Let's break down the two mathematical expressions shown in the image:

1. Left Expression: $\frac{76}{90} - \frac{42}{90}$

   Both fractions have the same denominator (90), so you can directly subtract the numerators: $\frac{76 - 42}{90} = \frac{34}{90}$

   Simplifying $\frac{34}{90}$, we divide both the numerator and the denominator by 2: $\frac{34}{90} = \frac{17}{45}$

   The result is: $\frac{17}{45} = 1 \frac{5}{9}$

2. Right Expression: $\frac{1725}{1000} + 1 \frac{3}{4} - \frac{375}{900}$

   First, convert the mixed number $1 \frac{3}{4}$ to an improper fraction: $1 \frac{3}{4} = \frac{7}{4}$

   Now the expression becomes: $\frac{1725}{1000} + \frac{7}{4} - \frac{375}{900}$

   The next step is to convert all fractions to have a common denominator. The least common denominator (LCD) for 1000, 4, and 900 is 18000.

   • Convert $\frac{1725}{1000}$ to have a denominator of 18000: $\frac{1725}{1000} = \frac{31050}{18000}$

   • Convert $\frac{7}{4}$ to have a denominator of 18000: $\frac{7}{4} = \frac{31500}{18000}$

   • Convert $\frac{375}{900}$ to have a denominator of 18000: $\frac{375}{900} = \frac{7500}{18000}$

   Now the expression becomes: $\frac{31050}{18000} + \frac{31500}{18000} - \frac{7500}{18000}$

   Combine the numerators: $\frac{31050 + 31500 - 7500}{18000} = \frac{55050}{18000}$

   Simplify $\frac{55050}{18000}$ by dividing both the numerator and denominator by 450: $\frac{55050}{18000} = \frac{1223}{400}$

3. Final Expression: The original expression is divided by $\frac{59}{100}$: $\frac{\frac{1223}{400}}{\frac{59}{100}} = \frac{1223}{400} \times \frac{100}{59}$

   Multiply the numerators and denominators: $\frac{1223 \times 100}{400 \times 59} = \frac{122300}{23600} = \frac{6115}{1180}$

   Simplifying $\frac{6115}{1180}$ by dividing both the numerator and denominator by 5: $\frac{6115}{1180} = \frac{1223}{236}$

Would you like further details or clarification?

Relative Questions:

1. How do you simplify fractions effectively?
2. What is the least common denominator, and how is it used?
3. Can you explain how to convert mixed numbers to improper fractions?
4. What are the methods to simplify large fractions?
5. Why is it useful to work with a common denominator in fraction operations?

Tip:

When dealing with multiple fractions, always try to find the least common denominator early, as it simplifies the overall process.