common exercise in math. It helps you understand the relationship between percentages and fractions. Here's how you do it:

If you have a percent, it means you have it out of 100. For example, 25% is the same as saying 25 out of 100. To convert this percent to a fraction:
  • Write the percent as a fraction with a denominator of 100.
  • Next, simplify the fraction if possible.
For example, to convert 25% to a fraction:
  • Write it as 25/100.
  • Simplify 25/100 by dividing both the numerator and the denominator by their greatest common divisor, which is 25 in this case. So, 25/100 simplifies to 1/4.
It's that simple!
Mixed Number to Improper Fraction
Mixed numbers are a combination of a whole number and a fraction. An improper fraction is when the numerator is larger than the denominator. Here's how to convert a mixed number to an improper fraction:

Consider the mixed number 8 1/4. Follow these steps:
  • Multiply the whole number part (8) by the denominator of the fractional part (4).
  • Add the numerator (1) to the result of the previous step. In this case, 8 * 4 = 32, and then add the numerator: 32 + 1 = 33.
  • The improper fraction is now the result over the original denominator: 33/4.
This method works for any mixed number. Just multiply, add, and place the result over the denominator.
Simplifying Fractions
Simplifying fractions means reducing them to their simplest form. This involves making the numerator and the denominator as small as possible while still having the same value. Here's how to simplify a fraction:

First, find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that can divide both numbers without leaving a remainder. Use these steps:
  • Divide the numerator and the denominator by their GCD.
  • This will give you the fraction in its simplest form.
For example, consider the fraction 33/400:
  • The GCD of 33 and 400 is 1, as there are no common factors other than 1.
  • Thus, 33/400 is already in its simplest form.
If you have a fraction like 18/24, find the GCD of 18 and 24, which is 6. Divide both by 6 to get 3/4. That's the simplified fraction!

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Most popular questions from this chapter

In the following exercises, solve. Last year Bernard bought a new car for \(\$ 30,000\) . This year the car is worth \(\$ 24,000\) . Find the percent decrease.

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Without solving the problem 鈥�44 is 80% of what number鈥�, think about what the solution might be. Should it be a number that is greater than 44 or less than 44? Explain your reasoning.

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