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Chapter 6: Problem 74

In the following exercises, convert each fraction to a percent. $$\frac{11}{12}$$

Short Answer

Expert verified
91.67%

Step by step solution

01

- Understand the fraction

The fraction given is \(\frac{11}{12}\). To convert this fraction to a percent, we need to multiply it by 100.
02

- Perform the multiplication

Multiply the fraction by 100 to convert it to a percent: \[ \frac{11}{12} \times 100 \ = \frac{11 \times 100}{12} \ = \frac{1100}{12} \ \text{鈮� 91.67 (rounding to two decimal places)} \]
03

- Write the final answer

The fraction \(\frac{11}{12}\) is approximately equal to 91.67%.

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Key Concepts

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

Fractions
A fraction represents a part of a whole. It is written as \(\frac{a}{b}\) where \(a\) is the numerator and \(b\) is the denominator. The numerator signifies how many parts of the whole we are considering, while the denominator indicates the total number of equal parts the whole is divided into. For example, in \(\frac{11}{12}\), 11 is the numerator, and 12 is the denominator.

Fractions can be simplified, multiplied, divided, added, or subtracted. To convert a fraction to a percentage, multiplying by 100 can directly change the fraction into a percent form. This step is crucial for comparison purposes or to understand the fraction's proportion in a more relatable way.
Percentages
A percentage is a way to express a number as a part of 100. It is denoted using the percent sign (%). For instance, 25% is equivalent to 25 out of 100 or \(\frac{25}{100}\). This is useful in various real-life situations such as finding discounts, determining interest rates, or calculating grades.

Conversion from fractions to percentages involves straightforward multiplication. Simply multiply the fraction by 100 and convert it into a percent. For example, converting \(\frac{11}{12}\) to a percentage:
\[ \frac{11}{12} \times 100 \]
This multiplication helps scale the fraction to better understand its size relative to 100 and eases comparison across different proportions.
Mathematical Operations
Mathematical operations including addition, subtraction, multiplication, and division are fundamental in manipulating numbers. In the context of converting fractions to percentages, multiplication is the key operation.

Here's how it works:
  • Start with the fraction, say \(\frac{11}{12}\).
  • Multiply the fraction by 100: \[ \frac{11}{12} \times 100 = \frac{1100}{12} \]
  • Simplify the resulting fraction (if necessary): \[ \frac{1100}{12} = 91.67 \]
  • Convert the final result to percentage by adding the percent sign, resulting in 91.67%.

It鈥檚 important to follow these steps to ensure accuracy. Using a calculator can simplify the process and help with complex fractions.

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Most popular questions from this chapter

In the following exercises, solve the percent problem. Oxana bought a dresser at a garage sale for \(\$ 20 .\) she refinished it, then added a 250\(\%\) markup before advertising it for sale. What price did she ask for the dresser?

In the following exercises, translate and solve using proportions. 6\(\%\) of what number is \(\$ 24 ?\)

Solve the applications of percents. A grilled chicken salad at a popular fast food restaurant contains 650 milligrams (mg) of sodium, which is 27% of the recommended daily amount. What is the total recommended daily amount of sodium?

In the following exercises, solve the percent problem. Find the simple interest earned after 5 years on \(\$ 3000\) invested at an interest rate of 4.2\(\% .\)

Tamanika got a raise in her hourly pay, from \(\$ 15.50\) to \(\$ 17.55 .\) Find the percent increase.
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