To solve \( 1 + \frac{3}{4} : \frac{1}{8} \), let's break it down step by step.

### Step 1: Division of fractions
The colon \( : \) indicates division, so the expression becomes:
\[
1 + \frac{3}{4} \div \frac{1}{8}
\]
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore:
\[
\frac{3}{4} \div \frac{1}{8} = \frac{3}{4} \times \frac{8}{1} = \frac{3 \times 8}{4 \times 1} = \frac{24}{4} = 6
\]

### Step 2: Adding the whole number
Now, add the result to 1:
\[
1 + 6 = 7
\]

Thus, the final answer is \( \boxed{7} \).

Would you like more details or have any questions?

### Related Questions:
1. How would you solve \( 2 + \frac{5}{6} : \frac{1}{3} \)?
2. What is the result of \( \frac{7}{8} : \frac{2}{5} \)?
3. How do you simplify complex fractions?
4. How do you multiply and divide fractions?
5. What is the reciprocal of a fraction, and how is it used?

### Tip:
When dividing fractions, remember that you multiply by the reciprocal of the second fraction!

Learn how to solve the math problem 1 + 3/4 ÷ 1/8 with step-by-step instructions. This covers division of fractions, using the reciprocal method, and addition. Suitable for students in Grades 5-7.

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