Solve Vertical Subtraction: 505 minus 367 Step-by-Step

Q: Why can't I just borrow directly from the hundreds place?

You must borrow step-by-step through each place value! Think of it like borrowing money - you can't skip your friend and go directly to their parent. First borrow from hundreds to tens, then from tens to ones.

Q: How do I check if my subtraction is correct?

Use addition to check! Add your answer to the number you subtracted. If you get the original number, you're right: $138 + 367 = 505$ ✓

Q: What if I get confused with all the borrowing?

Take it slow! Work from right to left, one column at a time. Write down what each digit becomes after borrowing. Practice with easier problems first, like $203 - 145$.

Q: Is there a different way to solve 505 - 367?

Yes! You could think of it as counting up: How much do you add to 367 to get 505? Count: 367 + 3 = 370, 370 + 30 = 400, 400 + 105 = 505. Total: 3 + 30 + 105 = 138.

Vertical Subtraction with Borrowing Across Zeros

$\begin{aligned} &505 \\ -& \\ &367 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 a shortage of 2 digits, and then we place

00:06 5 is less than 7

00:09 The tens digit also equals 0 so we can't borrow from it 0

00:12 We'll borrow a hundred from the hundreds for the tens

00:16 So now instead of 0 we'll have 10, in the tens!

00:22 And now we'll borrow ten from the tens for the ones

00:25 Which will turn the tens from 10 to 9

00:29 So now instead of 5 we'll have 15, in the ones!

00:33 Now we subtract ones from ones, and place in ones

00:38 Subtract tens from tens, and place in tens

00:42 Subtract hundreds from hundreds, and place in hundreds

00:46 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &505 \\ -& \\ &367 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem of subtracting $367$ from $505$ , we'll follow these steps:

Step 1: Start at the ones place. Subtract $7$ from $5$ . Since $5$ is smaller than $7$ , we need to borrow from the tens place.
Step 2: Move to the tens place, before borrowing. There is $0$ in the tens place, so we cannot borrow directly. We must borrow from the hundreds place.
Step 3: Borrow $1$ from the hundreds place, reducing it to $4$ . The tens place becomes $10$ .
Step 4: Now borrow $1$ from the $10$ in the tens place, making it $9$ . The $5$ in the ones place becomes $15$ .
Step 5: Now subtract $7$ from $15$ , which gives us $8$ .
Step 6: In the tens place, subtract $6$ from $9$ , resulting in $3$ .
Step 7: In the hundreds place, subtract $3$ from $4$ , resulting in $1$ .

Putting it all together, we have:

$505 - 367 = 138$

Therefore, the solution to the problem is $\textbf{138}$ , which corresponds to choice 2.

Final Answer

138

Key Points to Remember

Essential concepts to master this topic

Borrowing Rule: When subtracting larger digits, borrow from left column
Zero Technique: Borrow from hundreds: 5 becomes 4, 0 becomes 10
Verification: Add your answer to subtrahend: 138 + 367 = 505 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to borrow across multiple zeros
Don't skip the tens place when it's zero and try to borrow directly = wrong calculation! The zero blocks direct borrowing from hundreds to ones. Always borrow step-by-step: first from hundreds to tens, then from tens to ones.

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 can't I just borrow directly from the hundreds place?

You must borrow step-by-step through each place value! Think of it like borrowing money - you can't skip your friend and go directly to their parent. First borrow from hundreds to tens, then from tens to ones.

What happens when I borrow from a zero?

When you borrow from a zero, it becomes 10 (but you reduce the next column by 1). In this problem, when we borrowed from hundreds, the 0 in tens became 10, and the 5 in hundreds became 4.

How do I check if my subtraction is correct?

Use addition to check! Add your answer to the number you subtracted. If you get the original number, you're right: $138 + 367 = 505$ ✓

What if I get confused with all the borrowing?

Take it slow! Work from right to left, one column at a time. Write down what each digit becomes after borrowing. Practice with easier problems first, like $203 - 145$ .

Is there a different way to solve 505 - 367?

Yes! You could think of it as counting up: How much do you add to 367 to get 505? Count: 367 + 3 = 370, 370 + 30 = 400, 400 + 105 = 505. Total: 3 + 30 + 105 = 138.

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