simplify 36/99

2 min read 24-02-2025

The fraction 36/99 might seem daunting at first, but simplifying it is easier than you think. This guide will walk you through the process step-by-step, showing you how to reduce this fraction to its simplest form. We'll explore the concept of greatest common divisors (GCD) and demonstrate how to apply them to fraction simplification. By the end, you'll be able to simplify similar fractions with confidence.

Understanding Fraction Simplification

Simplifying a fraction means reducing it to its lowest terms. This means finding the greatest common divisor (GCD) of both the numerator (top number) and the denominator (bottom number) and dividing both by that number. The GCD is the largest number that divides evenly into both numbers without leaving a remainder.

Finding the Greatest Common Divisor (GCD) of 36 and 99

To simplify 36/99, we need to find the GCD of 36 and 99. There are a few ways to do this:

Method 1: Listing Factors

One method is to list all the factors (numbers that divide evenly) of 36 and 99, and then find the largest number that appears in both lists.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Factors of 99: 1, 3, 9, 11, 33, 99

The largest number that appears in both lists is 9. Therefore, the GCD of 36 and 99 is 9.

Method 2: Prime Factorization

Another method involves finding the prime factorization of both numbers. A prime number is a whole number greater than 1 that has only two divisors: 1 and itself.

Prime factorization of 36: 2 x 2 x 3 x 3 = 2² x 3²
Prime factorization of 99: 3 x 3 x 11 = 3² x 11

The common prime factors are 3² (or 9). Therefore, the GCD is 9.

Simplifying the Fraction

Now that we know the GCD is 9, we can simplify the fraction:

36/99 = (36 ÷ 9) / (99 ÷ 9) = 4/11

Therefore, the simplest form of 36/99 is 4/11.

Practice Problems

Try simplifying these fractions using the methods described above:

12/18
24/36
15/45

Solutions:

12/18 simplifies to 2/3
24/36 simplifies to 2/3
15/45 simplifies to 1/3

Conclusion

Simplifying fractions like 36/99 is a fundamental skill in mathematics. By understanding the concept of the greatest common divisor and employing either the factor listing or prime factorization method, you can easily reduce fractions to their simplest forms. Remember, practice makes perfect! The more you work with fractions, the faster and more intuitive this process will become. Now you can confidently tackle similar fraction simplification problems.