Solve the Subtraction Problem: 664 minus 275 in Vertical Format

Q: What does 'borrowing' actually mean in subtraction?

Borrowing means taking 10 from the next column to the left. When you borrow 1 from the tens place, it becomes 10 in the ones place, so 4 becomes 14.

Q: Why do I need to borrow twice in this problem?

You borrow whenever the top digit is smaller than the bottom digit. In 664 - 275, you need to borrow for both 4 - 5 and 5 - 7 after the first borrowing!

Q: Can I check my answer without adding?

Yes! You can also estimate: $ 664 - 275 $ is close to $ 660 - 280 = 380 $, so 389 makes sense as the answer.

Q: What if I forget to reduce the borrowed column?

Always remember: when you borrow from a column, that digit gets 1 smaller. When you borrow to a column, that digit gets 10 larger!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Each time we consider a shortage of 2 digits, and then we'll place

00:06 4 is less than 5

00:10 Therefore we subtract 1 from the tens and add this amount to the ones

00:14 So now instead of 4 we'll have 14

00:20 Subtract the ones from the ones plus ten

00:23 Place in ones

00:28 5 is less than 7

00:32 Therefore we subtract 1 from the hundreds and add this amount to the tens

00:37 So now instead of 5 we'll have 15

00:41 Subtract the tens from the tens plus ten

00:46 Place in tens

00:51 Subtract hundreds from hundreds, and place in hundreds

00:57 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\begin{aligned} &664 \\ -& \\ &275\\ &\underline{\phantom{776}} & \\ \end{aligned}$

2

Step-by-step solution

To solve this problem, we will perform a detailed step-by-step subtraction:

Step 1: Write the numbers in column format, aligning them by place value:

$\begin{array}{c} 664 \\ -275 ~~~\\ \hline \end{array}$

Step 2: Start subtracting from the rightmost column (units place):
Subtract the units: $4 - 5$ . Since 4 is smaller than 5, we need to borrow from the tens place.
- Borrow 1 from the tens (making it 5), the 4 becomes 14: $(14 - 5 = 9).$
Step 3: Move to the tens place:
Since we borrowed 1, we have the tens as 5 now, perform: $5 - 7$ . Again, 5 is smaller than 7, so borrow from the hundreds place.
- Borrow 1 from the hundreds (making it 5), the 5 becomes 15: $(15 - 7 = 8).$
Step 4: Now, proceed to the hundreds place:
After borrowing, the hundreds place is 5 (originally 6, minus 1 borrowed), perform: $5 - 2$ .
- No need to borrow here, simply calculate: $(5 - 2 = 3).$
Step 5: Compile the final result from top to bottom:
$389$

Therefore, the answer to the subtraction $664 - 275$ is $\mathbf{389}$ .

3

Final Answer

389

Key Points to Remember

Essential concepts to master this topic

Rule: Always align digits by place value before subtracting
Technique: Borrow from left column: 4 becomes 14, subtract 14 - 5 = 9
Check: Add result to subtrahend: 389 + 275 = 664 ✓

Common Mistakes

Avoid these frequent errors

Subtracting smaller from larger digit regardless of position
Don't subtract 4 - 5 = 1 by switching to 5 - 4 = 1 in the ones place! This ignores place value and gives wrong answers like 401. Always borrow from the next column when the top digit is smaller.

Practice Quiz

Test your knowledge with interactive questions

$\begin{aligned} &105 \\ -& \\ &~~~~3 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

FAQ

Everything you need to know about this question

What does 'borrowing' actually mean in subtraction?

+

Borrowing means taking 10 from the next column to the left. When you borrow 1 from the tens place, it becomes 10 in the ones place, so 4 becomes 14.

Why do I need to borrow twice in this problem?

+

You borrow whenever the top digit is smaller than the bottom digit. In 664 - 275, you need to borrow for both 4 - 5 and 5 - 7 after the first borrowing!

How do I keep track of all the borrowing?

+

Write small numbers above the original digits to show the changes. For example, cross out 6 and write 5, then cross out 6 and write 15 for the tens place.

Can I check my answer without adding?

+

Yes! You can also estimate: $664 - 275$ is close to $660 - 280 = 380$ , so 389 makes sense as the answer.

What if I forget to reduce the borrowed column?

+

Always remember: when you borrow from a column, that digit gets 1 smaller. When you borrow to a column, that digit gets 10 larger!

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Solve the Subtraction Problem: 664 minus 275 in Vertical Format

Vertical Subtraction with Multi-Digit Borrowing

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