Equivalent Fractions, Simplification, and Solving Proportions

The image contains three sections of math problems written in Khmer. I will solve each section step-by-step.

The sections are:
I. ស្វែងរកចំនួនក្នុងប្រអប់ (Find the number in the box) - This involves finding equivalent fractions.
II. សរុបប្រភាគខាងក្រោម (Simplify the following fractions) - This involves reducing fractions to their simplest form.
III. តតើសេង្ហត្ម x និង y ខាងក្រោម (Determine x and y in the following equations) - This involves solving proportions for variables and .

We need to find the missing value ( ) in each equivalent fraction.

To get from the denominator to , we multiply by ( ). Therefore, we must multiply the numerator by as well.

The missing number is .

To get from the denominator to , we divide by ( ). Therefore, we must divide the numerator by .

The missing number is .

To get from the denominator to , we multiply by ( ). Therefore, we must multiply the numerator by .

The missing number is .

We need to simplify each fraction by dividing the numerator and denominator by their Greatest Common Divisor (GCD).

The GCD of and is .

The GCD of and is .

We can find the GCD by successive division. Both are divisible by :

Now, both and are divisible by :

(Alternatively, the GCD of and is : , ).

Since ends in and ends in , both are divisible by .

Both and are divisible by :

(Alternatively, the GCD of and is : , ).

We need to solve for the unknown variables and using the property of equivalent fractions (cross-multiplication).

Cross-multiply:

Divide by :

First, simplify the right side: .
So, the equation is:

Cross-multiply:

Divide by :

First, simplify the left side: .
So, the equation is:

Cross-multiply:

Cross-multiply:

Divide by :

Simplify the fraction by dividing numerator and denominator by :

As a decimal: .