Simplify $\frac{36}{90}$
To simplify the fraction \(\frac{36}{90}\), we aim to express it in its lowest terms. This is achieved by dividing both the numerator and the denominator by their greatest common divisor (GCD). Identifying common factors is the key to reducing the fraction effectively.
We first determine the prime factorization of both the numerator, \(36\), and the denominator, \(90\).
For the numerator:
\[36 = 6 \times 6 = (2 \times 3) \times (2 \times 3) = 2^2 \times 3^2\]
For the denominator:
\[90 = 9 \times 10 = (3 \times 3) \times (2 \times 5) = 2^1 \times 3^2 \times 5^1\]
To find the greatest common divisor (GCD), we identify the common prime factors in the factorizations and select the lowest power of each.
The common prime factors are \(2\) and \(3\).
The lowest power of \(2\) is \(2^1\).
The lowest power of \(3\) is \(3^2\).
Therefore, the GCD is:
\[\text{GCD}(36, 90) = 2^1 \times 3^2 = 2 \times 9 = 18\]
Now that we have identified the GCD as \(18\), we divide both the numerator and the denominator by \(18\) to simplify the fraction:
\[\frac{36 \div 18}{90 \div 18} = \frac{2}{5}\]
The fraction is now in its simplest form.
The fraction \(\frac{36}{90}\) simplifies to \(\boxed{\frac{2}{5}}\).
Simplifying fractions is essential in daily life, such as when following a recipe. If a recipe calls for \(\frac{36}{90}\) of a cup of an ingredient, it is much easier to measure out \(\frac{2}{5}\) of a cup. Understanding how to reduce fractions allows you to work with more manageable numbers in cooking, budgeting, or even adjusting time schedules during your day.