Subtract 275467 - 186382: Multi-digit Subtraction Practice

Q: How do I know which column to borrow from?

Always borrow from the column immediately to the left. If that column is 0, keep moving left until you find a digit you can borrow from.

Q: What happens when I borrow from a column with 0?

You need to keep borrowing from columns further left! Change each 0 to 9 as you go, until you reach a column with a digit you can actually borrow from.

Q: How can I check if my subtraction answer is correct?

Use addition to check! Add your answer to the number you subtracted: $ 89085 + 186382 $. If you get the original number $ 275467 $, you're right!

Q: Why does borrowing work mathematically?

Borrowing is really regrouping! You're trading 1 from a higher place value for 10 in the lower place value. Since $ 1 \text{ hundred} = 10 \text{ tens} $, the total value stays the same.

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 Subtract ones from ones, and place in ones

00:09 6 is less than 8

00:13 In this case, we borrow a hundred from the hundreds place, for the tens

00:17 Which will turn the hundreds from 0 to 3

00:21 And now we'll have 16 instead of 6, in tens!

00:26 Subtract tens from tens, and place in tens

00:31 Subtract hundreds from hundreds, and place in hundreds

00:36 5 is less than 6

00:40 Therefore we borrow ten thousand from the ten thousands place, for the thousands

00:44 Which will turn the ten thousands from 7 to 6

00:47 And now we'll have 15 instead of 5, in thousands!

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

00:57 6 is less than 8

01:00 Therefore we borrow from the hundred thousands place, for the ten thousands

01:05 Which will turn the hundred thousands from 2 to 1

01:09 And now we'll have 16 instead of 6, in ten thousands!

01:12 Subtract ten thousands from ten thousands, and place

01:16 Subtract hundred thousands from hundred thousands, and place

01:20 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

$\begin{aligned} &275467 \\ -& \\ &186382 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

2

Step-by-step solution

To solve this problem, follow these steps for vertical subtraction:

Step 1: Start at the rightmost column (the units place) with $7 - 2$ . This equals $5$ .
Step 2: Move to the tens place with $6 - 8$ . Since 6 is smaller than 8, we need to borrow 1 from the hundreds column. This makes it $16 - 8 = 8$ .
Step 3: Adjust the hundreds column: originally $5$ , reduced by 1 due to borrowing, making it $4$ . Thus, $4 - 3 = 1$ .
Step 4: Next, consider the thousands column: $4 - 6$ . Since 4 is smaller than 6, borrow 1 from the ten thousand column, making it $14 - 6 = 8$ .
Step 5: The ten thousands column was $7$ , reduced by 1 due to borrowing. Thus $6 - 8$ requires further borrowing.
Step 6: Borrow from the hundred thousand column, changing the left remaining digits to $16 - 8 = 8$ .
Step 7: Finally, the hundred thousand column $2$ has been reduced to $16$ , with subtraction from zero now yielding: $1 - 1 = 0$ .

Following these steps, each digit ultimately gives the final answer:

$275467 - 186382 = 89085$

Thus, the solution to the problem is $89085$ .

3

Final Answer

89085

Key Points to Remember

Essential concepts to master this topic

Alignment: Line up digits by place value before subtracting
Borrowing: When top digit is smaller, borrow 10 from the left column: $16 - 8 = 8$
Verification: Add your answer to the smaller number to check: $89085 + 186382 = 275467$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to reduce the borrowed digit
Don't borrow 1 from the hundreds place and keep it as 5 = wrong calculation! When you borrow, the digit becomes smaller. Always reduce the borrowed digit by 1 before continuing.

Practice Quiz

Test your knowledge with interactive questions

$\begin{aligned} &15 \\ -& \\ &~~4 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

FAQ

Everything you need to know about this question

Why do I need to borrow when the top number is smaller?

+

You can't subtract a larger digit from a smaller one and get a positive result! Borrowing lets you 'take' 10 from the next column to make subtraction possible.

How do I know which column to borrow from?

+

Always borrow from the column immediately to the left. If that column is 0, keep moving left until you find a digit you can borrow from.

What happens when I borrow from a column with 0?

+

You need to keep borrowing from columns further left! Change each 0 to 9 as you go, until you reach a column with a digit you can actually borrow from.

How can I check if my subtraction answer is correct?

+

Use addition to check! Add your answer to the number you subtracted: $89085 + 186382$ . If you get the original number $275467$ , you're right!

Why does borrowing work mathematically?

+

Borrowing is really regrouping! You're trading 1 from a higher place value for 10 in the lower place value. Since $1 \text{ hundred} = 10 \text{ tens}$ , the total value stays the same.

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Subtract 275467 - 186382: Multi-digit Subtraction Practice

Multi-digit Subtraction with Borrowing

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