Problem 76 - Algebra 1: Concepts and Skills

Question

Write the fraction as a percent. $$ \frac{11}{20} $$

Step-by-Step Solution

Answer

The fraction \(\frac{11}{20}\) as a percentage is \(55\%\).

Step 1: Divide Numerator by Denominator

In the fraction \(\frac{11}{20}\), divide the numerator \(11\) by the denominator \(20\). The result we obtain will be in decimal form.

Step 2: Convert to Percentage

To convert a decimal to a percentage, multiply by 100. Doing this will derive a direct percentage form of the decimal.

Step 3: Add Percentage Symbol

After obtaining the percentage value, add the percentage symbol '%' to the final answer. This denotes that the value is now in percentage form.

Key Concepts

Fractions

Fractions are a fundamental way of representing parts of a whole number. They consist of two integers separated by a slash, where the top number is called the numerator and represents the part, and the bottom number is the denominator, which represents the whole. For example, in the fraction \( \frac{11}{20} \), 11 is the numerator and 20 is the denominator.

Fractions help us understand how a piece of information relates to a whole set. They are often used in everyday situations such as cooking or dividing things equally. Think of a fraction as dividing a pizza into slices; the number of slices you get when it's cut is the denominator, and the number of slices you take for yourself is the numerator.

• Numerator: Represents the number of parts you have.
• Denominator: Represents the total number of equal parts.

Understanding fractions lays the groundwork for converting them into decimals and percentages. By dividing the numerator by the denominator, we can easily turn a fraction into a decimal, which leads us to the next step in conversions.

Decimals

Decimals are another way to represent numbers and are particularly useful when dealing with divisions that have a precise or repeating nature. In essence, a decimal is a fraction where the denominator is a power of 10. Taking our fraction \( \frac{11}{20} \), when we divide 11 by 20, we get 0.55, which is a decimal.

Decimals provide a straightforward method for expressing portions of a whole. They are efficient for calculations and easy to read, particularly for financial transactions or scientific measurements. The key steps to convert a fraction to a decimal include:

• Perform the division: Divide the numerator by the denominator.
• Write down the quotient: The answer from your division becomes the decimal form.

Decimals bridge the gap between fractions and percentages, as we can easily convert decimals to percentages by understanding their representation in hundredths.

Percentages

Percentages are widely used to represent proportions and tell us how the number relates to 100. They are an alternative representation of fractions and decimals that makes comparison and interpretation simpler. To convert a decimal to a percentage, we multiply by 100. Continuing with our decimal 0.55, the percentage becomes 55% when multiplied by 100.

The percentage symbol '%' indicates the number is a part of the whole constituted by 100 parts. Understanding percentages is crucial in various situations like evaluating discounts, interpreting statistical data, and examining interest rates.

• Multiply by 100: Convert the decimal to a percentage by multiplying it by 100.
• Add the percentage symbol '%': To denote that the number is in percentage form.

Being able to convert fractions into percentages allows us to communicate data effectively, making it easier to understand comparisons and changes over time.