Problem 8 - Prealgebra

Question

Write each percent as a fraction with denominator \(100 .\) $$35 \%$$

Step-by-Step Solution

Answer

35% as a fraction is \( \frac{35}{100} \).

Step 1: Identify the Given Percent

The given percentage is 35%. This needs to be converted into a fraction.

Step 2: Convert Percent to Fraction

To convert 35% into a fraction with a denominator of 100, write it as \[ \frac{35}{100} \]

Key Concepts

percent

A percent is a way of expressing a number as a part of 100. It comes from the Latin word "per centum," meaning "by the hundred." When you see a percentage like 35%, it simply means 35 out of every 100. This makes percentages easy to understand and use when comparing proportions.

To effectively work with percentages, it helps to understand that the symbol "%" indicates a relationship to the number 100. Often, percentages are used in contexts like discounts, statistics, and to describe changes in data. Whenever you deal with percentages, remember that you are handling parts of a whole that add up to 100.

fractions

Fractions represent parts of a whole and consist of a numerator (top number) and a denominator (bottom number). The numerator indicates how many parts you have, while the denominator shows the total number of equal parts the whole is divided into.

Converting percentages to fractions involves writing the percentage as a fraction of 100. For example, 35% becomes \(\frac{35}{100}\). This conversion is straightforward because percentages are inherently out of 100, just like our general understanding of fractions. Through this conversion, we translate percentages into a format that is familiar and easier to manipulate in mathematical calculations.

• Numerator: Parts you have.
• Denominator: Total equal parts.

denominator of 100

When converting a percent to a fraction, the fraction will always have a denominator of 100. This is because percent literally means "per hundred." For instance, if you have a percentage of 35%, you would write this as a fraction with a numerator of 35 and a denominator of 100, resulting in \(\frac{35}{100}\).

Using 100 as the denominator makes the fraction a direct representation of the given percentage. This standard denominator ensures uniformity across various calculations and comparisons, simplifying the process of understanding proportions and mathematical operations involving fractions.

• Denominator of 100 is used consistently.
• Makes percentage representation straightforward.
• Simplifies comparisons and calculations.

mathematical conversion

Mathematical conversion is the process of changing a number or expression from one form to another. In the context of percentages and fractions, conversion helps translate one format into another that might be more suitable for computations or analysis.

Converting percentages to fractions is a two-step process:

• Step 1: Write the percent value as the numerator of the fraction.
• Step 2: Place 100 as the denominator, since the percent is based on 100.

For example, converting 35% to a fraction involves placing 35 over 100, making it \(\frac{35}{100}\). This method is a fundamental conversion skill in mathematics that aids in tasks ranging from basic arithmetic to complex problem-solving. Understanding conversions allows for greater flexibility in how mathematical information is presented and used.