Subtraction

Subtracting Two-Digit Numbers

Example: 75 – 48

1. Write the numbers in columns: Align the digits by place value (tens under tens, ones under ones).

                      75
                   – 48
                    ——–

2. Subtract the ones place:
– If the digit on top is smaller than the digit below, you need to borrow from the tens place.
– Here, 5 (ones) is smaller than 8, so borrow 1 from the tens place, turning 7 into 6.
– The 5 becomes 15.
– Now subtract: 15 – 8 = 7.

3. Subtract the tens place:
– Subtract the tens digits: 6 – 4 = 2.

The result is 27.

                       75
                   –  48
                     ——–
                       27

Subtracting Three-Digit Numbers

Example: 452 – 279

1. Write the numbers in columns:

                 452
              – 279
                ——–

2. Subtract the ones place:
– 2 (ones) is smaller than 9, so borrow 1 from the tens place.
– The 5 turns into 4, and the 2 becomes 12.
– Now subtract: 12 – 9 = 3.

3. Subtract the tens place:
– 4 (tens) is smaller than 7, so borrow 1 from the hundreds place.
– The 4 becomes 14 (after borrowing), and the 4 in the hundreds place becomes 3.
– Now subtract: 14 – 7 = 7.

4. Subtract the hundreds place:
– Subtract the hundreds digits: 3 – 2 = 1.

The result is 173.

                           452
                        – 279
                         ———
                           173

Subtracting Four-Digit Numbers

Example: 7326 – 4897

1. Write the numbers in columns:

                  7326
               – 4897
               ————–

2. Subtract the ones place:
– 6 (ones) is smaller than 7, so borrow 1 from the tens place.
– The 2 turns into 1, and the 6 becomes 16.
– Now subtract: 16 – 7 = 9.

3. Subtract the tens place:
– 1 (tens) is smaller than 9, so borrow 1 from the hundreds place.
– The 3 becomes 2, and the 1 becomes 11.
– Now subtract: 11 – 9 = 2.

4. Subtract the hundreds place:
– 2 (hundreds) is smaller than 8, so borrow 1 from the thousands place.
– The 7 becomes 6, and the 2 becomes 12.
– Now subtract: 12 – 8 = 4.

5. Subtract the thousands place:
– Subtract the thousands digits: 6 – 4 = 2.

The result is 2429.

                   7326
                – 4897
                 ———–
                   2429  

Subtracting 4-digit number with and without borrowing

 Subtracting 4-Digit Numbers Without Borrowing

When subtracting without borrowing, each digit in the top number is greater than or equal to the corresponding digit in the bottom number.

Example: 7534 – 2412

1. Write the numbers in columns:

                       7534
                   – 2412
                     ——–

2. Subtract the ones place:
– Subtract 4 (ones) from 2 (ones): 4 – 2 = 2.

3. Subtract the tens place:
– Subtract 3 (tens) from 1 (tens): 3 – 1 = 2.

4. Subtract the hundreds place:
– Subtract 5 (hundreds) from 4 (hundreds): 5 – 4 = 1.

5. Subtract the thousands place:
– Subtract 7 (thousands) from 2 (thousands): 7 – 2 = 5.

The result is 5122.

                              7534
                           – 2412
                          ———–
                            5122

 Subtracting 4-Digit Numbers With Borrowing

When subtracting with borrowing, you need to borrow from the next higher place value if the top digit is smaller than the bottom digit.

Example: 7326 – 4897

1. Write the numbers in columns:

                     7326
                   – 4897
                    ———-

2. Subtract the ones place:
– The digit in the ones place of the top number (6) is smaller than the digit in the bottom number (7).
– Borrow 1 from the tens place (2 becomes 1), and add 10 to the ones place (6 becomes 16).
– Now subtract: 16 – 7 = 9.

3. Subtract the tens place:
– The digit in the tens place of the top number (1) is smaller than the digit in the bottom number (9).
– Borrow 1 from the hundreds place (3 becomes 2), and add 10 to the tens place (1 becomes 11).
– Now subtract: 11 – 9 = 2.

4. Subtract the hundreds place:
– The digit in the hundreds place of the top number (2) is smaller than the digit in the bottom number (8).
– Borrow 1 from the thousands place (7 becomes 6), and add 10 to the hundreds place (2 becomes 12).
– Now subtract: 12 – 8 = 4.

5. Subtract the thousands place:
– Subtract the remaining thousands: 6 – 4 = 2.

The result is 2429.

                  7326
                – 4897
               ————–
                  2429

 

 Summary:
– Without borrowing: Subtract each digit directly since the top number’s digits are larger than or equal to the bottom number’s digits.
– With borrowing: When the digit in the top number is smaller than the bottom number’s digit, borrow from the next left column, adjust the values, then subtract.–

Subtraction facts

When subtracting numbers up to 10,000, students deal with four-digit numbers. The basic process is the same as with smaller numbers, but it’s essential to pay attention to borrowing (regrouping) and lining up digits correctly.

Key Concepts

1. Place Value:
– Numbers up to 10,000 have digits in the ones, tens, hundreds, and thousands places.
– For example, in the number 8,356:
– 8 is in the thousands place.
– 3 is in the hundreds place.
– 5 is in the tens place.
– 6 is in the ones place.

2. Subtraction Without Borrowing:
– Subtract each digit starting from the right (ones) and moving left (tens, hundreds, thousands).
– Example: 7,542 – 3,321

– Ones: 2 – 1 = 1
– Tens: 4 – 2 = 2
– Hundreds: 5 – 3 = 2
– Thousands: 7 – 3 = 4
– Result: 4,221

3. Subtraction With Borrowing:
– When a digit in the top number is smaller than the digit below it, you need to borrow from the next higher place value.
– Example: 6,503 – 2,678
– Ones: 3 is smaller than 8, so borrow 1 from the tens place (0 becomes 9), making 3 into 13. Now subtract: 13 – 8 = 5.
– Tens: 9 is smaller than 7, so borrow 1 from the hundreds place (5 becomes 4), making 9 into 19. Now subtract: 19 – 7 = 2.
– Hundreds: 4 is smaller than 6, so borrow 1 from the thousands place (6 becomes 5), making 4 into 14. Now subtract: 14 – 6 = 8.
– Thousands: 5 – 2 = 3.
– Result: 3,825

4. Subtraction Across Zeros:
– Special attention is needed when subtracting from numbers that include zeros.
– Example: 8,004 – 2,987
– Ones: 4 is smaller than 7, so borrow 1 from the tens place. Since the tens place is 0, borrow from the hundreds place, turning 0 into 9 and making the 4 into 14. Now subtract: 14 – 7 = 7.
– Tens: Now you have 9 – 8 = 1.
– Hundreds: After borrowing, 0 became 9, so subtract: 9 – 9 = 0.
– Thousands: 8 – 2 = 6.
– Result: 6,017

Word problem

Here are some subtraction word problems involving 4-digit numbers:


1. Problem: A school library had 3,452 books. After a book donation drive, 1,687 books were given away. How many books are left in the library?
Solution: 3,452 – 1,687 = 1,765 
Answer: 1,765 books are left in the library.

2. Problem: A concert sold 6,120 tickets. On the day of the event, 2,583 people couldn’t attend and returned their tickets. How many tickets are still valid?
Solution: 6,120 – 2,583 = 3,537 
Answer: 3,537 tickets are still valid.

3. Problem: A store had 8,294 items in stock. After a big sale, 3,406 items were sold. How many items are left in stock?
Solution: 8,294 – 3,406 = 4,888 
Answer: 4,888 items are left in stock.

4. Problem: A town consumed 5,820 gallons of water in one day. The next day, the consumption was reduced by 2,497 gallons. How much water was consumed the next day?
-Solution: 5,820 – 2,497 = 3,323 
Answer: 3,323 gallons of water were consumed the next day.

 

 

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