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To solve this problem, we need to use the information provided about the ratios of segments along the line \( A \rightarrow B \rightarrow C \rightarrow D \).

### Given Information
1. The ratio of \( AB \) to \( AC \) is \( 3 : 5 \).
2. The ratio of \( AC \) to \( AD \) is \( 5 : 6 \).

We are asked to find the ratio of \( AB \) to \( AD \).

### Solution
Let's analyze each ratio in terms of a common length unit to find the overall ratio.

#### Step 1: Setting up Variables
1. Let \( AB = 3x \) and \( AC = 5x \) based on the ratio \( AB : AC = 3 : 5 \).
2. Since \( AC : AD = 5 : 6 \), we can let \( AD = 6x \).

#### Step 2: Finding \( AB : AD \)
Now that we have:
- \( AB = 3x \)
- \( AD = 6x \)

The ratio \( AB : AD \) is:
\[
AB : AD = 3x : 6x = 3 : 6 = 1

The points A, B, C, and D are on a straight line. The ratio of AB to AC is 3 : 5. The ratio of AC to AD is 5 : 6. What is the ratio of AB to AD?

Learn how to solve for the ratio of AB to AD when given that AB:AC = 3:5 and AC:AD = 5:6. This solution walks through setting up variables based on given ratios and simplifying the final ratio. Ideal for students in Grades 7-9 working on ratio and proportion concepts.

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