Let's solve the differences in the given image step by step.

Problem 1:

$\frac{7}{15} - \frac{1}{5}$ We need a common denominator. The least common denominator (LCD) of 15 and 5 is 15.

$\frac{1}{5} = \frac{3}{15}$

Now subtract: $\frac{7}{15} - \frac{3}{15} = \frac{4}{15}$

Problem 2:

$\frac{4}{5} - \frac{2}{4}$ We need a common denominator. The least common denominator of 5 and 4 is 20.

Convert both fractions: $\frac{4}{5} = \frac{16}{20}, \quad \frac{2}{4} = \frac{10}{20}$

Now subtract: $\frac{16}{20} - \frac{10}{20} = \frac{6}{20} = \frac{3}{10}$

Problem 3:

$\frac{5}{8} - \frac{2}{7}$ The least common denominator of 8 and 7 is 56.

Convert both fractions: $\frac{5}{8} = \frac{35}{56}, \quad \frac{2}{7} = \frac{16}{56}$

Now subtract: $\frac{35}{56} - \frac{16}{56} = \frac{19}{56}$

Problem 4:

$\frac{8}{9} - \frac{2}{6}$ We need a common denominator. The least common denominator of 9 and 6 is 18.

Convert both fractions: $\frac{8}{9} = \frac{16}{18}, \quad \frac{2}{6} = \frac{6}{18}$

Now subtract: $\frac{16}{18} - \frac{6}{18} = \frac{10}{18} = \frac{5}{9}$

Problem 5:

$\frac{1}{4} - 2 \frac{3}{5}$ First, convert the mixed number $2 \frac{3}{5}$ into an improper fraction: $2 \frac{3}{5} = \frac{13}{5}$

We need a common denominator. The least common denominator of 4 and 5 is 20.

Convert both fractions: $\frac{1}{4} = \frac{5}{20}, \quad \frac{13}{5} = \frac{52}{20}$

Now subtract: $\frac{5}{20} - \frac{52}{20} = \frac{-47}{20}$

This simplifies to $-2 \frac{7}{20}$.

If you'd like further details or have questions, feel free to ask!

Related Questions:

1. What is the general process for finding the least common denominator?
2. How do you convert a mixed number into an improper fraction?
3. Can you explain how to simplify fractions after subtracting?
4. What should you do if the result of a subtraction is negative?
5. How do you handle cases where the denominators are the same from the start?

Tip:

Always check whether your fractions can be simplified after performing operations like subtraction or addition!