what is the simplest form of 238/4

less than a minute read 26-12-2024

The simplest form of a fraction is when the numerator (top number) and denominator (bottom number) have no common factors other than 1. This is also known as simplifying the fraction or reducing the fraction to its lowest terms. Let's find the simplest form of 238/4.

Understanding Fraction Simplification

To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder.

Finding the GCD of 238 and 4

List the factors:
- Factors of 238: 1, 2, 7, 14, 17, 34, 119, 238
- Factors of 4: 1, 2, 4
Identify the greatest common factor: The largest number that appears in both lists is 2.

Simplifying the Fraction

Now that we've found the GCD (2), we divide both the numerator and the denominator by it:

238 ÷ 2 = 119 4 ÷ 2 = 2

Therefore, the simplest form of 238/4 is 119/2.

Can we simplify further?

Let's check if 119 and 2 have any common factors other than 1. The factors of 119 are 1, 7, 17, and 119. The only factor 119 shares with 2 is 1. This confirms that 119/2 is indeed the simplest form.

Converting to a Mixed Number (Optional)

While 119/2 is the simplest form as a fraction, we can also express it as a mixed number. A mixed number combines a whole number and a fraction.

To convert 119/2 to a mixed number, we perform the division:

119 ÷ 2 = 59 with a remainder of 1.

This means 119/2 is equal to 59 1/2.

Conclusion

The simplest form of the fraction 238/4 is 119/2, or expressed as a mixed number, 59 1/2. Remember, simplifying fractions involves finding the greatest common divisor and dividing both the numerator and denominator by it. This process ensures the fraction is in its most reduced and efficient form.