Subtraction Within 10000

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Answer Key & Explanations

Subtraction Within 10000 · Grade 4 · Worksheet 2

1. A school library has 8,425 books. If 3,768 books are checked out, how many books remain in the library? Answer: 4657 Solution: Start with the total number of books: 8,425 Subtract the number of books checked out: 3,768 Set up the subtraction problem: 8,425 - 3,768 Subtract the ones place: 5 - 8, need to borrow from tens place After borrowing: 15 - 8 = 7 Subtract the tens place: 1 - 6 (after borrowing), need to borrow…
   Full step-by-step solution

   Step 1: Start with the total number of books: 8,425 Step 2: Subtract the number of books checked out: 3,768 Step 3: Set up the subtraction problem: 8,425 - 3,768 Step 4: Subtract the ones place: 5 - 8, need to borrow from tens place Step 5: After borrowing: 15 - 8 = 7 Step 6: Subtract the tens place: 1 - 6 (after borrowing), need to borrow from hundreds place Step 7: After borrowing: 11 - 6 = 5 Step 8: Subtract the hundreds place: 3 - 7 (after borrowing), need to borrow from thousands place Step 9: After borrowing: 13 - 7 = 6 Step 10: Subtract the thousands place: 7 - 3 = 4 Step 11: The final answer is 4,657 4,657 books remain in the library.

2. Alex is saving money to buy a new bicycle that costs $2805. Alex already has $990. How much more money does Alex need to save to buy the bicycle? Answer: 1815 Solution: Find the total cost of the bicycle: $2805. Find how much Alex already has: $990. Subtract the savings from the total cost: $2805 - $990 = $1815.
   Full step-by-step solution

   Step 1: Find the total cost of the bicycle: $2805. Step 2: Find how much Alex already has: $990. Step 3: Subtract the savings from the total cost: $2805 - $990 = $1815. Alex needs $1815 more to buy the bicycle.

3. Mason's house is 9515 meters from school. Mason has already walked 6034 meters. How many more meters does Mason need to walk to reach school? Answer: 3481 Solution: Find the total distance to school: 9515 meters. Find how far Mason has already walked: 6034 meters. Subtract the distance walked from the total distance: 9515 - 6034 = 3481.
   Full step-by-step solution

   Step 1: Find the total distance to school: 9515 meters. Step 2: Find how far Mason has already walked: 6034 meters. Step 3: Subtract the distance walked from the total distance: 9515 - 6034 = 3481. Mason needs to walk 3481 more meters to reach school.

4. Noah's school collected 8,416 canned goods for a food drive. After distributing some to local families, there were 5,276 canned goods left. How many canned goods were distributed to the families? Answer: 3,140 Solution: Start with the total number of canned goods collected: 8,416. Subtract the number of canned goods left: 5,276. Set up the subtraction: 8,416 - 5,276.
   Full step-by-step solution

   Step 1: Start with the total number of canned goods collected: 8,416. Step 2: Subtract the number of canned goods left: 5,276. Step 3: Set up the subtraction: 8,416 - 5,276. Step 4: Subtract the ones place: 6 - 6 = 0. Step 5: Subtract the tens place: 1 - 7. Since 1 is less than 7, borrow 1 hundred from the hundreds place. The hundreds place becomes 3 (since 4 - 1 = 3), and the tens place becomes 11. Then, 11 - 7 = 4. Step 6: Subtract the hundreds place: 3 - 2 = 1. Step 7: Subtract the thousands place: 8 - 5 = 3. Step 8: The result is 3,140. Step 9: Check: 3,140 + 5,276 = 8,416. The answer is 3,140 canned goods.

5. 9,305 - 4,728 = ? Answer: 4577 Solution: Start with the ones place: 5 - 8. Since 5 is smaller than 8, we need to regroup from the tens place. The tens place is 0, so we cannot regroup from there.
   Full step-by-step solution

   Step 1: Start with the ones place: 5 - 8. Since 5 is smaller than 8, we need to regroup from the tens place. Step 2: The tens place is 0, so we cannot regroup from there. We need to regroup from the hundreds place. Step 3: Regroup from the hundreds place: 3 hundreds becomes 2 hundreds, and 10 tens are added to the tens place (0 tens becomes 10 tens). Step 4: Now regroup from the tens place: Take 1 ten from the 10 tens, leaving 9 tens. Add 10 ones to the ones place (5 ones becomes 15 ones). Step 5: Subtract ones: 15 - 8 = 7 Step 6: Subtract tens: 9 - 2 = 7 Step 7: Subtract hundreds: 2 - 7. Since 2 is smaller than 7, we need to regroup from the thousands place. Step 8: Regroup from the thousands place: 9 thousands becomes 8 thousands, and 10 hundreds are added to the hundreds place (2 hundreds becomes 12 hundreds). Step 9: Subtract hundreds: 12 - 7 = 5 Step 10: Subtract thousands: 8 - 4 = 4 Step 11: The final answer is 4,577.

6. 9,375 - 4,826 = ? Answer: 4549 Solution: 9,375 - 4,826 Subtract the ones place: 5 - 6 (we need to regroup) Borrow 1 ten from the 7 tens, making it 6 tens, and add 10 to the 5 ones to get 15 ones 15 - 6 = 9 Subtract the tens place: 6 - 2 = 4 Subtract the hundreds place: 3 - 8 (we need to regroup) Borrow 1 thousand from the 9 thousands,…
   Full step-by-step solution

   Step 1: Write the problem vertically: 9,375 - 4,826 Step 2: Subtract the ones place: 5 - 6 (we need to regroup) Borrow 1 ten from the 7 tens, making it 6 tens, and add 10 to the 5 ones to get 15 ones 15 - 6 = 9 Step 3: Subtract the tens place: 6 - 2 = 4 Step 4: Subtract the hundreds place: 3 - 8 (we need to regroup) Borrow 1 thousand from the 9 thousands, making it 8 thousands, and add 10 to the 3 hundreds to get 13 hundreds 13 - 8 = 5 Step 5: Subtract the thousands place: 8 - 4 = 4 Step 6: Combine the results: 4,549 The answer is 4,549.

7. 4235 - 1876 = ? Answer: 2359 Solution: Write the problem vertically: 4235 - 1876 Subtract the ones column: 5 - 6, need to regroup from tens column.
   Full step-by-step solution

   Step 1: Write the problem vertically: 4235 - 1876 Step 2: Subtract the ones column: 5 - 6, need to regroup from tens column. 3 tens becomes 2 tens, 15 ones - 6 ones = 9 ones Step 3: Subtract the tens column: 2 - 7, need to regroup from hundreds column. 2 hundreds becomes 1 hundred, 12 tens - 7 tens = 5 tens Step 4: Subtract the hundreds column: 1 - 8, need to regroup from thousands column. 4 thousands becomes 3 thousands, 11 hundreds - 8 hundreds = 3 hundreds Step 5: Subtract the thousands column: 3 - 1 = 2 thousands Step 6: Combine the results: 2 thousands + 3 hundreds + 5 tens + 9 ones = 2359 The answer is 2359.

8. A factory produced 3,275 toy cars on Monday and 1,948 toy cars on Tuesday. How many more toy cars did the factory produce on Monday than on Tuesday? Answer: C. 1,327 Solution: The factory produced 3,275 toy cars on Monday and 1,948 toy cars on Tuesday.
   Full step-by-step solution

   Step 1: The factory produced 3,275 toy cars on Monday and 1,948 toy cars on Tuesday. Step 2: To find how many more were produced on Monday, subtract Tuesday's production from Monday's production: 3,275 - 1,948 Step 3: Start with the ones place: 5 - 8, we need to borrow from the tens place. The 7 becomes 6, and the 5 becomes 15. 15 - 8 = 7 Step 4: Move to the tens place: 6 - 4 = 2 Step 5: Move to the hundreds place: 2 - 9, we need to borrow from the thousands place. The 3 becomes 2, and the 2 becomes 12. 12 - 9 = 3 Step 6: Move to the thousands place: 2 - 1 = 1 Step 7: The result is 1,327 The correct answer is 1,327.

9. Emma is helping her school organize a book drive. The school's goal was to collect 9,135 books. So far, they have collected 5,789 books. How many more books does the school need to collect to reach its goal? Answer: 3346 Solution: The goal is 9,135 books. They have collected 5,789 books. To find how many more are needed, subtract: 9,135 - 5,789 Start with the ones place: 5 - 9.
   Full step-by-step solution

   Step 1: The goal is 9,135 books. They have collected 5,789 books. Step 2: To find how many more are needed, subtract: 9,135 - 5,789 Step 3: Start with the ones place: 5 - 9. Since 5 is less than 9, we need to borrow from the tens place. Step 4: The tens digit is 3. Borrow 1 ten, making it 2 tens. The ones place becomes 15. Now, 15 - 9 = 6. Step 5: Move to the tens place: 2 - 8. Since 2 is less than 8, we need to borrow from the hundreds place. Step 6: The hundreds digit is 1. Borrow 1 hundred, making it 0 hundreds. The tens place becomes 12. Now, 12 - 8 = 4. Step 7: Move to the hundreds place: 0 - 7. Since 0 is less than 7, we need to borrow from the thousands place. Step 8: The thousands digit is 9. Borrow 1 thousand, making it 8 thousands. The hundreds place becomes 10. Now, 10 - 7 = 3. Step 9: Move to the thousands place: 8 - 5 = 3. Step 10: The result is 3,346. Step 11: Check by adding: 3,346 + 5,789 = 9,135. The answer is 3,346 more books.