Place Value Patterns

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Answer Key & Explanations

Place Value Patterns · Grade 3 · Worksheet 2

1. 648 ÷ 10 = ? Answer: 64.8 Solution: Write 648 as 648.0 to help see the decimal point. When dividing by 10, each digit moves one place to the right.
   Full step-by-step solution

   Step 1: Write 648 as 648.0 to help see the decimal point. Step 2: When dividing by 10, each digit moves one place to the right. Step 3: The hundreds digit 6 moves to the tens place, the tens digit 4 moves to the ones place, and the ones digit 8 moves to the tenths place. Step 4: So 648 ÷ 10 = 64.8. The answer is 64.8.

2. 624 ÷ 10 = ? Answer: 62.4 Solution: Write 624 as 600 + 20 + 4. Divide each part by 10: 600 ÷ 10 = 60, 20 ÷ 10 = 2, 4 ÷ 10 = 0.4. Add the results: 60 + 2 + 0.4 = 62.4.
   Full step-by-step solution

   Step 1: Write 624 as 600 + 20 + 4. Step 2: Divide each part by 10: 600 ÷ 10 = 60, 20 ÷ 10 = 2, 4 ÷ 10 = 0.4. Step 3: Add the results: 60 + 2 + 0.4 = 62.4. Step 4: Using place value: the 6 moves from the hundreds place to the tens place (60), the 2 moves from the tens place to the ones place (2), and the 4 moves from the ones place to the tenths place (0.4). The answer is 62.4.

3. Liam is collecting trading cards. He has 245 cards in his main collection and his friend gives him 38 more cards. How many trading cards does Liam have in total now? Answer: 283 Solution: Liam starts with 245 trading cards. His friend gives him 38 more cards. This means we need to add 38 to 245.
   Full step-by-step solution

   Let's solve this step-by-step. Step 1: Liam starts with 245 trading cards. Step 2: His friend gives him 38 more cards. This means we need to add 38 to 245. Step 3: Write the addition: 245 + 38 Step 4: Add the ones place first: 5 + 8 = 13 Write down 3 in the ones place, and carry over 1 to the tens place. Step 5: Add the tens place: 4 + 3 = 7, plus the carried 1 makes 8. Write down 8 in the tens place. Step 6: The hundreds place: 2 (no other hundreds to add), so write down 2. Step 7: Combine the digits: Hundreds: 2, Tens: 8, Ones: 3 So the total is 283. Step 8: Check: 245 + 38 = 283. Therefore, Liam now has 283 trading cards in total.

4. Liam is organizing his baseball card collection. He has 8 binders and wants to put the same number of cards in each binder. If he has a total of 456 cards, how many cards should go in each binder? Answer: 57 Solution: We are told that Liam has 456 cards total and 8 binders. He wants to put the same number of cards in each binder. This means we need to divide the total number of cards by the number of binders.
   Full step-by-step solution

   We are told that Liam has 456 cards total and 8 binders. He wants to put the same number of cards in each binder. This means we need to divide the total number of cards by the number of binders. Step 1: Write the division problem 456 ÷ 8 Step 2: Break down the division First, 8 times 5 is 40, but we are dividing into 456. Let's see how many times 8 goes into 45 (the first two digits of 456). 8 × 5 = 40, which is less than 45. 8 × 6 = 48, which is too big. So, 8 goes into 45 five times. Step 3: Multiply and subtract 5 × 8 = 40 45 − 40 = 5 Step 4: Bring down the next digit (6) Now we have 56. Step 5: Divide 56 by 8 8 × 7 = 56 exactly. Step 6: Write the result The quotient is 57. Step 7: Check 57 × 8 = 456, which matches the total number of cards. So, each binder should have 57 cards.

5. A rectangular swimming pool is divided into square tiles on the bottom. There are 25 rows of tiles from the shallow end to the deep end, and 40 columns of tiles across the width. If you visualize this grid pattern of tiles, how many tiles cover the bottom of the pool? Answer: 1000 Solution: The pool bottom has 25 rows of tiles Each row contains 40 tiles To find the total number of tiles, multiply the number of rows by the number of tiles in each row 25 × 40 = 1000 There are 1000 tiles covering the bottom of the pool The answer is 1000
   Full step-by-step solution

   Step 1: The pool bottom has 25 rows of tiles Step 2: Each row contains 40 tiles Step 3: To find the total number of tiles, multiply the number of rows by the number of tiles in each row Step 4: 25 × 40 = 1000 Step 5: There are 1000 tiles covering the bottom of the pool Step 6: The answer is 1000

6. 361 × 10 = ? Answer: 3610 Solution: Write 361 in expanded form: 300 + 60 + 1. Multiply each part by 10: 300 × 10 = 3000, 60 × 10 = 600, 1 × 10 = 10. Add the results: 3000 + 600 + 10 = 3610.
   Full step-by-step solution

   Step 1: Write 361 in expanded form: 300 + 60 + 1. Step 2: Multiply each part by 10: 300 × 10 = 3000, 60 × 10 = 600, 1 × 10 = 10. Step 3: Add the results: 3000 + 600 + 10 = 3610. Step 4: Notice the pattern: the digits 3, 6, 1 all shift one place to the left, and a 0 is added in the ones place. The answer is 3610.

7. A rectangular swimming pool is tiled with square tiles arranged in a grid pattern. There are 32 rows of tiles and 24 columns of tiles. If you visualize this tiled pool floor, how many tiles are there in total? Answer: 768 Solution: The pool has 32 rows of tiles and 24 columns of tiles. To find the total number of tiles, multiply the number of rows by the number of columns. Calculate 32 × 24.
   Full step-by-step solution

   Step 1: The pool has 32 rows of tiles and 24 columns of tiles. Step 2: To find the total number of tiles, multiply the number of rows by the number of columns. Step 3: Calculate 32 × 24. Step 4: First multiply 32 × 20 = 640 Step 5: Then multiply 32 × 4 = 128 Step 6: Add the two results: 640 + 128 = 768 Step 7: There are 768 tiles in total.

8. Noah is organizing his comic book collection. He has 8 boxes and wants to put 45 comic books in each box. How many comic books can Noah store in all his boxes? Answer: 360 Solution: Noah has 8 boxes Each box holds 45 comic books Multiply the number of boxes by the number of comic books per box: 8 × 45 Calculate 8 × 45 = 360 Noah can store 360 comic books in all his boxes.
   Full step-by-step solution

   Step 1: Noah has 8 boxes Step 2: Each box holds 45 comic books Step 3: Multiply the number of boxes by the number of comic books per box: 8 × 45 Step 4: Calculate 8 × 45 = 360 Noah can store 360 comic books in all his boxes.

9. 734 - 100 = ? Answer: 634 Solution: Look at the number 734. It has 7 hundreds, 3 tens, and 4 ones. Subtracting 100 means we take away 1 hundred.
   Full step-by-step solution

   Step 1: Look at the number 734. It has 7 hundreds, 3 tens, and 4 ones. Step 2: Subtracting 100 means we take away 1 hundred. So 7 hundreds become 6 hundreds. Step 3: The tens digit (3) and ones digit (4) do not change. Step 4: The new number is 6 hundreds, 3 tens, and 4 ones, which is 634. Answer: 634