Question

In one town are 25 drivers under the age of 21 . There are a total of 225 drivers in town. What is the fraction of drivers under 21 ? A. \(\frac{1}{10}\) B. \(\frac{1}{9}\) C. \(\frac{1}{8}\) D. \(\frac{1}{5}\)

Short answer

B. \(\frac{1}{9}\)

Step-by-step solution

Identify the given numbers

Determine the number of drivers under the age of 21 and the total number of drivers. There are 25 drivers under the age of 21 and a total of 225 drivers.

Write the fraction

Express the fraction as \(\frac{\text{number of drivers under 21}}{\text{total number of drivers}}\). This gives us \(\frac{25}{225}\).

Simplify the fraction

Simplify the fraction \(\frac{25}{225}\) by finding the greatest common divisor (GCD) of 25 and 225, which is 25. Divide both the numerator and the denominator by 25: \(\frac{25 \div 25}{225 \div 25} = \frac{1}{9}\).

Select the correct answer

Compare the simplified fraction, \(\frac{1}{9}\), with the provided options. The correct answer is B. \(\frac{1}{9}\).

Key concepts

simplifying fractions

Simplifying fractions is a key concept in basic math that helps make calculations easier. When given a fraction like \(\frac{25}{225}\), simplifying it means reducing it to its simplest form. This involves finding a number that both the numerator (top number) and the denominator (bottom number) can be divided by evenly. This common number is called the Greatest Common Divisor (GCD).
In our example, both 25 and 225 can be divided by 25. So, we divide both to get \(\frac{1}{9}\). Simplifying makes fractions easier to compare and understand.
Remember, a fraction is simplified when the numerator and the denominator have no common divisors other than 1. This makes the fraction cleaner and more readable.

greatest common divisor

To simplify fractions, you need to understand the Greatest Common Divisor (GCD). The GCD of two numbers is the largest number that divides both of them without leaving a remainder. For example, when working with \(\frac{25}{225}\), you look for the GCD of 25 and 225. Let's break it down.
\(\text{Factors of 25: 1, 5, 25}\)
\(\text{Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225}\)
The largest common factor is 25, so the GCD is 25. Now, you divide both the numerator and the denominator by this number: \(\frac{25 \div 25}{225 \div 25} = \frac{1}{9}\). Using the GCD to simplify fractions ensures you find the simplest form efficiently.

basic math operations

Basic math operations like addition, subtraction, multiplication, and division form the foundation for understanding fractions. When simplifying fractions, you mainly use division to reduce the fraction to its simplest form. Let's walk through the example in the exercise:
First, set up the fraction: \(\frac{25}{225}\).
Then, find the GCD (25 in this case) and divide both the numerator and the denominator by this number:
\(\text{Numerator: } 25 \div 25 = 1\)
\(\text{Denominator: } 225 \div 25 = 9\)
The simplified fraction is \(\frac{1}{9}\), which matches the correct answer in the exercise. By using division, a basic math operation, you managed to simplify the fraction and solve the problem efficiently.