Solve Three-Digit Subtraction: 478 minus 289 in Vertical Format

Q: Why do I need to borrow when the top digit is smaller?

When you can't subtract a larger digit from a smaller one, borrowing lets you 'trade' 1 from the next column for 10 in the current column. This makes subtraction possible!

Q: What happens to the digit I borrow from?

The digit you borrow from gets reduced by 1. If you borrow from 7 in the tens place, it becomes 6. Don't forget this step!

Q: How do I keep track of all the borrowing?

Work column by column from right to left. Write small numbers above to show your borrowing, like crossing out the original digit and writing the new one above it.

Q: Can I check my subtraction answer?

Yes! Add your answer to the number you subtracted. If you get back to your starting number, you're correct: $189 + 289 = 478$ ✓

Subtraction with Regrouping

$\begin{aligned} &478 \\ -& \\ &289\\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Each time we consider borrowing 2 digits, and then we'll place

00:06 8 is less than 9

00:10 So we'll subtract 1 from the tens place, and add this amount to the ones

00:14 Meaning now instead of 8 we'll have 18

00:19 We'll subtract the ones from the ones plus ten

00:23 We'll place in the ones place

00:35 So we'll subtract 1 from the hundreds, and add this amount to the tens

00:40 Meaning now instead of 6 we'll have 16

00:44 We'll subtract the tens from the tens plus ten

00:49 We'll place in the tens place

00:54 Subtract hundreds from hundreds, and place in hundreds

00:57 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &478 \\ -& \\ &289\\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve the problem of subtracting 289 from 478, we perform the following steps:

Setup: Write the numbers in column form, aligning by place value:
$\begin{aligned} & 478 \\ - & 289 \\ \end{aligned}$
Subtract Ones: Start from the rightmost column (ones place):
$8 - 9$ . Since 8 is smaller than 9, borrow 1 from the tens place (7), making it 6 and converting the 8 to 18.
Now, perform $18 - 9 = 9$ .
Subtract Tens: Move to the tens column, now having $6$ from borrowing from the previous step:
$6 - 8$ . Again, since 6 is less than 8, borrow 1 from the hundreds place (4), making it 3 and converting the 6 to 16.
Now, perform $16 - 8 = 8$ .
Subtract Hundreds: Finally, subtract the hundreds column:
$3 - 2 = 1$ .
Assemble the result: The completed subtraction gives us $189$ .

Therefore, the solution to the problem is $189$ , which corresponds to choice 2.

Final Answer

189

Key Points to Remember

Essential concepts to master this topic

Borrowing Rule: When minuend digit is smaller, borrow from next column
Regrouping Technique: Convert 8 to 18 when borrowing from tens place
Verification: Add your answer to subtrahend: 189 + 289 = 478 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to reduce the borrowed-from digit
Don't borrow 1 from the tens place and forget to change 7 to 6 = incorrect remaining digits! This leaves the borrowing incomplete and gives wrong final answers. Always reduce the digit you borrowed from by 1 each time.

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

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

When you can't subtract a larger digit from a smaller one, borrowing lets you 'trade' 1 from the next column for 10 in the current column. This makes subtraction possible!

What happens to the digit I borrow from?

The digit you borrow from gets reduced by 1. If you borrow from 7 in the tens place, it becomes 6. Don't forget this step!

How do I keep track of all the borrowing?

Work column by column from right to left. Write small numbers above to show your borrowing, like crossing out the original digit and writing the new one above it.

Can I check my subtraction answer?

Yes! Add your answer to the number you subtracted. If you get back to your starting number, you're correct: $189 + 289 = 478$ ✓

What if I need to borrow multiple times in one problem?

That's normal! In this problem, we borrowed from both the tens and hundreds places. Just handle one column at a time and work systematically from right to left.

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