Estimating sums and differences of greater numbers | Math, 3rd ... - Free Printable

Let's analyze the image you've provided. It contains two arithmetic problems: one addition and one subtraction, each with a step-by-step breakdown.

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Problem 1: Addition

$$
\begin{array}{r}
5,835 \\
+ 4,232 \\
\hline
10,067 \\
\end{array}
$$

But in the image, the result shown is 10,000, which is incorrect.

Let’s compute it correctly:

#### Step-by-step:
- Units place: $5 + 2 = 7$
- Tens place: $3 + 3 = 6$
- Hundreds place: $8 + 2 = 10$ → write down 0, carry over 1
- Thousands place: $5 + 4 = 9$, plus carry-over 1 → $10$

So:
$$
5,835 + 4,232 = 10,067
$$

✔ Correct answer: 10,067

But in the image, it shows 10,000, which seems to be an approximation or a mistake.

Also, below this, there’s a red calculation:
$$
6,000 + 4,000 = 10,000
$$
This is rounding the numbers:
- $5,835 \approx 6,000$
- $4,232 \approx 4,000$
- Sum ≈ $10,000$

So this is an estimate, not the exact sum.

---

Problem 2: Subtraction

$$
\begin{array}{r}
9,383 \\
- 3,645 \\
\hline
5,738 \\
\end{array}
$$

But in the image, the result shown is 5,000, again incorrect.

Let’s compute it correctly:

#### Step-by-step:
- Units place: $3 - 5$ → can't do, borrow from tens.
- Tens digit is 8 → becomes 7, units become 13.
- $13 - 5 = 8$
- Tens place: $7 - 4 = 3$
- Hundreds place: $3 - 6$ → can't do, borrow from thousands.
- Thousands digit is 9 → becomes 8, hundreds become 13.
- $13 - 6 = 7$
- Thousands place: $8 - 3 = 5$

So:
$$
9,383 - 3,645 = 5,738
$$

✔ Correct answer: 5,738

Below this, the image shows:
$$
9,000 - 4,000 = 5,000
$$
Which is a rounded estimate:
- $9,383 \approx 9,000$
- $3,645 \approx 4,000$
- Difference ≈ $5,000$

Again, this is not the exact value, but a rough estimate.

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✔ Summary

| Problem | Exact Answer | Estimate (shown) |
|--------|--------------|------------------|
| $5,835 + 4,232$ | 10,067 | 10,000 |
| $9,383 - 3,645$ | 5,738 | 5,000 |

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🔍 Explanation of the Image

The image appears to show:
- Exact calculations (in blue)
- Rounded estimates (in red/purple), used to check reasonableness
- The arrows and circled digits likely highlight rounding steps or key places (e.g., thousands)

For example:
- In addition: rounding 5,835 → 6,000 and 4,232 → 4,000 → sum ≈ 10,000
- In subtraction: rounding 9,383 → 9,000 and 3,645 → 4,000 → difference ≈ 5,000

These estimates help verify that the actual answers are reasonable.

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🟩 Final Answer:

- Correct sum: $5,835 + 4,232 = \boxed{10,067}$
- Correct difference: $9,383 - 3,645 = \boxed{5,738}$

The values shown as 10,000 and 5,000 are estimates, not exact results.