To evaluate \( 12.45 \div 20 \), we will perform the division step by step.
### Step 1: Set Up the Division
We start by setting up the division of \( 12.45 \) by \( 20 \). Since \( 12.45 \) is a decimal number, we can treat it as \( 124.5 \) (by moving the decimal point one place to the right) and divide by \( 20 \).
### Step 2: Determine How Many Times 20 Fits into 124
Next, we need to see how many times \( 20 \) fits into \( 124 \).
- \( 20 \times 1 = 20 \)
- \( 20 \times 2 = 40 \)
- \( 20 \times 3 = 60 \)
- \( 20 \times 4 = 80 \)
- \( 20 \times 5 = 100 \)
- \( 20 \times 6 = 120 \)
Since \( 20 \times 6 = 120 \) is the largest multiple of \( 20 \) that is less than or equal to \( 124 \), we write \( 6 \) above the division line.
### Step 3: Subtract to Find the Remainder
Now, we subtract \( 120 \) from \( 124 \):
\[
124 - 120 = 4
\]
So, we have a remainder of \( 4 \).
### Step 4: Bring Down the Next Digit
Next, we bring down the next digit from \( 12.45 \), which is \( 5 \), making it \( 45 \).
### Step 5: Determine How Many Times 20 Fits into 45
Now, we need to see how many times \( 20 \) fits into \( 45 \):
- \( 20 \times 1 = 20 \)
- \( 20 \times 2 = 40 \)
Since \( 20 \times 2 = 40 \) is the largest multiple of \( 20 \) that is less than or equal to \( 45 \), we write \( 2 \) above the division line next to \( 6 \).
### Step 6: Subtract to Find the New Remainder
Now, we subtract \( 40 \) from \( 45 \):
\[
45 - 40 = 5
\]
So, we have a new remainder of \( 5 \).
### Step 7: Bring Down Another Zero
Since \( 5 \) is not divisible by \( 20 \), we bring down another \( 0 \) (making it \( 50 \)).
### Step 8: Determine How Many Times 20 Fits into 50
Now, we need to see how many times \( 20 \) fits into \( 50 \):
- \( 20 \times 1 = 20 \)
- \( 20 \times 2 = 40 \)
- \( 20 \times 3 = 60 \)
Since \( 20 \times 2 = 40 \) is the largest multiple of \( 20 \) that is less than or equal to \( 50 \), we write \( 2 \) above the division line next to \( 62 \).
### Step 9: Subtract to Find the New Remainder
Now, we subtract \( 40 \) from \( 50 \):
\[
50 - 40 = 10
\]
So, we have a new remainder of \( 10 \).
### Step 10: Bring Down Another Zero
We bring down another \( 0 \) (making it \( 100 \)).
### Step 11: Determine How Many Times 20 Fits into 100
Now, we need to see how many times \( 20 \) fits into \( 100 \):
- \( 20 \times 5 = 100 \)
Since \( 20 \times 5 = 100 \), we write \( 5 \) above the division line next to \( 622 \).
### Step 12: Subtract to Find the Remainder
Now, we subtract \( 100 \) from \( 100 \):
\[
100 - 100 = 0
\]
So, we have a remainder of \( 0 \).
### Final Answer
Putting it all together, we find that:
\[
12.45 \div 20 = 0.6225
\]
