Subtraction Within 1000

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Answer Key & Explanations

Subtraction Within 1000 · Grade 3 · Worksheet 1

1. The school library had 823 books on the shelves. During inventory, they discovered that 456 books were checked out by students. How many books were still on the library shelves? Answer: 367 Solution: Start with the total number of books: 823 Subtract the books that were checked out: 456 Set up the subtraction problem: 823 - 456 Subtract the ones place: 3 - 6 (we need to regroup) Regroup from the tens place: 823 becomes 8 hundreds, 1 ten, and 13 ones Now subtract ones: 13 - 6 = 7 Subtract…
   Full step-by-step solution

   Step 1: Start with the total number of books: 823 Step 2: Subtract the books that were checked out: 456 Step 3: Set up the subtraction problem: 823 - 456 Step 4: Subtract the ones place: 3 - 6 (we need to regroup) Step 5: Regroup from the tens place: 823 becomes 8 hundreds, 1 ten, and 13 ones Step 6: Now subtract ones: 13 - 6 = 7 Step 7: Subtract tens: 1 - 5 (we need to regroup again) Step 8: Regroup from the hundreds place: 8 hundreds becomes 7 hundreds and 10 tens, plus the 1 ten we had = 11 tens Step 9: Now subtract tens: 11 - 5 = 6 Step 10: Subtract hundreds: 7 - 4 = 3 Step 11: Combine the results: 300 + 60 + 7 = 367 The answer is 367.

2. The school library had 823 books on the shelves. During a reading event, students checked out 467 books to read at home. How many books are left in the library? Answer: 356 Solution: Start with the total number of books: 823 Subtract the books that were checked out: 467 Set up the subtraction problem: 823 - 467 Subtract the ones place: 3 - 7 (can't do, so regroup) Regroup from tens place: 2 tens becomes 1 ten, and 13 ones Now subtract ones: 13 - 7 = 6 Subtract tens place: 1…
   Full step-by-step solution

   Step 1: Start with the total number of books: 823 Step 2: Subtract the books that were checked out: 467 Step 3: Set up the subtraction problem: 823 - 467 Step 4: Subtract the ones place: 3 - 7 (can't do, so regroup) Step 5: Regroup from tens place: 2 tens becomes 1 ten, and 13 ones Step 6: Now subtract ones: 13 - 7 = 6 Step 7: Subtract tens place: 1 - 6 (can't do, so regroup) Step 8: Regroup from hundreds place: 8 hundreds becomes 7 hundreds, and 11 tens Step 9: Now subtract tens: 11 - 6 = 5 Step 10: Subtract hundreds: 7 - 4 = 3 Step 11: Combine the results: 300 + 50 + 6 = 356 The answer is 356.

3. Liam has 750 marbles in his collection. He gives 285 marbles to his friend Noah for a school project. How many marbles does Liam have left? Answer: 465 Solution: Liam starts with 750 marbles. He gives away 285 marbles, so we subtract: 750 - 285. Subtract the ones place: 0 - 5, we need to borrow from the tens place.
   Full step-by-step solution

   Step 1: Liam starts with 750 marbles. Step 2: He gives away 285 marbles, so we subtract: 750 - 285. Step 3: Subtract the ones place: 0 - 5, we need to borrow from the tens place. The tens place is 5, so we borrow 1, making it 4 tens, and the ones become 10. 10 - 5 = 5. Step 4: Subtract the tens place: 4 - 8, we need to borrow from the hundreds place. The hundreds place is 7, so we borrow 1, making it 6 hundreds, and the tens become 14. 14 - 8 = 6. Step 5: Subtract the hundreds place: 6 - 2 = 4. Step 6: Combine the results: 465. The answer is 465.

4. Noah collected 528 trading cards. He decided to give 349 of his cards to his friend Liam. How many trading cards does Noah have left? Answer: 179 Solution: Start with the total number of cards: 528 Subtract the cards given away: 528 - 349 Subtract the ones place: 8 - 9 (can't do, so regroup) Regroup from tens place: 2 tens becomes 1 ten, and 8 ones becomes 18 ones Now subtract ones: 18 - 9 = 9 Subtract tens place: 1 - 4 (can't do, so regroup)…
   Full step-by-step solution

   Step 1: Start with the total number of cards: 528 Step 2: Subtract the cards given away: 528 - 349 Step 3: Subtract the ones place: 8 - 9 (can't do, so regroup) Step 4: Regroup from tens place: 2 tens becomes 1 ten, and 8 ones becomes 18 ones Step 5: Now subtract ones: 18 - 9 = 9 Step 6: Subtract tens place: 1 - 4 (can't do, so regroup) Step 7: Regroup from hundreds place: 5 hundreds becomes 4 hundreds, and 1 ten becomes 11 tens Step 8: Now subtract tens: 11 - 4 = 7 Step 9: Subtract hundreds: 4 - 3 = 1 Step 10: Combine the results: 1 hundred, 7 tens, and 9 ones = 179 The answer is 179.

5. A farmer plants corn in a rectangular field that measures 85 meters long and 42 meters wide. If the farmer builds a fence around the entire field, what is the total length of the fence in meters? Answer: 254 Solution: The problem asks for the length of fence around a rectangular field, which means we need to find the perimeter. The formula for perimeter of a rectangle is: Perimeter = 2 × (length + width) The field is 85 meters long and 42 meters wide, so: Perimeter = 2 × (85 + 42) First, add the length and…
   Full step-by-step solution

   Step 1: The problem asks for the length of fence around a rectangular field, which means we need to find the perimeter. Step 2: The formula for perimeter of a rectangle is: Perimeter = 2 × (length + width) Step 3: The field is 85 meters long and 42 meters wide, so: Perimeter = 2 × (85 + 42) Step 4: First, add the length and width: 85 + 42 = 127 Step 5: Then multiply by 2: 2 × 127 = 254 Step 6: The total length of fence needed is 254 meters.

6. Liam's school is collecting cans for a food drive. On Monday, they collected 324 cans. On Tuesday, they collected 187 cans. How many more cans did they collect on Monday than on Tuesday? Answer: 137 Solution: Write the subtraction problem: 324 - 187 Start with the ones place: 4 - 7 (we can't do this, so we need to regroup) Regroup from the tens place: Take 1 ten from the 2 tens, leaving 1 ten, and add 10 ones to the 4 ones, making 14 ones Now subtract ones: 14 - 7 = 7 Move to the tens place: We have…
   Full step-by-step solution

   Step 1: Write the subtraction problem: 324 - 187 Step 2: Start with the ones place: 4 - 7 (we can't do this, so we need to regroup) Step 3: Regroup from the tens place: Take 1 ten from the 2 tens, leaving 1 ten, and add 10 ones to the 4 ones, making 14 ones Step 4: Now subtract ones: 14 - 7 = 7 Step 5: Move to the tens place: We have 1 ten (after regrouping) - 8 tens (we can't do this, so we need to regroup again) Step 6: Regroup from the hundreds place: Take 1 hundred from the 3 hundreds, leaving 2 hundreds, and add 10 tens to the 1 ten, making 11 tens Step 7: Now subtract tens: 11 - 8 = 3 Step 8: Move to the hundreds place: We have 2 hundreds - 1 hundred = 1 hundred Step 9: Combine the results: 1 hundred + 3 tens + 7 ones = 137 The answer is 137.

7. Liam collected 528 trading cards. He decided to give 349 of his cards to his younger brother Noah. How many trading cards does Liam have left? Answer: 179 Solution: Start with the total number of cards: 528 Subtract the cards given away: 528 - 349 Subtract the ones place: 8 - 9 (can't do, so regroup) Regroup from tens place: 2 tens becomes 1 ten, and 8 ones becomes 18 ones Now subtract ones: 18 - 9 = 9 Subtract tens place: 1 - 4 (can't do, so regroup)…
   Full step-by-step solution

   Step 1: Start with the total number of cards: 528 Step 2: Subtract the cards given away: 528 - 349 Step 3: Subtract the ones place: 8 - 9 (can't do, so regroup) Step 4: Regroup from tens place: 2 tens becomes 1 ten, and 8 ones becomes 18 ones Step 5: Now subtract ones: 18 - 9 = 9 Step 6: Subtract tens place: 1 - 4 (can't do, so regroup) Step 7: Regroup from hundreds place: 5 hundreds becomes 4 hundreds, and 1 ten becomes 11 tens Step 8: Now subtract tens: 11 - 4 = 7 Step 9: Subtract hundreds: 4 - 3 = 1 Step 10: Combine the results: 100 + 70 + 9 = 179 The answer is 179.

8. 725 - 489 = ? Answer: 236 Solution: Write the numbers vertically, aligning digits by place value. 725 - 489 Subtract the ones column (5 - 9). Since 5 is smaller than 9, we cannot subtract directly.
   Full step-by-step solution

   Let's subtract 489 from 725 step-by-step. **Step 1: Write the numbers vertically, aligning digits by place value.** ``` 725 - 489 ----- ``` **Step 2: Subtract the ones column (5 - 9).** Since 5 is smaller than 9, we cannot subtract directly. We borrow 1 from the tens column. The 2 in the tens column becomes 1, and the 5 in the ones column becomes 15. Now subtract: 15 - 9 = 6. Write 6 in the ones place of the answer. ``` 7 1(15) - 4 8 9 --------- 6 ``` **Step 3: Subtract the tens column (1 - 8).** Now we have 1 (after borrowing) in the tens column. Since 1 is smaller than 8, we borrow 1 from the hundreds column. The 7 in the hundreds column becomes 6, and the 1 in the tens column becomes 11. Now subtract: 11 - 8 = 3. Write 3 in the tens place of the answer. ``` 6(11)(15) - 4 8 9 ---------- 3 6 ``` **Step 4: Subtract the hundreds column (6 - 4).** We have 6 in the hundreds column (after lending to the tens column). Subtract: 6 - 4 = 2. Write 2 in the hundreds place of the answer. ``` 6(11)(15) - 4 8 9 ---------- 2 3 6 ``` **Step 5: Write the final answer.** The result is 236. **Final check:** 725 - 489 = 236. We can verify: 489 + 236 = 725, which is correct.