Evaluate the
31.42 -17.853 - 6.43

Options

A. 7.137
B. 7.237
C. 7.337
D. 7.437

Answer

To evaluate the expression \( 31.42 - 17.853 - 6.43 \), we will follow these steps:

### Step 1: Convert to Like Decimals
First, we need to convert all the numbers to have the same number of decimal places.

- \( 31.42 \) can be written as \( 31.420 \) (adding a zero).
- \( 17.853 \) already has three decimal places.
- \( 6.43 \) can be written as \( 6.430 \) (adding a zero).

Now we have:
\[ 31.420 - 17.853 - 6.430 \]

### Step 2: Perform the First Subtraction
Now, we will subtract \( 17.853 \) from \( 31.420 \).

Align the numbers by their decimal points:
```
31.420
- 17.853
```

Starting from the rightmost digit:
- In the thousandths place: \( 0 - 3 \) (we need to borrow, making it \( 10 - 3 = 7 \))
- In the hundredths place: \( 2 - 5 \) (we need to borrow again, making it \( 12 - 5 = 7 \))
- In the tenths place: \( 3 - 8 \) (we need to borrow, making it \( 13 - 8 = 5 \))
- In the units place: \( 1 - 7 \) (we need to borrow, making it \( 11 - 7 = 4 \))
- In the tens place: \( 2 - 1 = 1 \)

So, the result of the first subtraction is:
\[ 31.420 - 17.853 = 13.567 \]

### Step 3: Perform the Second Subtraction
Now we will subtract \( 6.430 \) from \( 13.567 \).

Align the numbers by their decimal points:
```
13.567
- 6.430
```

Starting from the rightmost digit:
- In the thousandths place: \( 7 - 0 = 7 \)
- In the hundredths place: \( 6 - 3 = 3 \)
- In the tenths place: \( 5 - 4 = 1 \)
- In the units place: \( 3 - 6 \) (we need to borrow, making it \( 13 - 6 = 7 \))
- In the tens place: \( 1 - 0 = 1 \)

So, the result of the second subtraction is:
\[ 13.567 - 6.430 = 7.137 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{7.137} \]