Estimating Sums & Differences Worksheets - Free Printable

To solve the problems presented in the image, we need to estimate the results of large numbers by rounding them to the nearest ten thousand. Let's go through each problem step by step.

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Estimating Sums

#### Problem 1:
Numbers:
- $ 273,895 $
- $ 460,987 $

Step 1: Round each number to the nearest ten thousand.
- For $ 273,895 $: The digit in the thousands place is 3, which is less than 5. So, round down to $ 270,000 $.
- For $ 460,987 $: The digit in the thousands place is 0, which is less than 5. So, round down to $ 460,000 $.

Step 2: Add the rounded numbers.
$$
270,000 + 460,000 = 730,000
$$

Answer:
$$
\boxed{730,000}
$$

#### Problem 2:
Numbers:
- $ 734,207 $
- $ 237,107 $

Step 1: Round each number to the nearest ten thousand.
- For $ 734,207 $: The digit in the thousands place is 4, which is less than 5. So, round down to $ 730,000 $.
- For $ 237,107 $: The digit in the thousands place is 7, which is 5 or greater. So, round up to $ 240,000 $.

Step 2: Add the rounded numbers.
$$
730,000 + 240,000 = 970,000
$$

Answer:
$$
\boxed{970,000}
$$

#### Problem 3:
Numbers:
- $ 5,234,789 $
- $ 2,754,368 $

Step 1: Round each number to the nearest ten thousand.
- For $ 5,234,789 $: The digit in the thousands place is 7, which is 5 or greater. So, round up to $ 5,230,000 $.
- For $ 2,754,368 $: The digit in the thousands place is 4, which is less than 5. So, round down to $ 2,750,000 $.

Step 2: Add the rounded numbers.
$$
5,230,000 + 2,750,000 = 7,980,000
$$

Answer:
$$
\boxed{7,980,000}
$$

#### Problem 4:
Numbers:
- $ 6,038,945 $
- $ 5,953,876 $

Step 1: Round each number to the nearest ten thousand.
- For $ 6,038,945 $: The digit in the thousands place is 8, which is 5 or greater. So, round up to $ 6,040,000 $.
- For $ 5,953,876 $: The digit in the thousands place is 3, which is less than 5. So, round down to $ 5,950,000 $.

Step 2: Add the rounded numbers.
$$
6,040,000 + 5,950,000 = 11,990,000
$$

Answer:
$$
\boxed{11,990,000}
$$

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Estimating Differences

#### Problem 1:
Numbers:
- $ 7,234,897 $
- $ 2,456,789 $

Step 1: Round each number to the nearest ten thousand.
- For $ 7,234,897 $: The digit in the thousands place is 4, which is less than 5. So, round down to $ 7,230,000 $.
- For $ 2,456,789 $: The digit in the thousands place is 6, which is 5 or greater. So, round up to $ 2,460,000 $.

Step 2: Subtract the rounded numbers.
$$
7,230,000 - 2,460,000 = 4,770,000
$$

Answer:
$$
\boxed{4,770,000}
$$

#### Problem 2:
Numbers:
- $ 8,456,789 $
- $ 4,234,567 $

Step 1: Round each number to the nearest ten thousand.
- For $ 8,456,789 $: The digit in the thousands place is 6, which is 5 or greater. So, round up to $ 8,460,000 $.
- For $ 4,234,567 $: The digit in the thousands place is 4, which is less than 5. So, round down to $ 4,230,000 $.

Step 2: Subtract the rounded numbers.
$$
8,460,000 - 4,230,000 = 4,230,000
$$

Answer:
$$
\boxed{4,230,000}
$$

#### Problem 3:
Numbers:
- $ 9,876,543 $
- $ 3,456,789 $

Step 1: Round each number to the nearest ten thousand.
- For $ 9,876,543 $: The digit in the thousands place is 6, which is 5 or greater. So, round up to $ 9,880,000 $.
- For $ 3,456,789 $: The digit in the thousands place is 6, which is 5 or greater. So, round up to $ 3,460,000 $.

Step 2: Subtract the rounded numbers.
$$
9,880,000 - 3,460,000 = 6,420,000
$$

Answer:
$$
\boxed{6,420,000}
$$

#### Problem 4:
Numbers:
- $ 6,543,210 $
- $ 2,345,678 $

Step 1: Round each number to the nearest ten thousand.
- For $ 6,543,210 $: The digit in the thousands place is 3, which is less than 5. So, round down to $ 6,540,000 $.
- For $ 2,345,678 $: The digit in the thousands place is 5, which is 5 or greater. So, round up to $ 2,350,000 $.

Step 2: Subtract the rounded numbers.
$$
6,540,000 - 2,350,000 = 4,190,000
$$

Answer:
$$
\boxed{4,190,000}
$$

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Final Answers:

1. $ \boxed{730,000} $
2. $ \boxed{970,000} $
3. $ \boxed{7,980,000} $
4. $ \boxed{11,990,000} $
5. $ \boxed{4,770,000} $
6. $ \boxed{4,230,000} $
7. $ \boxed{6,420,000} $
8. $ \boxed{4,190,000} $

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Thus, the final boxed answers are:
$$
\boxed{730,000, 970,000, 7,980,000, 11,990,000, 4,770,000, 4,230,000, 6,420,000, 4,190,000}
$$