Place Value Patterns

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Place Value Patterns · Grade 3 · Worksheet 1

1. Noah is organizing his comic book collection. He has 4 large boxes, and each box can hold 125 comic books. How many comic books can Noah store in all his boxes? Answer: 500 Solution: Noah has 4 boxes. Each box holds 125 comic books. To find the total number of comic books, multiply the number of boxes by the number of comic books per box: 4 × 125.
   Full step-by-step solution

   Step 1: Noah has 4 boxes. Step 2: Each box holds 125 comic books. Step 3: To find the total number of comic books, multiply the number of boxes by the number of comic books per box: 4 × 125. Step 4: Calculate 4 × 125 = 500. The answer is 500.

2. A factory packages toy cars in boxes. Each box holds 100 cars. If the factory has 2,450 toy cars to package, how many complete boxes can they fill? Answer: 24 Solution: We know each box holds 100 toy cars, and the factory has 2,450 toy cars. We need to find how many complete boxes can be filled. Determine the operation.
   Full step-by-step solution

   Step 1: Understand the problem. We know each box holds 100 toy cars, and the factory has 2,450 toy cars. We need to find how many complete boxes can be filled. Step 2: Determine the operation. To find the number of boxes, we divide the total number of cars by the number of cars per box: 2450 ÷ 100. Step 3: Perform the division. Dividing by 100 is the same as moving the decimal point two places to the left: 2450 ÷ 100 = 24.50. Step 4: Interpret the result. The result 24.50 means we can fill 24 full boxes, and there will be some cars left over (0.50 of a box, which is 50 cars, but not enough for another full box). Step 5: Conclusion. Since the question asks for complete boxes, we take the whole number part: 24. Final answer: 24

3. Noah is organizing his marble collection into boxes. He has 5 boxes and wants to put exactly 125 marbles in each box. How many marbles can Noah arrange in all the boxes? Answer: 625 Solution: Noah has 5 boxes Each box holds 125 marbles To find the total marbles, multiply the number of boxes by the marbles per box 5 × 125 = 625 Noah can arrange 625 marbles in all the boxes.
   Full step-by-step solution

   Step 1: Noah has 5 boxes Step 2: Each box holds 125 marbles Step 3: To find the total marbles, multiply the number of boxes by the marbles per box Step 4: 5 × 125 = 625 Noah can arrange 625 marbles in all the boxes.

4. Noah is building a bookshelf for his classroom. He has 8 shelves and wants to put exactly 45 books on each shelf. How many books can Noah arrange on all the shelves? Answer: 360 Solution: Noah has 8 shelves Each shelf holds 45 books Multiply the number of shelves by the number of books per shelf: 8 × 45 Calculate 8 × 40 = 320 Calculate 8 × 5 = 40 Add the results: 320 + 40 = 360 The answer is 360.
   Full step-by-step solution

   Step 1: Noah has 8 shelves Step 2: Each shelf holds 45 books Step 3: Multiply the number of shelves by the number of books per shelf: 8 × 45 Step 4: Calculate 8 × 40 = 320 Step 5: Calculate 8 × 5 = 40 Step 6: Add the results: 320 + 40 = 360 The answer is 360.

5. 472 + 100 = ? Answer: 572 Solution: Look at the number 472. It has 4 hundreds, 7 tens, and 2 ones. Adding 100 means we add 1 to the hundreds place.
   Full step-by-step solution

   Step 1: Look at the number 472. It has 4 hundreds, 7 tens, and 2 ones. Step 2: Adding 100 means we add 1 to the hundreds place. Step 3: 4 hundreds + 1 hundred = 5 hundreds. Step 4: The tens and ones digits stay the same: 7 tens and 2 ones. Step 5: So the new number is 572. The answer is 572.

6. 753 + 100 = ? Answer: 853 Solution: Write 753 in expanded form: 700 + 50 + 3. Adding 100 means adding 1 to the hundreds place: 700 + 100 = 800. The tens and ones places stay the same: 50 and 3.
   Full step-by-step solution

   Step 1: Write 753 in expanded form: 700 + 50 + 3. Step 2: Adding 100 means adding 1 to the hundreds place: 700 + 100 = 800. Step 3: The tens and ones places stay the same: 50 and 3. Step 4: Combine: 800 + 50 + 3 = 853. The answer is 853.

7. 573 - 100 = ? Answer: 473 Solution: Look at the number 573. It has 5 hundreds, 7 tens, and 3 ones. Subtracting 100 means taking away 1 hundred.
   Full step-by-step solution

   Step 1: Look at the number 573. It has 5 hundreds, 7 tens, and 3 ones. Step 2: Subtracting 100 means taking away 1 hundred. So we subtract 100 from the hundreds place. Step 3: 5 hundreds - 1 hundred = 4 hundreds. Step 4: The tens and ones digits stay the same: 7 tens and 3 ones. Step 5: Combine the new hundreds, tens, and ones: 4 hundreds, 7 tens, 3 ones = 473. The answer is 473.

8. 85 × 10 = ? Answer: 850 Solution: Write 85 as 8 tens and 5 ones. Multiply each part by 10: 8 tens × 10 = 8 hundreds (800), and 5 ones × 10 = 5 tens (50). Add the results: 800 + 50 = 850.
   Full step-by-step solution

   Step 1: Write 85 as 8 tens and 5 ones. Step 2: Multiply each part by 10: 8 tens × 10 = 8 hundreds (800), and 5 ones × 10 = 5 tens (50). Step 3: Add the results: 800 + 50 = 850. Step 4: Notice the pattern: 85 × 10 = 850. The digits 8 and 5 moved one place to the left, and a 0 was added at the end. The answer is 850.

9. Noah is building a bookshelf for his classroom. He needs to cut a board that is 156 centimeters long into 4 equal pieces. How long will each piece be in centimeters? Answer: 39 Solution: Noah has a board that is 156 centimeters long. He needs to cut it into 4 equal pieces.
   Full step-by-step solution

   Step 1: Noah has a board that is 156 centimeters long. Step 2: He needs to cut it into 4 equal pieces. Step 3: To find the length of each piece, divide the total length by the number of pieces: 156 ÷ 4 Step 4: Calculate 156 ÷ 4 = 39 Step 5: Each piece will be 39 centimeters long. The answer is 39.