91Ó°ÊÓ

To add or subtract fractions, finding a common denominator is essential. A common denominator is a shared multiple of the denominators of the fractions you’re working with. It allows you to add or subtract the numerators directly.
For example, if you have fractions with denominators 10 and 100, like in the given problem, you need to adjust them to share the same denominator. This does not change the value of the fractions; it merely allows the arithmetic to be performed more easily.
In our problem, the denominators are 10 and 100, so we look for a common denominator - specifically, the least common multiple of 10 and 100.

Understanding the concept of the least common multiple (LCM) is key in many areas of arithmetic, including finding common denominators for adding fractions. The LCM of two numbers is the smallest number that is a multiple of both.
In our exercise, to find the LCM of 10 and 100, we consider the multiples of each:

• Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
• Multiples of 100: 100, 200, 300, 400, ...

From this, it's clear that 100 is the smallest multiple that both numbers share.
Once you've identified the LCM, you can proceed to convert the fractions so they have this common denominator, enabling straightforward addition.

Simplifying fractions is an important skill that involves reducing the fraction to its simplest form. A fraction is in its simplest form when the numerator and denominator have no common factors other than 1.
In our exercise, after finding the common denominator and adding the fractions, we get \[ \frac{93}{100} \].
To check if this fraction can be simplified further, we look for any common factors between 93 and 100. Since 93 and 100 share no common factors besides 1, \[ \frac{93}{100} \] is already in simplest form.
Simplifying fractions ensures that the solution is as easy to understand as possible, and sometimes can reveal aspects of the numbers involved that weren’t initially obvious.