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

To solve this subtraction problem, we'll use the vertical subtraction method:

• Step 1: Arrange the numbers in a column, aligning them by place value. The number 76 is our minuend, and 8 is our subtrahend.

• Step 2: We start the subtraction from the rightmost column, the units place.

• Step 3: Subtract 8 from 6 in the units column. Since 8 is greater than 6, we need to borrow from the tens column.

Let's break down the subtraction:

Since 8 cannot be subtracted directly from 6, we borrow 10 from the tens place.
This makes the 6 into 16 (i.e., $6 + 10 = 16$), and the 7 in the tens place becomes 6.

Now subtract in the units column:
$16 - 8 = 8$

Next, move to the tens column. After borrowing to help the units column:
$6$ remains as it is. There is nothing to subtract in the tens column (conceptually subtracting zero), so $6$ stays as $6$.

As a result, the difference is:
$68$

Therefore, the solution to the subtraction $76 - 8$ is $68$.

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

• Step 1: Set up the subtraction problem vertically, aligning the digits by place value.
• Step 2: Begin with the units place.
• Step 3: Consider any necessary borrowing from the higher place value.
• Step 4: Complete the subtraction in all place values.

Now, let's work through each step:

Step 1: Align the numbers vertically as follows:

$\begin{array}{c} 1 & 1 & 8 \\ - & & 9 \\ \hline \end{array}$

Step 2: Start from the units column. Here we have $8$ (minuend) and $9$ (subtrahend). Since $8$ is less than $9$, we cannot directly subtract.

Step 3: Borrow 1 from the tens place of $118$ which makes the tens place $0$, and the $8$ in the units place becomes $18$.

Step 4: Compute $18 - 9 = 9$. Place the result under the units column.

Step 5: In the tens column, now we have $0 - 0 = 0$ since after borrowing, the tens of $118$ are reduced.

Step 6: In the hundreds column, copy the $1$ as there is no subtraction required here.

The final subtraction will look like this:

$\begin{array}{c} 1 & 0 & 18 \\ - & & 9 \\ \hline 1 & 0 & 9 \\ \end{array}$

The answer to $118 - 9$ is $\textbf{109}$.

Therefore, the solution to the subtraction problem is $109$.

To solve this problem, we need to perform the vertical subtraction of $8$ from $227$. Let's break down the steps:

• Step 1: Write the subtraction problem in column form: Place $227$ above $8$, aligning the digits on the right.
• Step 2: Perform the subtraction starting from the rightmost digit (the units place).
  
  • The units digit of the minuend is $7$ and the subtrahend is $8$. Since $7 < 8$, we need to borrow:
  • Borrow 1 from the tens place (turning the $2$ into $1$), making it $17$ instead of $7$.
  • $17 - 8 = 9$. Write the $9$ below the line in the units place.
• Step 3: Move to the tens digit:
  
  • After borrowing, the digit left in the tens place of the minuend is $1$.
  • Subtract: $1 - 0 = 1$ (since there is no subtrahend digit in the tens place).
• Step 4: Move to the hundreds digit:
  
  • The hundreds digit is $2$ and since we haven't changed it, it remains $2$.
  • Since there are no digits to subtract from in the hundreds place, the digit remains $2$.

Now, combining the results from each digit, the final answer becomes $219$.

Therefore, the solution to the problem is $219$.

To solve this problem of subtracting 6 from 354, we'll follow these steps:

• Step 1: Set up the problem with the two numbers aligned by their place values.
• Step 2: Start subtracting from the rightmost digits (units).
• Step 3: Subtract each column, handling any necessary regrouping (borrowing).

Now, let's solve it:

Step 1: Write the numbers with the larger number on top:

$\begin{array}{c} 354 \\ -\phantom{0}6 \\ \hline \end{array}$

Step 2: Subtract the numbers starting with the units place:

• Units: $4 - 6$ can't be performed as 4 is less than 6; we'll need to borrow from the tens column.
• To borrow, reduce the tens digit (5) by 1 (making it 4), and add 10 to the units digit (4) making it 14.
• Subtract $14 - 6 = 8$.
• Tens: Now, since we borrowed 1 from the tens, we have 4 left. Thus, $4 - 0 = 4$.
• Hundreds: The hundreds digit: $3 - 0 = 3$.

So the subtraction yields:

$\begin{array}{c} 354 \\ -\phantom{0}6 \\ \hline 348 \\ \end{array}$

Therefore, the solution to the problem is $348$.

To solve this problem, we'll perform a vertical subtraction:

• Step 1: Set up the subtraction vertically
  Write the larger number, 473, above and align the smaller number, 5, beneath it on the far right:

$\begin{aligned} &473 \\ -& \\ &~~~5 \\ \underline{\phantom{776}} & \\ \end{aligned}$

• Step 2: Subtract each column, starting from the right
  - Units: We have 3 minus 5. Since 3 is smaller than 5, we need to regroup by borrowing. Take 1 ten from the tens place.
  - After borrowing, the tens digit decreases by 1 (from 7 to 6), and the units place becomes 13 (3 + 10 = 13).
  - Now, subtract 5 from 13, which equals 8.
• Step 3: Move to the tens column
  - After borrowing, subtract 0 from 6, which leaves 6.
• Step 4: Move to the hundreds column
  - Finally, subtract 0 from 4, which leaves 4.

The result of the subtraction is:

Therefore, the solution to the problem is $468$.

To solve the problem of subtracting 7 from 625, we will use vertical subtraction. The alignment and borrowing process is as follows:

• Align the numbers vertically. Here, we have $625$ minus $7$, where $7$ is in the units place.
• Start with the rightmost digit. Since we have $5$ in the units place of 625 and need to subtract $7$, borrowing is necessary because 5 is smaller than 7.
• Borrow from the tens place: - The tens digit in 625 is $2$. We decrease $2$ by $1$, making it $1$. - This means we now have $15$ (10 + 5) in the units place for our subtraction.
• Subtract: $15 - 7 = 8$. Write $8$ in the units place of the result.
• Move to the tens place: substract $1 - 0 = 1$ as there is no number to subtract other than $0$.
• Finally, move to the hundreds place: $6 - 0 = 6$. Thus, the hundreds digit remains $6$.
• This leaves us with the final subtraction result: $618$.

Therefore, the solution to the problem is $618$.

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

• Step 1: Identify the digits involved in subtraction, starting with the units place.

• Step 2: Apply the subtraction rules column by column, performing borrowing if necessary.

• Step 3: Write down the result of each step and obtain the final answer.

Let's work through these steps:

Step 1: We are subtracting 6 from 782. Write the number 782 above the number 6, aligning them to the right:
$\begin{array}{c} 782 \\ - \phantom{\ }6 \\ \hline \end{array}$

Step 2: Begin the subtraction with the units digit (rightmost digits).

The units digit of 782 is 2, and we need to subtract 6 from it. Since 2 is smaller than 6, we must borrow from the tens place.

Borrow 1 from the tens digit (8), making it 7, and convert it to ten units. Now, add the borrowed 10 to the 2, making it 12 in the units place.

Now subtract 6 from 12, which gives us 6.

Step 3: Move to the tens place where we have adjusted the previous digit, 8 (now 7), which doesn’t involve subtraction as the only subtraction required was in the units place.

The hundreds digit remains unchanged as no borrowing affected it.

Therefore, we write this subtraction out as follows:

$\begin{array}{c} 782 \\ - \phantom{\ }6 \\ \hline \phantom{0}776 \\ \end{array}$

Therefore, the solution to the problem is $776$.

To subtract $7$ from $833$, follow these steps:

• Start at the ones column: subtract $7$ from $3$. Since $3$ is smaller than $7$, we need to borrow from the tens column.
• Regroup: Change the $3$ in the tens column to $2$ (since we borrow one group of ten) and add $10$ to the ones place turning $3$ into $13$.
• Subtract again in the ones place: $13 - 7 = 6$.
• Move to the tens column. Now that it’s $2$, proceed to subtract: $2 - 0 = 2$ (since there's no borrowing needed from the hundreds place).
• In the hundreds column, subtract: $8 - 0 = 8$ (since no borrowing from any higher place value is needed).

Therefore, the complete difference is $\mathbf{826}$.

To solve the subtraction of 9 from 767, we will perform the following steps:

• Step 1: Set up the subtraction in a vertical format:
  $\begin{array}{c} 767 \\ - 9 \\ \hline \end{array}$
• Step 2: Start with the units column (rightmost column). We have 7 in the units place of the number 767. Since 7 is greater than 9, we need to regroup.
• Step 3: Regroup by borrowing 1 ten from the tens place (left to the units), changing the 6 in the tens column to a 5, and making the units 10 + 7 = 17.
• Step 4: Now, subtract the units place: 17 - 9 = 8.
• Step 5: Move to the tens column. After regrouping, we have 5 in the tens place. Subtract 0 (nothing was subtracted here beyond initial borrowing), so it remains 5.
• Step 6: Finally, look at the hundreds column. Since no borrowing affected this column, simply bring the 7 down.

The resulting number after subtracting 9 from 767 is 758.

Therefore, the solution to the subtraction problem is $758$.

To solve this problem, we will perform subtraction using the vertical method:

• Step 1: Set up the subtraction problem:
  Write the minuend, 576, above the subtrahend, 8, aligning the digits by place value:

$\begin{aligned} &576 \\ -& \\ &~~~8 \\ &\underline{\phantom{776}} \end{aligned}$

• Step 2: Start with the ones column:
  Since we have 6 in the ones column of 576, we don't need to regroup:

The subtraction becomes $6 - 8$, which is impossible as we cannot subtract a larger number from a smaller number without regrouping.

• Step 3: Move to the tens column.
  Since we have 7 tens in 576, we can regroup one ten to the ones column:
• Change the 7 in the tens place to 6 and turn the 6 in the ones place into 16.
• Now subtract 16 ones - 8 ones = 8 ones.

The subtraction in the ones column now reads 16 - 8 = 8.

• Step 4: Subtract the tens column:
  After regrouping, the tens column subtraction becomes 6 (in tens from 576) - 0 (in tens from 8):

$6 - 0 = 6$

• Step 5: Subtract the hundreds column:
  The hundreds remain unchanged as the subtrahend does not have hundreds:

$5 - 0 = 5$

The subtraction is complete: $576 - 8 = 568$.

Therefore, the solution to the problem is $568$.