A line segment measuring 28.254cm is divided into three parts. If lengths of two line segments are 11.678 cm and 7.158 cm, then find the measure of third part.

Options

A. 4.112cm
B. 5.646cm
C. 9.264cm
D. 9.418cm

Answer

To find the measure of the third part of the line segment, we will follow these steps:

### Step 1: Add the lengths of the two known segments.
We have two segments measuring 11.678 cm and 7.158 cm. We need to add these two lengths together.

**Calculation:**
\[ 11.678 \, \text{cm} + 7.158 \, \text{cm} \]

Aligning the decimal points:
```
11.678
+ 7.158
__________
```
Now, adding the numbers column by column:
- In the thousandths place: \(8 + 8 = 16\) (write down 6 and carry over 1)
- In the hundredths place: \(7 + 5 + 1 = 13\) (write down 3 and carry over 1)
- In the tenths place: \(6 + 1 + 1 = 8\)
- In the units place: \(1 + 7 = 8\)
- In the tens place: \(1 + 0 = 1\)

So, the total length of the two segments is:
\[ 18.836 \, \text{cm} \]

### Step 2: Subtract the total length of the two segments from the total length of the line segment.
Now, we need to find the length of the third part by subtracting the sum of the two segments from the total length of the line segment, which is 28.254 cm.

**Calculation:**
\[ 28.254 \, \text{cm} - 18.836 \, \text{cm} \]

Aligning the decimal points:
```
28.254
- 18.836
__________
```
Now, subtracting the numbers column by column:
- In the thousandths place: \(4 - 6\) (we need to borrow, so it becomes \(14 - 6 = 8\))
- In the hundredths place: \(5 - 3 = 2\)
- In the tenths place: \(2 - 8\) (we need to borrow, so it becomes \(12 - 8 = 4\))
- In the units place: \(7 - 8\) (we need to borrow, so it becomes \(17 - 8 = 9\))
- In the tens place: \(2 - 1 = 1\)

So, the length of the third part is:
\[ 9.418 \, \text{cm} \]

### Final Answer:
The measure of the third part is **9.418 cm**.

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