Examples with solutions for Vertical Subtraction: 3-digit subtraction with the regrouping of tens

Exercise #1

amp;186amp;amp;  29amp;776amp; \begin{aligned} &186 \\ -& \\ &~~29 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem of subtracting 29 from 186 using vertical subtraction, we will follow these steps:

  • Step 1: Set up the subtraction problem by writing 186 above 29, aligning them based on place value (units, tens, hundreds).
  • Step 2: Begin subtracting from the rightmost column (units).
  • Step 3: If the top digit in a column is smaller than the bottom digit, regroup from the next left column.
  • Step 4: Write the result beneath the line for each column.

Let's work through the subtraction problem:
186
- 29
--------

Step 1: Start with the units column: 696 - 9. Because 6 is less than 9, we need to regroup.

Step 2: Look at the tens column. From the tens column represented as 8, we borrow 1 ten (equivalent to 10 units), converting 8 tens to 7, and adding 10 to the units column, making it 16.

Step 3: Now subtract in the units column: 169=716 - 9 = 7.

Step 4: Move to the tens column. After borrowing, we have 7 tens minus 2 tens: 72=57 - 2 = 5.

Step 5: Finally, subtract the hundreds column: 10=11 - 0 = 1, as no borrowing was needed here.

Combine these results from each column to obtain the final answer: 157.

Therefore, the solution to the problem is 157157, which matches choice 3 from the provided options.

Answer

157

Exercise #2

amp;234amp;amp;  26amp;776amp; \begin{aligned} &234 \\ -& \\ &~~26 \\ &\underline{\phantom{776}} & \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve the subtraction problem 23426 234 - 26 using vertical subtraction, we follow these steps:

  • Step 1: Align the numbers by place value.
    234
    - 26
    776\underline{\phantom{776}}

  • Step 2: Subtract the digits starting from the right (units place):
    - Subtract the digits in the units place: Since 4 < 6, we need to borrow. Borrow 1 from the tens place of 234 (making the tens digit 2 into 1), turn 4 into 14 in the units place.
    - Now, 146=814 - 6 = 8.

  • Step 3: Move to the tens place:
    - Because we borrowed 1, the top digit in the tens column is now 2 (originally 3, but reduced to 2 because we borrowed 1 for the units place).
    - Subtract the digits in the tens place: 22=02 - 2 = 0.

  • Step 4: Move to the hundreds place:
    The hundreds place is straightforward as there's no borrowing involved and the top digit is still 2, so 20=22 - 0 = 2.

Putting it all together, the calculation becomes:
234 234
26 - 26
208\underline{208}

Therefore, the solution to the problem is 208\textbf{208}.

Answer

208

Exercise #3

amp;357amp;amp;  19amp;776amp; \begin{aligned} &amp;357 \\ -&amp; \\ &amp;~~19 \\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we need to perform the vertical subtraction of the numbers given:

  • 357 as the minuend

  • 19 as the subtrahend

Let's go through the steps to find the result:

Step 1: Align the numbers vertically based on their place values:
      357
-     19
  ______

Step 2: Start subtracting from the rightmost digits.
- Subtract the units place: 797 - 9. Since 7 is smaller than 9, we need to borrow 1 ten (10) from the tens column.

Step 3: After borrowing:
- The 7 becomes 17.
- The tens column changes from 5 to 4.

Now, subtract: 179=817 - 9 = 8.

Step 4: Move to the tens place:
- Subtract: 41=34 - 1 = 3.

Step 5: Move to the hundreds place:
- There is no need for regrouping here, so simply bring down the 3.

The subtraction is complete, giving us:
       338

Therefore, the solution to the subtraction problem is 338 338 . This corresponds to choice 2 in the provided answer choices.

Answer

338

Exercise #4

amp;482amp;amp;  65amp;776amp; \begin{aligned} &amp;482 \\ -&amp; \\ &amp;~~65 \\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Step-by-Step Solution

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

  • Step 1: Set up the numbers for vertical subtraction.

  • Step 2: Perform subtraction starting from the rightmost digit (units place).

  • Step 3: Apply regrouping whenever the top digit is smaller than the digit below.

Now, let's work through each step:
Step 1: Write the numbers in vertical format aligning by place value:

48265 \begin{array}{c} 482 \\ - 65 \\ \hline \end{array}

Step 2: Subtract the digits in the units place:25 \quad 2 - 5 . Since 2 is smaller than 5, we need to regroup.

Regrouping: Borrow 10 from the tens place, making 2 become 12. The 8 in the tens place decreases by 1 to 7.

4amp;87amp;12  amp;6amp;5 \begin{array}{c} 4 &amp;\cancel{8}7 \, &amp;12 \\ -\ \ &amp;6&amp;5 \\ \hline \end{array}

Subtract in the units place: 125=7 12 - 5 = 7 .

Step 3: Move to the tens place: Now subtract 76=1 7 - 6 = 1 .

Finally, subtract in the hundreds place: As there’s no digit to subtract from 4, it remains 4 4 .

Therefore, after performing the subtraction, the result is:

417 \begin{array}{c} 417 \\ \end{array}

Thus, the solution to the problem is 417 417 , which corresponds to choice 2.

Therefore, the solution to the problem is 417 417 .

Answer

417

Exercise #5

amp;577amp;amp;  18amp;776amp; \begin{aligned} &amp;577 \\ -&amp; \\ &amp;~~18 \\ &amp;\underline{\phantom{776}} &amp; \\ \end{aligned}

Video Solution

Step-by-Step Solution

To solve this problem, we'll use vertical subtraction, often referred to as column subtraction. The given problem is:

amp;577amp;amp;  18776amp; \begin{aligned} &amp;577 \\ -&amp; \\ &amp;~~18 \\ \underline{\phantom{776}} &amp; \\ \end{aligned}

We'll perform the subtraction step by step:

  • Step 1: Subtract the rightmost column (units):
    - From 7, subtract 8. Since 8 is larger than 7, borrow 1 from the tens column of 577.
    - Borrowing makes the 7 into 17 in the units column and the 7 in the tens column into 6.

  • Step 2: Subtract in the tens column:
    - From the borrowed 6 in the tens column, subtract 1, giving us 5.

  • Step 3: Subtract the hundreds column:
    - There is no borrowing needed here. Simply bring down the 5 as there is no corresponding number to subtract from the subtrahend, yielding 5.

Hence, the calculation becomes:

amp;5amp;76amp;amp;17amp;amp;1amp;amp;82342 \begin{aligned} &amp;5 &amp;\cancel{7}6 &amp;&amp;17 \\ - \\ &amp;&amp;1 &amp;&amp;8 \\ \overline{\phantom{2342}} \\ \end{aligned}

Therefore, the solution to the subtraction problem is 559 559 .

Answer

559