Math worksheet for estimating sums by rounding numbers.

Problem Explanation:

The task involves estimating sums by rounding numbers to their greatest place value and then to the nearest ten and nearest hundred. Let's solve each part step by step.

---

Part 1: Estimate Sums (Round each addend to its greatest place value)

#### Question 9: \( 35 + 42 \)
- Step 1: Identify the greatest place value for each number.
- For 35, the greatest place value is the tens place (30).
- For 42, the greatest place value is the tens place (40).
- Step 2: Round each number to its greatest place value.
- \( 35 \approx 40 \)
- \( 42 \approx 40 \)
- Step 3: Add the rounded numbers.
- \( 40 + 40 = 80 \)

Answer: \( 40 + 40 = 80 \)

#### Question 10: \( 455 + 229 \)
- Step 1: Identify the greatest place value for each number.
- For 455, the greatest place value is the hundreds place (400).
- For 229, the greatest place value is the hundreds place (200).
- Step 2: Round each number to its greatest place value.
- \( 455 \approx 500 \)
- \( 229 \approx 200 \)
- Step 3: Add the rounded numbers.
- \( 500 + 200 = 700 \)

Answer: \( 500 + 200 = 700 \)

#### Question 11: \( 272 + 593 \)
- Step 1: Identify the greatest place value for each number.
- For 272, the greatest place value is the hundreds place (200).
- For 593, the greatest place value is the hundreds place (600).
- Step 2: Round each number to its greatest place value.
- \( 272 \approx 300 \)
- \( 593 \approx 600 \)
- Step 3: Add the rounded numbers.
- \( 300 + 600 = 900 \)

Answer: \( 300 + 600 = 900 \)

#### Question 12: \( 15 + 39 \)
- Step 1: Identify the greatest place value for each number.
- For 15, the greatest place value is the tens place (10).
- For 39, the greatest place value is the tens place (40).
- Step 2: Round each number to its greatest place value.
- \( 15 \approx 20 \)
- \( 39 \approx 40 \)
- Step 3: Add the rounded numbers.
- \( 20 + 40 = 60 \)

Answer: \( 20 + 40 = 60 \)

#### Question 13: \( 216 + 536 \)
- Step 1: Identify the greatest place value for each number.
- For 216, the greatest place value is the hundreds place (200).
- For 536, the greatest place value is the hundreds place (500).
- Step 2: Round each number to its greatest place value.
- \( 216 \approx 200 \)
- \( 536 \approx 500 \)
- Step 3: Add the rounded numbers.
- \( 200 + 500 = 700 \)

Answer: \( 200 + 500 = 700 \)

#### Question 14: \( 44 + 29 \)
- Step 1: Identify the greatest place value for each number.
- For 44, the greatest place value is the tens place (40).
- For 29, the greatest place value is the tens place (30).
- Step 2: Round each number to its greatest place value.
- \( 44 \approx 40 \)
- \( 29 \approx 30 \)
- Step 3: Add the rounded numbers.
- \( 40 + 30 = 70 \)

Answer: \( 40 + 30 = 70 \)

---

Part 2: Estimate Sums (Round each addend to the nearest ten and nearest hundred)

#### Question 15: \( 133 + 560 \)
- Step 1: Round each number to the nearest ten.
- \( 133 \approx 130 \)
- \( 560 \approx 560 \)
- Step 2: Round each number to the nearest hundred.
- \( 133 \approx 100 \)
- \( 560 \approx 600 \)

Answers:
- Nearest Ten: \( 130 + 560 \)
- Nearest Hundred: \( 100 + 600 \)

#### Question 16: \( 119 + 239 \)
- Step 1: Round each number to the nearest ten.
- \( 119 \approx 120 \)
- \( 239 \approx 240 \)
- Step 2: Round each number to the nearest hundred.
- \( 119 \approx 100 \)
- \( 239 \approx 200 \)

Answers:
- Nearest Ten: \( 120 + 240 \)
- Nearest Hundred: \( 100 + 200 \)

#### Question 17: \( 89 + 71 \)
- Step 1: Round each number to the nearest ten.
- \( 89 \approx 90 \)
- \( 71 \approx 70 \)
- Step 2: Round each number to the nearest hundred.
- \( 89 \approx 100 \)
- \( 71 \approx 100 \)

Answers:
- Nearest Ten: \( 90 + 70 \)
- Nearest Hundred: \( 100 + 100 \)

---

Final Answers:

#### Part 1:
1. \( 40 + 40 = 80 \)
2. \( 500 + 200 = 700 \)
3. \( 300 + 600 = 900 \)
4. \( 20 + 40 = 60 \)
5. \( 200 + 500 = 700 \)
6. \( 40 + 30 = 70 \)

#### Part 2:
1. \( 130 + 560 \) (Nearest Ten), \( 100 + 600 \) (Nearest Hundred)
2. \( 120 + 240 \) (Nearest Ten), \( 100 + 200 \) (Nearest Hundred)
3. \( 90 + 70 \) (Nearest Ten), \( 100 + 100 \) (Nearest Hundred)

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Part 1:} \\
1. 40 + 40 = 80 \\
2. 500 + 200 = 700 \\
3. 300 + 600 = 900 \\
4. 20 + 40 = 60 \\
5. 200 + 500 = 700 \\
6. 40 + 30 = 70 \\
\\
\text{Part 2:} \\
15. \text{Nearest Ten: } 130 + 560, \text{Nearest Hundred: } 100 + 600 \\
16. \text{Nearest Ten: } 120 + 240, \text{Nearest Hundred: } 100 + 200 \\
17. \text{Nearest Ten: } 90 + 70, \text{Nearest Hundred: } 100 + 100 \\
\end{array}
}
\]