what is the 15 of 40

2 min read 15-04-2025

What is 15/40 Simplified? Understanding Fractions

The question "What is 15/40?" is essentially asking us to simplify the fraction 15/40 to its lowest terms. This means finding the greatest common divisor (GCD) of both the numerator (15) and the denominator (40), and then dividing both by that GCD. Let's break it down step-by-step.

Finding the Greatest Common Divisor (GCD)

The GCD is the largest number that divides evenly into both 15 and 40 without leaving a remainder. One way to find the GCD is to list the factors of each number:

Factors of 15: 1, 3, 5, 15
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

The largest number that appears in both lists is 5. Therefore, the GCD of 15 and 40 is 5.

Simplifying the Fraction

Now that we know the GCD is 5, we divide both the numerator and the denominator of the fraction 15/40 by 5:

15 ÷ 5 = 3 40 ÷ 5 = 8

This simplifies the fraction to 3/8.

Understanding the Result

Therefore, 15/40 simplified is equal to 3/8. This means that 15/40 and 3/8 represent the same value; they are equivalent fractions. Imagine a pizza cut into 40 slices. If you have 15 slices, it's the same as having 3 slices of a pizza cut into 8 slices.

Other Methods for Finding the GCD

Besides listing factors, there are other methods for finding the GCD, such as:

Prime Factorization: Break down both numbers into their prime factors. The GCD is the product of the common prime factors raised to the lowest power. For example:
- 15 = 3 x 5
- 40 = 2 x 2 x 2 x 5 = 2³ x 5
The only common prime factor is 5, so the GCD is 5.
Euclidean Algorithm: This is a more efficient method for larger numbers. It involves repeatedly dividing the larger number by the smaller number and taking the remainder until the remainder is 0. The last non-zero remainder is the GCD.

Converting Fractions to Decimals and Percentages

While 3/8 is the simplified fraction, you can also express this value as a decimal or a percentage:

Decimal: 3 ÷ 8 = 0.375
Percentage: 0.375 x 100% = 37.5%

In conclusion, 15/40 simplifies to the equivalent fraction 3/8, which is equal to 0.375 or 37.5%. Understanding how to simplify fractions is a fundamental skill in mathematics.