Question

what is the solution to the problem shown?
3,041 - 628 = ?

a. 3,013
b. 3,241
c. 2,413
d. 2,423

Explanation:

Step1: Subtract the two numbers

We need to calculate \( 3041 - 628 \).
First, subtract the units place: \( 1 - 8 \), but we can't do that, so we borrow 1 from the tens place. The tens place is 4, so it becomes 3, and the units place becomes \( 11 - 8 = 3 \).

Step2: Subtract the tens place

Now the tens place is 3 (after borrowing), and we subtract 2: \( 3 - 2 = 1 \).

Step3: Subtract the hundreds place

The hundreds place is 0, but we need to subtract 6, so we borrow 1 from the thousands place. The thousands place becomes 2, and the hundreds place becomes \( 10 - 6 = 4 \)? Wait, no, wait. Wait, the original number is 3041. Let's do it properly:

\( 3041 - 628 \):

• Thousands place: 3 (but we will borrow for hundreds place)
• Hundreds place: 0, so we borrow 1 from thousands place (3 becomes 2), so hundreds place becomes 10. Then we borrow 1 from hundreds place (10 becomes 9) to give to tens place (4 becomes 5)? Wait, no, let's use the standard subtraction:

\(

$$\begin{align*} &\quad3\ 0\ 4\ 1\\ &-\quad\ 6\ 2\ 8\\ &\overline{\quad\quad\quad\quad} \end{align*}$$

\)

Starting from the rightmost digit (units):

Units: \( 1 - 8 \). Can't do, so borrow 1 from tens. Tens is 4, becomes 3, units becomes \( 11 - 8 = 3 \).

Tens: \( 3 - 2 = 1 \) (since we borrowed 1 for units, tens was 4, now 3).

Hundreds: \( 0 - 6 \). Can't do, so borrow 1 from thousands. Thousands is 3, becomes 2, hundreds becomes \( 10 \). Now borrow 1 from hundreds (10 becomes 9) to give to tens? Wait, no, tens is already done. Wait, hundreds place: we need to subtract 6 from 0, so we borrow 1 from thousands (3→2), so hundreds becomes 10. Then we subtract 6 from 10? No, wait, no. Wait, the number is 3041, which is 3 thousands, 0 hundreds, 4 tens, 1 unit.

To subtract 628 (6 hundreds, 2 tens, 8 units), we do:

• Units: 1 - 8. Borrow 1 from tens: tens becomes 3, units becomes 11. 11 - 8 = 3.
• Tens: 3 - 2 = 1.
• Hundreds: 0 - 6. Can't do, so borrow 1 from thousands: thousands becomes 2, hundreds becomes 10. Now subtract 6 from 10? No, wait, no. Wait, the hundreds place is 0, so when we borrow from thousands (3→2), the hundreds place becomes 10. Then we subtract 6 from 10? No, that's not right. Wait, no, the hundreds place in 3041 is 0, so to subtract 6 (hundreds place of 628), we need to borrow from the thousands place. So thousands place 3 becomes 2, hundreds place becomes 10. But then we have to subtract 6 from 10? No, that's not correct. Wait, no, the correct way is:

\( 3041 - 628 = 3041 - 600 - 20 - 8 \)

\( 3041 - 600 = 2441 \)

\( 2441 - 20 = 2421 \)

\( 2421 - 8 = 2413 \)

Wait, that's different from my earlier mistake. Let's do it step by step:

\( 3041 - 628 \):

• Subtract 600 from 3041: \( 3041 - 600 = 2441 \)
• Subtract 20 from 2441: \( 2441 - 20 = 2421 \)
• Subtract 8 from 2421: \( 2421 - 8 = 2413 \)

So \( 3041 - 628 = 2413 \)

Answer:

C. 2,413