Problem 40 - Elementary Algebra

Question

For exercises 39-46, rewrite the percent as a fraction. Simplify the fraction into lowest terms. $$ 9 \% $$

Step-by-Step Solution

Answer

\( \frac{9}{100} \)

Step 1: Convert Percent to Fraction

Rewrite 9% as a fraction by placing 9 over 100. So, \( 9\text{\textperthousand} = \frac{9}{100} \).

Step 2: Simplify the Fraction

Check the fraction \( \frac{9}{100} \) to see if it can be simplified. Here, 9 and 100 have no common factors other than 1, hence \( \frac{9}{100} \) is already in its simplest form.

Key Concepts

percent to fraction conversion

To convert a percent into a fraction, follow these simple steps:

• First, remove the percent sign (%) from the number.
• Next, write the number as the numerator (top part) of a fraction.
• Then, put 100 as the denominator (bottom part) of the fraction.

For example, if you have 9%, remove the % to get 9. Then, place 9 over 100, so you get the fraction \(\frac{9}{100}\).
This method works every time because percentages are always based on 100.

simplifying fractions

When you simplify a fraction, you look for the greatest common divisor (GCD) of both the numerator and the denominator.

• First, find all the factors of the numerator.
• Next, find all the factors of the denominator.
• Then, identify the largest factor that both numbers share.
• Finally, divide the numerator and the denominator by this GCD.

For example, with \(\frac{9}{100}\), we check the factors:

• The factors of 9 are 1, 3, and 9.
• The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

The only common factor between 9 and 100 is 1, so \(\frac{9}{100}\) is already simplified.

lowest terms

A fraction is in its lowest terms when the numerator and the denominator have no common factors other than 1.
Here’s how to ensure your fraction is in its simplest form:

• After finding that the greatest common divisor (GCD) is 1, you can be certain the fraction is in its lowest terms.
• If the GCD were higher than 1, you would divide both the numerator and the denominator by this number.

In our example, \(\frac{9}{100}\) is already in its lowest terms because the GCD of 9 and 100 is 1.
This process is important because fractions in their simplest form are easier to read and understand.