348 divided by 52 in a fraction

2 min read 21-02-2025

Expressing 348 Divided by 52 as a Fraction: A Step-by-Step Guide

Dividing one number by another is a fundamental arithmetic operation. We can represent this division as a fraction. This article will guide you through expressing 348 divided by 52 as a fraction, simplifying it to its lowest terms. Let's dive in!

Understanding Fractions and Division

A fraction represents a part of a whole. It's written as a numerator (top number) over a denominator (bottom number). The division operation is closely related; dividing one number by another is equivalent to expressing that division as a fraction. In other words, "a divided by b" can be written as a/b.

Expressing 348 Divided by 52 as a Fraction

To express 348 divided by 52 as a fraction, we simply write 348 as the numerator and 52 as the denominator:

348/52

Simplifying the Fraction

This fraction can be simplified by finding the greatest common divisor (GCD) of 348 and 52. The GCD is the largest number that divides both the numerator and denominator without leaving a remainder.

One way to find the GCD is to list the factors of each number and find the largest factor they have in common. Alternatively, you can use the Euclidean algorithm, a more efficient method for larger numbers.

Let's use the factorization method:

Factors of 348: 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348
Factors of 52: 1, 2, 4, 13, 26, 52

The largest common factor is 4.

Reducing the Fraction

Now we divide both the numerator and the denominator by the GCD (4):

348 ÷ 4 = 87 52 ÷ 4 = 13

Therefore, the simplified fraction is:

87/13

Converting to a Mixed Number (Optional)

While 87/13 is perfectly acceptable, we can also express it as a mixed number. To do this, we perform the division:

87 ÷ 13 = 6 with a remainder of 9

This means that 87/13 can be written as:

6 and 9/13

This indicates that 87 divided by 13 equals 6 with a remainder of 9 out of 13.

Conclusion

We've successfully expressed 348 divided by 52 as the fraction 348/52. By finding the greatest common divisor (4) and simplifying, we obtained the equivalent and simplified fraction 87/13, or the mixed number 6 and 9/13. Remember that both representations are correct and equivalent. Choosing between the improper fraction (87/13) and the mixed number (6 and 9/13) depends on the context of the problem.