Problem 60 - Algebra 1: Concepts and Skills

Question

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 10 \% $$

Step-by-Step Solution

Answer

10% as a fraction in simplest form is \(\frac{1}{10}\)

Step 1: Convert Percentage to Fraction

Begin by converting 10% to a fraction. This is done by writing 10 as the numerator and 100 as the denominator, as percentage is always out of 100. So, 10% as a fraction is \(\frac{10}{100}\)

Step 2: Simplify the Fraction

Next, simplify the fraction to its lowest form if possible. Both 10 and 100 are divisible by 10. Divide the numerator and the denominator by 10 to simplify the fraction. This results in a fraction \(\frac{1}{10}\)

Step 3: Express Fraction in Simplest Form

The fraction \(\frac{1}{10}\) is already in its simplest form because there is no common factor other than 1 for the numerator and the denominator. Therefore, the simplest form of 10% as a fraction is \(\frac{1}{10}\)

Key Concepts

Simplifying Fractions

Simplifying fractions is an essential skill in mathematics. It involves reducing fractions to their simplest or lowest terms. To simplify a fraction, you need to divide both the numerator and the denominator by the greatest common divisor (GCD).

Here's a quick guide:

• First, identify the greatest common divisor of the numerator and the denominator. This means finding the largest number that divides both exactly.
• Next, divide both the top (numerator) and bottom (denominator) numbers by this GCD.
• The result is a simplified fraction, which represents the same value as the original fraction.

In the case of converting 10% to a fraction, we initially get \(\frac{10}{100}\). By dividing both 10 and 100 by their GCD, which is 10, the fraction simplifies to \(\frac{1}{10}\).

Remember, a fraction is considered simplified when the only common factor between the numerator and the denominator is 1. This makes the fraction in its most reduced form, ensuring it's easier to work with in calculations.

Numerator and Denominator

Understanding the concepts of numerator and denominator is crucial when dealing with fractions. A fraction consists of two parts:

• Numerator: This is the top number of a fraction. It represents how many parts we have.
• Denominator: This is the bottom number. It tells us into how many parts the whole is divided.

For example, in the fraction \(\frac{10}{100}\):

• The numerator is 10, indicating that we have 10 parts.
• The denominator is 100, which tells us that the whole is divided into 100 equal parts.

Understanding these components helps in manipulating and simplifying fractions. It's essential for properly conveying what a fraction means.

By learning these basics, students can effectively convert percentages to fractions and perform other arithmetic operations involving fractions.

Fraction in Simplest Form

Writing a fraction in its simplest form means reducing it such that the numerator and the denominator have no common factors beyond 1. This makes the fraction as simple and manageable as possible.

To achieve the simplest form:

• First, simplify the fraction by dividing both the numerator and the denominator by their greatest common factor.
• Check again if they can be divided further until no further reduction is possible.

In our example, after converting 10% to a fraction, we have \(\frac{10}{100}\).

• Dividing both numbers by 10, their GCD, we end up with \(\frac{1}{10}\). Since 1 is a universal factor with no other common factors, this is as simple as it gets.

Writing fractions in simplest form is helpful in ensuring calculations are straightforward and results are easy to interpret. This is especially important in both academic problems and real-world applications.