Method for Multiplication, Multiplying 187 by 12

Here’s a visual layout showing how the HTU (Hundreds, Tens, Units) method works for multiplying 187 by 12:

Step-by-Step HTU Multiplication Layout

H T U
1 8 7 (This is 187)
× 1 2 (This is 12)
______________
3 7 4 (187 × 2)
+ 1 8 7 0 (187 × 10, shifted one place to the left)
______________
2 2 4 4 (Final result: 2244)

Explanation
1. Multiply 187 × 2:
- Multiply the units: 7 × 2 = 14 (write 4 in the units place, carry over 1).
- Multiply the tens: 8 × 2 = 16 + 1 (carry) = 17 (write 7 in the tens place, carry over 1).
- Multiply the hundreds: 1 × 2 = 2 + 1 (carry) = 3 (write 3 in the hundreds place).

Result: 374

2. Multiply 187 × 10:
- Multiply the units: 7 × 1 = 7.
- Multiply the tens: 8 × 1 = 8.
- Multiply the hundreds: 1 × 1 = 1.
- Shift one place to the left since we're multiplying by 10.

Result: 1870

3. Add the two results:
- 374 + 1870 = 2244.

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HTU (Hundreds, Tens, Units) Method for Multiplication

To multiply 187 by 12 using the HTU method, we break down the numbers into their Hundreds (H), Tens (T), and Units (U), then multiply step by step.

Step 1: Break down 187 by place value
187 has:
- H = 1 (Hundreds)
- T = 8 (Tens)
- U = 7 (Units)

We multiply 187 by 12, which is made of:
- T = 1 (Tens)
- U = 2 (Units)

Step 2: Multiply 187 by 2 (Units of 12)
Multiply each digit of 187 by 2.

- Units (7 × 2) = 14 → Write 4 in the units place, carry 1 to the tens.
- Tens (8 × 2) = 16 + 1 (carried over) = 17 → Write 7 in the tens place, carry 1 to the hundreds.
- Hundreds (1 × 2) = 2 + 1 (carried over) = 3 → Write 3 in the hundreds place.

So, 187 × 2 = 374.

Step 3: Multiply 187 by 10 (Tens of 12)
Multiplying by 10 means shifting the result one place to the left. Multiply each digit of 187 by 1.

- Units (7 × 1) = 7 → Write 7 under the tens place.
- Tens (8 × 1) = 8 → Write 8 under the hundreds place.
- Hundreds (1 × 1) = 1 → Write 1 under the thousands place.

So, 187 × 10 = 1870.

Step 4: Add the results
Now, add the two products (374 and 1870):

\[
\begin{array}{r}
\ 1870 \\
+ \ 374 \\
\hline
2244 \\
\end{array}
\]

Final Answer:
187 multiplied by 12 is 2244.

This method helps you clearly see how the place values work in multiplication.This visual format helps to clearly see how the numbers are lined up by their place values and how the multiplication flows.