The points L, M, N and O all lie on the same line segment, in that order, such that the ratio of L, M, colon, M, N, colon, N, OLM:MN:NO is equal to 1, colon, 6, colon, 1, .1:6:1. If L, O, equals, 16, commaLO=16, find N, O, .NO.

We are given that the points \( L \), \( M \), \( N \), and \( O \) all lie on the same line segment, with the ratio of the segments \( LM : MN : NO = 1 : 6 : 1 \), and that the total length of \( LO = 16 \).

To find the length of \( NO \), we can use the following approach:

### Step 1: Express the total length in terms of parts
The given ratio \( LM : MN : NO = 1 : 6 : 1 \) means that we can express each segment as a multiple of a common part, say \( x \). So:
\[
LM = 1x, \quad MN = 6x, \quad NO = 1x
\]
Thus, the total length of the segment \( LO \) is:
\[
LO = LM + MN + NO = 1x + 6x + 1x = 8x
\]

### Step 2: Solve for \( x \)
We are told that \( LO = 16 \). Therefore:
\[
8x = 16
\]
Solving for \( x \), we get:
\[
x = \frac{16}{8} = 2
\]

### Step 3: Find \( NO \)
Since \( NO = 1x \), we substitute \( x = 2 \) to get:
\[
NO = 1 \times 2 = 2
\]

Thus, the length of \( NO \) is \( \boxed{2} \).

Would you like more details or further clarification on this?

Here are some related questions for further practice:
1. If \( MN \) were given, how would you find the value of \( LM \)?
2. What if the total length \( LO \) was different, say 24? How would that change the calculation of \( NO \)?
3. How can you generalize the approach to solve any ratio problem like this?
4. If the ratio had included another segment, say \( NO : OP \), how would you solve for the length of \( NO \)?
5. How does the concept of ratios apply to real-world measurements?

**Tip**: Always check that the total length matches the sum of the segments when working with ratios to avoid calculation errors.

The points L, M, N, and O all lie on the same line segment, in that order, such that the ratio of LM:MN:NO is equal to 1:6:1. If LO = 16, find NO.

Learn how to solve a line segment problem where points L, M, N, and O lie on the same line with a ratio of 1:6:1, and LO = 16. This step-by-step guide covers the use of ratios and proportions to find NO. Suitable for Grades 6-8.

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