What is the distance KL + KO?

The number line having 8 ticks having labelled from left to right. First tick from left is labelled as K, third tick is at -5, fifth tick is labelled as L, and seventh tick is at 0 which labelled as O.

Let's break down the number line step by step based on the information provided:

1. There are 8 ticks, labelled from left to right.
2. The first tick is labelled as \( K \).
3. The third tick is at \( -5 \).
4. The fifth tick is labelled as \( L \).
5. The seventh tick is at \( 0 \) and labelled as \( O \).

### Step 1: Determine the positions of \( L \) and \( K \)

From the information given:
- The seventh tick is at 0 (which is \( O \)).
- The third tick is at \( -5 \).
  
We can assume that the distance between each consecutive tick is equal. Since the difference between the third tick (−5) and the seventh tick (0) is \( 5 \), and there are 4 tick intervals between them, each interval must represent:

\[
\frac{0 - (-5)}{4} = \frac{5}{4} = 1.25
\]

Thus, the distance between each tick is 1.25 units.

### Step 2: Calculate the position of \( L \) and \( K \)

- Since \( L \) is on the fifth tick, its position is \( -5 + 2(1.25) = -5 + 2.5 = -2.5 \).
- Since \( K \) is on the first tick, its position is \( -5 - 2(1.25) = -5 - 2.5 = -7.5 \).

### Step 3: Find the distances

1. The distance \( KL \):
   \[
   KL = L - K = (-2.5) - (-7.5) = -2.5 + 7.5 = 5
   \]
2. The distance \( KO \):
   \[
   KO = O - K = 0 - (-7.5) = 0 + 7.5 = 7.5
   \]

### Step 4: Add the distances \( KL + KO \)
\[
KL + KO = 5 + 7.5 = 12.5
\]

Thus, the total distance \( KL + KO \) is **12.5 units**.

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Would you like further details or have any questions?

Here are some related questions:
1. How would the result change if each tick represented 2 units instead of 1.25?
2. What is the distance between \( L \) and \( O \)?
3. How can we generalize the method to calculate distances on a number line with unknown tick spacing?
4. How would the calculation differ if the number of ticks increased to 10?
5. What if the tick values were fractional numbers?

**Tip:** Always check if the tick intervals are evenly spaced when working with number lines!

What is the distance KL + KO? The number line having 8 ticks having labelled from left to right. First tick from left is labelled as K, third tick is at -5, fifth tick is labelled as L, and seventh tick is at 0 which labelled as O.

Learn how to calculate the distance KL + KO on a number line with evenly spaced ticks. This problem involves key concepts of number line intervals and distance calculation, suitable for students in Grades 6-8. Step-by-step explanation provided.

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