Correct vs. incorrect way to add decimals: align decimal points, not digits.

Let’s solve the problem step by step.

We are adding two decimal numbers:
12.5 + 6.23

Step 1: Line up the decimal points

This is the correct way to add decimals — just like lining up place values (ones, tenths, hundredths).

Write them like this:

```
12.50 ← we can add a zero to make it easier (12.5 = 12.50)
+ 6.23
--------
```

Now line up the columns:

- Hundredths: 0 + 3 = 3
- Tenths: 5 + 2 = 7
- Ones: 2 + 6 = 8
- Tens: 1 + 0 = 1

So we get: 18.73

✔ That matches the left side of the image — which is marked correct.

---

What went wrong on the right?

They lined up from the right-hand side without caring about the decimal point:

```
12.5
+ 6.23
------
72.28 ← This is WRONG
```

How did they get that? Probably added as if all digits were aligned to the right:

Imagine writing:

```
125
+ 623
------
748 → but then somehow got 72.28? Maybe misaligned even more.
```

Actually, looking at their answer “72.28”, it seems they might have done:

- Added 5 + 3 = 8 (hundredths?)
- Then 2 + 2 = 4? But wrote 2? Doesn’t make sense.
Wait — maybe they treated it like:

```
12.5
+6.23
-----
```

And added:

- 5 + 3 = 8 → last digit
- 2 + 2 = 4 → but they wrote 2? Hmm.
Actually, let’s reverse-engineer their mistake.

If you ignore decimal points and just stack right-aligned:

```
12.5
+ 6.23
-------
```

If you pretend both are whole numbers and align right:

→ 125 + 623 = 748 → but they got 72.28? Not matching.

Alternatively, maybe they did:

Add 12.5 + 6.23 by doing:

- 12 + 6 = 18 → but they wrote 72? No.

Wait — look at their result: 72.28

That looks like they added:

- 12 + 6 = 18 → no
Maybe they swapped digits?

Another possibility: They added vertically without aligning decimals:

Like:

```
1 2 . 5
+ 6 . 2 3
-------------
```

But if they mistakenly put the 6 under the 2 (tens place), and 2 under the 5 (tenths), etc., they could get:

Tens column: 1 + nothing = 1? But they have 7 in tens place.

Actually, here’s what likely happened:

They wrote:

```
12.5
+ 6.23
------
```

Then added:

Start from right:

- 5 (tenths) + 3 (hundredths) → mismatched places → maybe they thought 5 is hundredths? So 5 + 3 = 8 → write 8
- Then 2 (ones) + 2 (tenths) → 2 + 2 = 4? But they wrote 2? Confusing.

Actually, looking again — their incorrect sum is 72.28

Let me try to see how someone gets 72.28 from 12.5 + 6.23.

What if they did:

12.5
+6.23
= ?

If they added 12 + 6 = 18 → not 72.

Wait — what if they multiplied? 12.5 × 6.23 ≈ 77.8 — not 72.28.

Alternatively, maybe they reversed the numbers?

6.23 + 12.5 — same thing.

Perhaps they did:

Added 12.5 + 6.23 as:

First, 12 + 6 = 18
Then .5 + .23 = .73
Total 18.73 — correct.

But in the wrong method, they may have done:

Aligned like this:

```
12.5
+ 6.23
------
```

And added:

Column by column from right, ignoring decimal:

Rightmost: 5 + 3 = 8 → write 8
Next: 2 + 2 = 4 → but they wrote 2? No.

Wait — look at their answer: 72.28

Digits: 7, 2, ., 2, 8

Compare to inputs: 1,2,.5 and 6,.2,3

Maybe they did:

- Took 1 (from 12.5) and 6 (from 6.23) → 1+6=7 → first digit
- Then 2 (from 12.5) and 2 (from 6.23) → 2+2=4? But they have 2? Not matching.

Actually, I think there's a typo or misrepresentation in the image’s wrong example. Because mathematically, if you truly line up from the right without regard to decimal, you’d get something else.

But regardless — the key teaching point is:

> When adding decimals, ALWAYS line up the decimal points. That ensures you’re adding tenths to tenths, hundredths to hundredths, ones to ones, etc.

In the correct version:

```
12.50
+ 6.23
-------
18.73
```

In the incorrect version shown, they probably misaligned so that:

The 6 was placed under the 2 (so 2+6=8 in ones place? But they have 2 in tens?).

Actually, looking closely at the image’s wrong calculation:

It shows:

```
1 2 . 5
+ 6 . 2 3
-----------
7 2 . 2 8
```

Ah! Now I see — they aligned the *last digits* together, meaning:

They put the 3 (of 6.23) under the 5 (of 12.5), so:

Positions become:

Thousands | Hundreds | Tens | Ones | . | Tenths | Hundredths
----------|----------|------|------|---|--------|-----------
| | 1 | 2 | . | 5 | 0 (assuming 12.50)
| | | 6 | . | 2 | 3 ← but wait, if aligned right, 6 would be under 2? Let's map:

If we force right-alignment:

Write 12.5 as _ _ 1 2 . 5
Write 6.23 as _ _ _ 6 . 2 3 → too many digits.

Better to pad with zeros:

12.50 → positions: tens=1, ones=2, tenths=5, hundredths=0
6.23 → tens=0, ones=6, tenths=2, hundredths=3

Correct alignment:

```
Tens Ones . Tenths Hundredths
1 2 . 5 0
+ 0 6 . 2 3
-----------------------------
1 8 . 7 3 → 18.73
```

Incorrect alignment (right-aligned):

So they might have written:

```
1 2 . 5
+ 6 . 2 3
---------------
```

And assumed the rightmost digits align:

So:

Hundredths: 5 (but 5 is tenths!) + 3 = 8 → write 8
Tenths: 2 (ones!) + 2 = 4? But they have 2? Not matching.

Wait — in their wrong answer, it's 72.28

Let me calculate what operation gives 72.28 from 12.5 and 6.23.

12.5 * 5.7824 = 72.28? Not helpful.

Perhaps they did:

12.5 + 6.23 = ?

But added 12 + 6 = 18, then .5 + .23 = .73, total 18.73 — correct.

I think the image’s "wrong" example has a calculation error in itself, but the point is clear: don't align from the right; align decimal points.

For educational purposes, we’ll stick to the correct method.

Final Answer:
18.73