Question

956 + 287 = 1,243
Let's explore why carrying works. First, write each number in expanded form.

Answer 1

Sure! To understand carrying in addition better, we can break each number down into its expanded form.

For 956:
- The digit 9 is in the hundreds place, so it represents \(9 \times 100 = 900\).
- The digit 5 is in the tens place, so it represents \(5 \times 10 = 50\).
- The digit 6 is in the ones place, so it represents \(6 \times 1 = 6\).

Putting it all together, we can express 956 in expanded form:
\[ 956 = 900 + 50 + 6 \]

Now for 287:
- The digit 2 is in the hundreds place, so it represents \(2 \times 100 = 200\).
- The digit 8 is in the tens place, so it represents \(8 \times 10 = 80\).
- The digit 7 is in the ones place, so it represents \(7 \times 1 = 7\).

Putting it all together, we can express 287 in expanded form:
\[ 287 = 200 + 80 + 7 \]

Now, let's add the two numbers together using their expanded forms:

\[
956 + 287 = (900 + 50 + 6) + (200 + 80 + 7)
\]

We can combine like terms:
\[
= (900 + 200) + (50 + 80) + (6 + 7)
\]

Now we calculate each part:
\[
= 1100 + 130 + 13
\]

Finally, we can add these totals together:
\[
1100 + 130 = 1230
\]
\[
1230 + 13 = 1243
\]

So, in the end, we confirm that:
\[
956 + 287 = 1243
\]

And this also illustrates why carrying is necessary when sums exceed 10 in any column. For example, when adding \(6 + 7\), we get \(13\), so we write down the \(3\) in the ones place and carry over the \(1\) to the tens place.