## Solving the Math Problem: 1 1/2 Divided by 1/6 - 7/8

This problem involves a combination of fractions, mixed numbers, division, and subtraction. Let's break it down step by step.

### 1. Convert Mixed Number to a Fraction

First, convert the mixed number 1 1/2 to an improper fraction:

**Multiply the whole number by the denominator:**1 * 2 = 2**Add the numerator:**2 + 1 = 3**Keep the same denominator:**3/2

Now the problem is: **(3/2) / (1/6) - (7/8)**

### 2. Divide Fractions

To divide fractions, we flip the second fraction and multiply:

**Flip the second fraction:**(1/6) becomes (6/1)**Multiply:**(3/2) * (6/1) = 18/2

Now the problem is: **18/2 - (7/8)**

### 3. Find a Common Denominator

Before we can subtract, the fractions need a common denominator. The least common multiple of 2 and 8 is 8.

**Convert 18/2 to an equivalent fraction with a denominator of 8:**(18/2) * (4/4) = 72/8

Now the problem is: **72/8 - (7/8)**

### 4. Subtract the Fractions

With the same denominator, we can simply subtract the numerators:

**72/8 - 7/8 = 65/8**

### 5. Simplify to a Mixed Number (Optional)

If desired, we can convert the improper fraction back to a mixed number:

**Divide the numerator by the denominator:**65 ÷ 8 = 8 with a remainder of 1**The whole number is 8, the remainder is the new numerator, and the denominator stays the same:**8 1/8

### Final Answer

Therefore, 1 1/2 divided by 1/6, minus 7/8, equals **65/8** or **8 1/8**.