48/15 simplified
Understand the Problem
The question is asking to simplify the fraction 48/15 to its lowest terms. To do this, we will find the greatest common divisor (GCD) of the numerator and denominator and divide both by this number.
Answer
The fraction \( \frac{48}{15} \) simplifies to \( \frac{16}{5} \).
Answer for screen readers
The simplified fraction is ( \frac{16}{5} ).
Steps to Solve
- Find the GCD of 48 and 15
To simplify the fraction $ \frac{48}{15} $, we first need to determine the greatest common divisor (GCD) of 48 and 15. The GCD is the largest number that can divide both numbers without leaving a remainder.
To find the GCD, we can use the prime factorization method:
- The prime factors of 48 are: $48 = 2^4 \times 3^1$
- The prime factors of 15 are: $15 = 3^1 \times 5^1$
The only common factor is 3, therefore the GCD is 3.
- Divide both the numerator and denominator by the GCD
Now that we have the GCD, we divide both parts of the fraction by this number:
$$ \frac{48 \div 3}{15 \div 3} $$
- Calculate the simplified fraction
By performing the division, we get:
$$ \frac{16}{5} $$
This is the fraction in its lowest terms.
The simplified fraction is ( \frac{16}{5} ).
More Information
When a fraction is simplified to its lowest terms, it means that the numerator and denominator share no common divisors other than 1. This process is essential to make fractions easier to work with, especially in calculations.
Tips
- Not finding the GCD correctly: Some may overlook the correct GCD or might not consider all factors. Always verify your factorization.
- Forgetting to divide both the numerator and denominator: It's important to perform the same operation on both parts to keep the fraction equivalent.
