Examples with solutions for Vertical Subtraction: 4-digits with 2 additional regrouping

Exercise #1

amp;1789amp;amp;  793amp;776amp; \begin{aligned} &1789 \\ -& \\ &~~793 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll carry out vertical subtraction by following these steps:

  • Step 1: Write the minuend and subtrahend vertically aligned, ensuring each digit stands in its respective column.
  • Step 2: Start subtracting from the rightmost column (units) and move leftwards, managing any requisite borrowing.

Let's execute the subtraction:

Step 1: Begin with the units column.

93=6 9 - 3 = 6

Step 2: Move to the tens column.

89 8 - 9

Since 8 is smaller than 9, we need to borrow 1 from the hundreds column, changing 8 to 18:

189=9 18 - 9 = 9

Step 3: Move to the hundreds column. Since we've borrowed 1, adjust accordingly.

67 6 - 7

Here, we again need to borrow from the thousands column making it 16:

167=9 16 - 7 = 9

Step 4: In the thousands column, after borrowing, we have:

10=0 1 - 0 = 0

Thus, compiling the subtractions, we are left with the final solution:

996 996

Therefore, the solution to the subtraction problem 1789793 1789 - 793 is 996 996 , which corresponds to choice 2.

Answer

996

Exercise #2

amp;2382amp;amp;  453amp;776amp; \begin{aligned} &2382 \\ -& \\ &~~453 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

Let's solve the problem using vertical subtraction with regrouping:

1. Start by aligning the numbers vertically by place value:

2382453 \begin{aligned} &2382 \\ - &\,453 \\ \end{aligned}

2. Perform subtraction starting from the units place (rightmost) column:

  • Units: 232 - 3. Since 22 is smaller than 33, we need to borrow from the tens place. Change 88 in the tens place to 77 and add 1010 to 22 to make it 1212. Now, 123=912 - 3 = 9.
  • Tens: Go to the tens column, which is now 757 - 5. Subtraction results in 22, as borrowing was resolved previously.
  • Hundreds: In the hundreds place, 343 - 4 is not possible without borrowing. Borrow from the thousands place: Change 22 to 11 (thousands place) and add 1010 to 33 (hundreds place), making it 1313. Now, 134=913 - 4 = 9.
  • Thousands: The thousands place subtraction is 101 - 0, which simply results in 11.

After completing the subtraction across each column, the final result is:

1929 \begin{aligned} &1929 \\ \end{aligned}

Thus, the solution to the subtraction problem is 19291929.

Answer

1929

Exercise #3

amp;3321amp;amp;  145amp;776amp; \begin{aligned} &3321 \\ -& \\ &~~145 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the problem 33211453321 - 145, we need to conduct vertical subtraction step by step. Let's proceed through each digit from right to left:

  • Units Place:
    Current digits: 1 (from 3321) and 5 (from 145).
    We need to subtract 5 from 1, which requires borrowing as 1 is less than 5.
    1: Borrow from tens place (2 becomes 1), making this 11.
    Now calculate: 115=611 - 5 = 6.
  • Tens Place:
    Current digits: 1 (left after borrowing from 2) and 4 (from 145).
    We need to subtract 4 from 1, which means we borrow as 1 is less than 4.
    21: Borrow from hundreds place (3 becomes 2), making this 11.
    Then calculate: 114=711 - 4 = 7.
  • Hundreds Place:
    Current digits: 2 (after borrowing from 3) and 1 (from 145).
    Now calculate: 21=12 - 1 = 1.
  • Thousands Place:
    Current digits: 3 (minuend) and no digit in subtrahend at this place.
    So, the result is unchanged: 30=33 - 0 = 3.

By following these step-by-step calculations, the result is 3321145=31763321 - 145 = 3176.

Therefore, the final difference is 31763176.

Answer

3176

Exercise #4

amp;4735amp;amp;  816amp;776amp; \begin{aligned} &4735 \\ -& \\ &~~816 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the subtraction problem 47358164735 - 816, we will perform each subtraction step by step:

Let's write the numbers vertically:

4735 0816      \begin{array}{c} 4735 \\ -~\phantom0816~~~~~ \\ \hline \end{array}

Step 1: Start from the rightmost digit (the units place):

  • We need to subtract 6 from 5. Since 5 is smaller than 6, we need to borrow from the tens place.

Step 2: Borrowing from the tens place:

  • The 3 (in the tens place) becomes 2, and the 5 (in the units place) becomes 15.

  • Now, subtract 6 from 15 to get 9 in the units place.

Step 3: Move to the tens place:

  • We now need to subtract 1 from 2 (since we have already borrowed 1 from the tens place).

  • This gives us 1 in the tens place.

Step 4: Move to the hundreds place:

  • Subtract 8 from 7. Since 7 is smaller than 8, we have to borrow from the thousands place.

Step 5: Borrowing from the thousands place:

  • The 4 (in the thousands place) becomes 3, and the 7 (in the hundreds place) becomes 17.

  • Now, subtract 8 from 17 to get 9 in the hundreds place.

Step 6: Move to the thousands place:

  • Subtract 0 from 3 (since no borrowing is needed here) to get 3 in the thousands place.

Putting it all together, the result is:

3919 \begin{array}{c} 3919 \\ \hline \end{array}

Thus, the solution to the subtraction problem 47358164735 - 816 is 39193919.

Answer

3919

Exercise #5

amp;5763amp;amp;  178amp;776amp; \begin{aligned} &5763 \\ -& \\ &~~178 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

We aim to solve 57635763 minus 178178 using vertical subtraction.

First, align the numbers by their place value:
15763  178 \begin{array}{c} \phantom{1}5763 \\ -~~178 \\ \hline \end{array}

Step 1: Start from the rightmost digit (units place).
Units: 383 - 8: Since 33 is less than 88, we need to borrow.

Borrow from the tens place:
The 66 in the tens becomes 55 (after borrowing 1), making the units place 1313.

So, 138=513 - 8 = 5.

Step 2: Move to the tens place now.
Tens: 575 - 7: Borrow again because 55 is less than 77.

Borrow from the hundreds place:
The 77 in the hundreds becomes 66, turning the tens into 1515.

So, 157=815 - 7 = 8.

Step 3: Now the hundreds place.
Hundreds: 61=56 - 1 = 5 (Simple subtraction, no borrowing needed).

Step 4: Finally, the thousands place, which is direct.
Thousands: 50=55 - 0 = 5.

Thus, after all stages of subtraction, the result is:
15763  178   5585 \begin{array}{c} \phantom{1}5763 \\ -~~178 \\ \hline ~~~ 5585 \\ \end{array}

Therefore, the solution to the subtraction problem is 55855585.

Answer

5585

Exercise #6

amp;6315amp;amp;1506amp;776amp; \begin{aligned} &6315 \\ -& \\ &1506 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Align the numbers by place value.
  • Step 2: Subtract each corresponding digit from right to left.
  • Step 3: Borrow from the left if the top digit is smaller than the bottom digit.

Now, let's work through each step:

Step 1: Align 6315 and 1506 vertically by place values:
63151506\begin{aligned} &6315 \\ -&1506 \\ \hline & \end{aligned}

Step 2: Start subtracting from the units place:

Units place: 565 - 6. Since 5 is smaller than 6, we need to borrow 1 from the tens place.
1 becomes 0 (in the tens place), and 5 becomes 15:
156=915 - 6 = 9.

Tens place: Now it’s 000 - 0. That gives us 00.

Hundreds place: 353 - 5 in the hundreds place. Since 3 is smaller than 5, we borrow 1 from the thousands place.
3 becomes 13 and 6 becomes 5:
135=813 - 5 = 8.

Thousands place: 51=45 - 1 = 4.

Therefore, the result of subtraction is 48094809.

According to the provided answer choices, the correct choice is choice 3, which is the number 48094809.

The solution to the problem is 48094809.

Answer

4809

Exercise #7

amp;7189amp;amp;2392amp;776amp; \begin{aligned} &7189 \\ -& \\ &2392 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll use the vertical subtraction method, breaking down the problem into each column from right to left:

  • Step 1: Start with the rightmost column (units).
    • Units: 92=79 - 2 = 7.
  • Step 2: Move to the tens column.
    • Tens: As 898 - 9 is not possible, regroup by borrowing 1 from the hundreds column, making it 189=918 - 9 = 9.
  • Step 3: Proceed to the hundreds column.
    • After borrowing, the hundreds column has 030 - 3 (as it was reduced from 1), borrow from the thousands column: 103=710 - 3 = 7.
  • Step 4: Finally, calculate the thousands column.
    • After borrowing from the thousands, it is now 62=46 - 2 = 4.

Putting it all together, we find that:

71892392=47977189 - 2392 = 4797.

The correct answer is 47974797.

Answer

4797

Exercise #8

amp;8731amp;amp;3252amp;776amp; \begin{aligned} &8731 \\ -& \\ &3252 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

The solution involves the vertical subtraction of 873132528731 - 3252. Let's break it down step-by-step:

  • Step 1: Align the numbers at the units column for vertical subtraction:
    amp;8amp;7amp;3amp;1amp;3amp;2amp;5amp;2 \begin{array}{c} &8 & 7 & 3 & 1 \\ - & 3 & 2 & 5 & 2 \\ \hline \end{array}

  • Step 2: Subtract the units place: 121 - 2. Since 11 is smaller than 22, we need to borrow from the tens.
    Borrowing from 33 (tens), which becomes 22, and the units position turns from 11 to 1111. Now subtract: 112=911 - 2 = 9.

  • Step 3: Move to the tens place: 252 - 5. Again, 22 is smaller than 55, borrow from the hundreds.
    Borrow from 77 (hundreds), which becomes 66, and the tens becomes 1212. Now subtract: 125=712 - 5 = 7.

  • Step 4: Move to the hundreds place: 626 - 2. This results in 44.

  • Step 5: Finally, move to the thousands place: 838 - 3. This results in 55.

  • Scale down the entire calculation:
    5479 5479

Therefore, the result of 873132528731 - 3252 is 5479\textbf{5479}.

This corresponds to choice 4:

5479

.

Answer

5479

Exercise #9

amp;9417amp;amp;3708amp;776amp; \begin{aligned} &9417 \\ -& \\ &3708 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Write the numbers vertically and align by their place value.
  • Step 2: Start subtracting from the rightmost digit (the units place).
  • Step 3: Move to the left, regroup as needed for each column.

Let's work through each step:

Step 1: Write the numbers vertically, aligning them by place value:

94173708 \begin{array}{r} 9417 \\ -3708 \\ \hline \end{array}

Step 2: Begin with the units column:

78 7 - 8

We can't subtract 8 from 7, so we need to regroup. We take 1 ten from the tens place, converting the 7 into 17.

Step 3: After regrouping:

178=9 17 - 8 = 9

Step 4: Move to the tens column:

00=0 0 - 0 = 0

No regrouping needed here.

Step 5: Move to the hundreds column:

47 4 - 7

We can't subtract 7 from 4, so we again regroup. We take 1 thousand from the thousands column, making the hundreds digit 14.

Step 6: After regrouping:

147=7 14 - 7 = 7

Step 7: Finally, the thousands column:

83=5 8 - 3 = 5

We now have each column solved.

Therefore, the result is 5709.

The solution to the problem is 5709 5709 .

Answer

5709

Exercise #10

amp;3614amp;amp;2035amp;776amp; \begin{aligned} &3614\\ -& \\ &2035 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

Let's solve the subtraction problem step by step:

First, align the numbers vertically by their place values:

3614 3 \, 6 \, 1 \, 4

2035- 2 \, 0 \, 3 \, 5

3189\underline{\phantom{3\, 1\, 8\, 9}}

We start the subtraction from the rightmost digit (ones place):

  • In the ones column, 454 - 5 is not possible, so we need to borrow. Borrow 1 from the tens place.

  • The 1 in the tens place becomes 0, and the 4 in the ones place becomes 14.

  • Perform the subtraction: 145=914 - 5 = 9.

Next, move to the tens column:

  • After borrowing, we now have 030 - 3, which is not possible. We need to borrow from the hundreds place.

  • The 6 in the hundreds place becomes 5, and the 0 in the tens place becomes 10.

  • Perform the subtraction: 103=710 - 3 = 7.

Move to the hundreds column:

  • We have 505 - 0, which results in 5.

Finally, address the thousands column:

32=13 - 2 = 1.

Placing it all together, the result of subtracting 2035 from 3614 is:

1579 \underline{1 \, 5 \, 7 \, 9}

Therefore, the solution to the problem is 1579 1579 .

Answer

1579