To evaluate \( 12.4 \times 14.6 \), we can follow these steps:
### Step 1: Remove the Decimals
First, we can ignore the decimal points and multiply the numbers as if they were whole numbers.
- Convert \( 12.4 \) to \( 124 \) (by multiplying by 10).
- Convert \( 14.6 \) to \( 146 \) (by multiplying by 10).
### Step 2: Multiply the Whole Numbers
Now, we will multiply \( 124 \) by \( 146 \).
#### Step 2.1: Multiply the Units
- \( 6 \times 4 = 24 \) (write down 4, carry over 2)
#### Step 2.2: Multiply the Tens
- \( 6 \times 2 = 12 \) (add the carry 2) → \( 12 + 2 = 14 \) (write down 4, carry over 1)
#### Step 2.3: Multiply the Hundreds
- \( 6 \times 1 = 6 \) (add the carry 1) → \( 6 + 1 = 7 \)
So, the first row of the multiplication gives us \( 744 \).
#### Step 2.4: Multiply the Next Digit (4 in 146)
Now, we will multiply \( 124 \) by \( 4 \) (which is actually \( 40 \) since it is in the tens place).
- \( 4 \times 4 = 16 \) (write down 6, carry over 1)
- \( 4 \times 2 = 8 \) (add the carry 1) → \( 8 + 1 = 9 \)
- \( 4 \times 1 = 4 \)
So, the second row gives us \( 4960 \) (remember to shift one position to the left).
#### Step 2.5: Multiply the Next Digit (1 in 146)
Now, we will multiply \( 124 \) by \( 1 \) (which is actually \( 100 \) since it is in the hundreds place).
- \( 1 \times 4 = 4 \)
- \( 1 \times 2 = 2 \)
- \( 1 \times 1 = 1 \)
So, the third row gives us \( 12400 \) (shift two positions to the left).
### Step 3: Add the Results
Now, we will add all the rows together:
```
744
4960
12400
------
18104
```
### Step 4: Place the Decimal
Now, we need to place the decimal point.
- In \( 12.4 \), there is 1 digit after the decimal.
- In \( 14.6 \), there is also 1 digit after the decimal.
- Therefore, in total, we have \( 1 + 1 = 2 \) digits after the decimal in our final answer.
So, we place the decimal point in \( 18104 \) to get \( 181.04 \).
### Final Answer
Thus, \( 12.4 \times 14.6 = 181.04 \).
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