Let's solve the subtraction of mixed numbers:

\[
5 \frac{2}{3} - 2 \frac{7}{8}
\]

### Step 1: Convert both mixed numbers to improper fractions.

1. \( 5 \frac{2}{3} \):
   \[
   5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3}
   \]

2. \( 2 \frac{7}{8} \):
   \[
   2 \frac{7}{8} = \frac{2 \times 8 + 7}{8} = \frac{16 + 7}{8} = \frac{23}{8}
   \]

### Step 2: Find a common denominator.
The least common denominator (LCD) of 3 and 8 is 24.

- Convert \( \frac{17}{3} \) to have a denominator of 24:
  \[
  \frac{17}{3} = \frac{17 \times 8}{3 \times 8} = \frac{136}{24}
  \]
  
- Convert \( \frac{23}{8} \) to have a denominator of 24:
  \[
  \frac{23}{8} = \frac{23 \times 3}{8 \times 3} = \frac{69}{24}
  \]

### Step 3: Subtract the fractions.
Now subtract the two improper fractions:
\[
\frac{136}{24} - \frac{69}{24} = \frac{136 - 69}{24} = \frac{67}{24}
\]

### Step 4: Convert back to a mixed number.
\[
\frac{67}{24} = 2 \frac{19}{24}
\]

Thus, the result is:
\[
5 \frac{2}{3} - 2 \frac{7}{8} = 2 \frac{19}{24}
\]

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. \( 7 \frac{1}{4} - 3 \frac{5}{6} \)
2. \( 6 \frac{2}{5} + 3 \frac{7}{10} \)
3. \( 8 \frac{3}{4} - 5 \frac{1}{2} \)
4. \( 4 \frac{5}{6} + 2 \frac{1}{3} \)
5. \( 3 \frac{7}{8} - 1 \frac{3}{4} \)

**Tip:** Always convert mixed numbers to improper fractions before performing operations like addition or subtraction.

Learn how to subtract mixed numbers with a step-by-step solution for the problem 5 2/3 - 2 7/8. This guide covers converting mixed numbers to improper fractions, finding a common denominator, and performing subtraction. Suitable for students in Grades 5-7.

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