Subtraction Within 10000

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Subtraction Within 10000 · Grade 4 · Worksheet 1

1. A rectangular garden is drawn with a length of 125 meters and a width of 80 meters. A triangular flower bed is placed inside the garden, with its base along the entire length of the garden and its height equal to the width of the garden. What is the area of the garden that is NOT covered by the flower bed? Answer: 5000 Solution: Calculate the area of the rectangular garden. Area of rectangle = length × width = 125 × 80 = 10,000 square meters. Calculate the area of the triangular flower bed.
   Full step-by-step solution

   Step 1: Calculate the area of the rectangular garden. Area of rectangle = length × width = 125 × 80 = 10,000 square meters. Step 2: Calculate the area of the triangular flower bed. The triangle has base = 125 meters and height = 80 meters. Area of triangle = (1/2) × base × height = (1/2) × 125 × 80 = (1/2) × 10,000 = 5,000 square meters. Step 3: Subtract the triangle's area from the rectangle's area to find the uncovered area. 10,000 - 5,000 = 5,000 square meters. The answer is 5000.

2. 9,305 - 4,768 = ? Answer: 4537 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 need to regroup from the hundreds place.
   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 need to regroup from the hundreds place. The hundreds place is 3, so we regroup 1 hundred as 10 tens, making the hundreds place 2 and the tens place 10. Step 3: Now regroup 1 ten from the tens place (which is now 10) to the ones place. The tens place becomes 9 and the ones place becomes 15. Step 4: Subtract ones: 15 - 8 = 7 Step 5: Subtract tens: 9 - 6 = 3 Step 6: Subtract hundreds: 2 - 7. Since 2 is smaller than 7, we need to regroup from the thousands place. Step 7: The thousands place is 9, so we regroup 1 thousand as 10 hundreds, making the thousands place 8 and the hundreds place 12. Step 8: Subtract hundreds: 12 - 7 = 5 Step 9: Subtract thousands: 8 - 4 = 4 Step 10: The final answer is 4,537.

3. Emma's school is collecting cans of food for a community drive. The fourth-grade goal was to collect 9,001 cans. So far, they have collected 3,487 cans. How many more cans does the fourth grade need to collect to reach their goal? Answer: 5,514 Solution: Write the numbers vertically, aligning by place value: 9,001 - 3,487. Start with the ones place: 1 - 7. Since 1 is less than 7, we need to borrow from the tens place.
   Full step-by-step solution

   Step 1: Write the numbers vertically, aligning by place value: 9,001 - 3,487. Step 2: Start with the ones place: 1 - 7. Since 1 is less than 7, we need to borrow from the tens place. Step 3: The tens digit is 0, so we borrow from the hundreds place. The hundreds digit is 0, so we borrow from the thousands place. Step 4: Borrow 1 thousand from the 9 thousands. The thousands place becomes 8, and the hundreds place becomes 10. Step 5: Borrow 1 hundred from the 10 hundreds. The hundreds place becomes 9, and the tens place becomes 10. Step 6: Borrow 1 ten from the 10 tens. The tens place becomes 9, and the ones place becomes 11. Step 7: Subtract the ones: 11 - 7 = 4. Step 8: Subtract the tens: 9 - 8 = 1. Step 9: Subtract the hundreds: 9 - 4 = 5. Step 10: Subtract the thousands: 8 - 3 = 5. Step 11: The result is 5,514. Check: 5,514 + 3,487 = 9,001. The answer is 5,514 cans.

4. A school is collecting books for their library. They received 4,285 books in the first week and 1,739 books in the second week. How many more books did they receive in the first week than in the second week? Answer: 2546 Solution: Identify the numbers: First week = 4,285 books, Second week = 1,739 books Set up the subtraction: 4,285 - 1,739 Subtract the ones place: 5 - 9 (can't do, so borrow from tens) Borrow from tens: 8 becomes 7, ones become 15 Subtract ones: 15 - 9 = 6 Subtract tens: 7 - 3 = 4 Subtract hundreds: 2 - 7…
   Full step-by-step solution

   Step 1: Identify the numbers: First week = 4,285 books, Second week = 1,739 books Step 2: Set up the subtraction: 4,285 - 1,739 Step 3: Subtract the ones place: 5 - 9 (can't do, so borrow from tens) Step 4: Borrow from tens: 8 becomes 7, ones become 15 Step 5: Subtract ones: 15 - 9 = 6 Step 6: Subtract tens: 7 - 3 = 4 Step 7: Subtract hundreds: 2 - 7 (can't do, so borrow from thousands) Step 8: Borrow from thousands: 4 becomes 3, hundreds become 12 Step 9: Subtract hundreds: 12 - 7 = 5 Step 10: Subtract thousands: 3 - 1 = 2 Step 11: Final answer: 2,546 The answer is 2546.

5. A rectangular garden has a length of 125.75 meters and a width of 84.25 meters. If a fence is placed around the entire perimeter of the garden, what is the total length of fencing needed in meters? Answer: 420 Solution: The perimeter of a rectangle is calculated using the formula: Perimeter = 2 × (length + width) Add the length and width: 125.75 + 84.25 = 210 Multiply by 2: 2 × 210 = 420 The total length of fencing needed is 420 meters.
   Full step-by-step solution

   Step 1: The perimeter of a rectangle is calculated using the formula: Perimeter = 2 × (length + width) Step 2: Add the length and width: 125.75 + 84.25 = 210 Step 3: Multiply by 2: 2 × 210 = 420 Step 4: The total length of fencing needed is 420 meters.