3rd Grade Math Worksheet featuring five practice problems for elementary students.

Let's solve each problem step by step:

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Problem 1: Which sign belongs in the blank?

Question:
21 + 15 ___ 18 + (20 - 5)

#### Step-by-Step Solution:
1. Simplify both sides of the expression.
- Left side: \( 21 + 15 = 36 \)
- Right side: \( 18 + (20 - 5) \)
- First, simplify inside the parentheses: \( 20 - 5 = 15 \)
- Then, add: \( 18 + 15 = 33 \)

2. Compare the results:
- Left side: \( 36 \)
- Right side: \( 33 \)

3. Determine the relationship:
- Since \( 36 > 33 \), the correct sign is \( > \).

#### Final Answer:
\[ \boxed{>} \]

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Problem 2: Solve for \( x \).

Question:
\( x - 6 = 10 \)

#### Step-by-Step Solution:
1. Isolate \( x \) by adding 6 to both sides of the equation:
\[
x - 6 + 6 = 10 + 6
\]
\[
x = 16
\]

#### Final Answer:
\[ \boxed{16} \]

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Problem 3: What is 269 rounded to the nearest hundred?

Question:
Round 269 to the nearest hundred.

#### Step-by-Step Solution:
1. Identify the digit in the hundreds place:
- In 269, the digit in the hundreds place is 2.
2. Look at the digit in the tens place to decide whether to round up or down:
- The digit in the tens place is 6.
- Since 6 is greater than or equal to 5, we round up the hundreds digit by 1.
3. Replace all digits to the right of the hundreds place with zeros:
- Rounding 269 up gives 300.

#### Final Answer:
\[ \boxed{300} \]

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Problem 4: Which sign gives in the blank?

Question:
460 ÷ 4 ___ 114

#### Step-by-Step Solution:
1. Simplify the left side of the expression:
- Perform the division: \( 460 \div 4 = 115 \)

2. Compare the results:
- Left side: \( 115 \)
- Right side: \( 114 \)

3. Determine the relationship:
- Since \( 115 > 114 \), the correct sign is \( > \).

#### Final Answer:
\[ \boxed{>} \]

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Problem 5: The sum of two numbers is 55. Their difference is 25. What are the two numbers?

Question:
The sum of two numbers is 55. Their difference is 25. Find the two numbers.

#### Step-by-Step Solution:
1. Let the two numbers be \( x \) and \( y \), where \( x > y \).
2. Set up the system of equations based on the given information:
\[
x + y = 55 \quad \text{(Equation 1)}
\]
\[
x - y = 25 \quad \text{(Equation 2)}
\]

3. Add Equation 1 and Equation 2 to eliminate \( y \):
\[
(x + y) + (x - y) = 55 + 25
\]
\[
2x = 80
\]
\[
x = 40
\]

4. Substitute \( x = 40 \) back into Equation 1 to solve for \( y \):
\[
40 + y = 55
\]
\[
y = 55 - 40
\]
\[
y = 15
\]

5. Verify the solution:
- Sum: \( 40 + 15 = 55 \) (correct)
- Difference: \( 40 - 15 = 25 \) (correct)

#### Final Answer:
\[ \boxed{40 \text{ and } 15} \]

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Final Answers:

1. \( \boxed{>} \)
2. \( \boxed{16} \)
3. \( \boxed{300} \)
4. \( \boxed{>} \)
5. \( \boxed{40 \text{ and } 15} \)