Problem 4 - Elementary Algebra

Question

For exercises 1-12, rewrite the decimal number as a fraction. Simplify the fraction to lowest terms. $$ 0.11 $$

Step-by-Step Solution

Answer

(0.11 = \(\frac{11}{100}\))

Step 1: Convert Decimal to Fraction

Write the decimal number 0.11 as a fraction. This can be expressed as \(\frac{11}{100}\).

Step 2: Simplify the Fraction

Check if the fraction \(\frac{11}{100}\) can be simplified further by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 11 and 100 is 1.

Step 3: Write the Simplified Fraction

Since the GCD is 1, \(\frac{11}{100}\) is already in its simplest form.

Key Concepts

simplifying fractions

Simplifying fractions means to make the fraction as simple as possible. For example, if you have \( \frac{4}{8} \), you can simplify it to \( \frac{1}{2} \). Simplifying makes fractions easier to work with and understand.
To simplify a fraction, you need to divide both the numerator (top number) and the denominator (bottom number) by the same number. This number is called the greatest common divisor (GCD).
In the problem you provided, \( \frac{11}{100} \) is already simplified because its GCD is 1. Therefore, no further simplification is necessary.

greatest common divisor

The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder. Finding the GCD is useful for simplifying fractions because you divide both parts of the fraction by this number.
You can find the GCD by listing the factors of each number and finding the largest one they have in common.

• For 11, the factors are 1 and 11.
• For 100, the factors are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

So, the only common factor between 11 and 100 is 1, which means the GCD is 1.
In our example, since the GCD is 1, the fraction \( \frac{11}{100} \) is already in its simplest form.

basic algebra

Understanding how to convert decimals to fractions and simplify them is part of basic algebra. Algebra is the branch of mathematics dealing with numbers and the rules for manipulating these numbers.
When converting a decimal to a fraction, you need to express it as a fraction with a denominator that is a power of 10. For instance, 0.11 becomes \( \frac{11}{100} \) because there are two decimal places. Basic algebra skills will help you simplify this fraction.
Here are some key steps:

• Write the decimal as a fraction over 1 (e.g., 0.11/1).
• Multiply both the numerator and the denominator by a power of 10 (e.g., 0.11 x 100/1 x 100 = 11/100).
• Find the GCD and simplify if possible.

Practicing these steps helps you become more comfortable with basic algebra and prepares you for more complex problems.