The Correct Answer and Explanation is:
The correct simplified fraction is 2/11.
To simplify a fraction means to reduce it to its simplest form, also known as its lowest terms. This is achieved by dividing both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). The GCD is the largest number that can divide both the numerator and the denominator without leaving a remainder. The resulting fraction will be equivalent to the original one but with the smallest possible whole numbers.
The fraction we need to simplify is 20/110.
First, we identify the numerator, which is 20, and the denominator, which is 110. We need to find a common number that can divide both 20 and 110. A simple way to start is to look for obvious common factors. Since both numbers end in a zero, we know they are both divisible by 10. This is often the quickest way to simplify when numbers end in zero.
Let’s divide both the numerator and the denominator by this common factor, 10:
- Divide the numerator by 10: 20 ÷ 10 = 2
- Divide the denominator by 10: 110 ÷ 10 = 11
After this division, we get the new fraction: 2/11.
Now, we must check if this new fraction can be simplified any further. To do this, we need to see if the new numerator (2) and the new denominator (11) share any common factors other than 1.
- The factors of 2 are 1 and 2.
- The factors of 11 are 1 and 11.
As you can see, the only common factor between 2 and 11 is 1. When the only common factor is 1, the fraction is in its simplest form. Both 2 and 11 are prime numbers, meaning they are only divisible by 1 and themselves, which makes it easy to confirm that they share no other factors.
Therefore, the fraction 20/110, when simplified completely, is 2/11.
