Problem 20 - Elementary Algebra Within Reach

Question

Convert the percent to a fraction. $$350 \%$$

Step-by-Step Solution

Answer

The fraction corresponding to 350% is \(\frac{7}{2}\).

Step 1: Write the percentage as a fraction over 100

Given 350%, express it as \(\frac{350}{100}\).

Step 2: Simplify the fraction

Since 350 and 100 share common factors, namely 50, the fraction can be simplified. Divide both the numerator and the denominator by 50 to do so. The simplified fraction thus becomes \(\frac{7}{2}\), which cannot be simplified further.

Key Concepts

Percent to Fraction Conversion

Converting a percentage to a fraction is a fundamental skill in mathematics, often used in various real-world scenarios. A percentage is essentially a fraction with a denominator of 100. This means that any percentage can be converted to a fraction by simply placing the percentage number over 100.
To convert 350% to a fraction, we start by writing it as \( \frac{350}{100} \). This places the "percent" number as the numerator, while 100 becomes the denominator.

Simplifying Fractions

Once a percentage is converted into a fraction, the next step is to simplify it. Simplifying fractions is the process of reducing a fraction to its simplest form, where the numerator and denominator have no common factors other than 1.
For the fraction \( \frac{350}{100} \), simplification involves dividing both the numerator and the denominator by their greatest common factor, which is 50 in this case. By simplifying, we transform the fraction into \( \frac{7}{2} \). This result is in its simplest form since 7 and 2 have no common factors other than 1.

Numerators and Denominators

Understanding numerators and denominators is crucial when working with fractions. The numerator is the top number in a fraction and represents how many parts we are considering. The denominator, the bottom number, signifies the total number of equal parts into which a whole is divided.
In the case of \( \frac{350}{100} \), 350 is the numerator, and 100 is the denominator. This fraction tells us that we are considering 350 parts out of 100 equal parts. Simplifying this fraction results in \( \frac{7}{2} \), where 7 is the new numerator, and 2 is the new denominator, reflecting a simpler ratio of the same value.

Common Factors in Fractions

The concept of common factors is essential for simplifying fractions effectively. A common factor is a number that divides exactly into two or more numbers. For instance, in \( \frac{350}{100} \), the numerators and denominators share common factors, with the largest being 50.

• To simplify a fraction, identify the greatest common factor of the numerator and the denominator.
• Divide both by this common factor to get the smallest possible numerator and denominator.

Applying this to our fraction \( \frac{350}{100} \), dividing both by 50 yields \( \frac{7}{2} \). This process not only simplifies calculations with fractions but also helps in making data more comprehensible.