Subtract 5 from 473: Vertical Format Arithmetic Problem

Q: Why do I need to borrow when subtracting 5 from 473?

You need to borrow because in the units column, 3 is smaller than 5. You can't subtract a larger digit from a smaller one, so you borrow 1 ten from the tens place, making it 13 - 5 = 8.

Q: What happens to the tens digit when I borrow?

When you borrow 1 ten, the tens digit decreases by 1. In this problem, 7 becomes 6 after borrowing. This is crucial to get the right answer!

Q: How do I know if I set up the problem correctly?

Make sure digits are aligned by place value: units under units, tens under tens, etc. The 5 should be directly under the 3 in 473.

Q: Can I just do 473 - 5 without the vertical format?

Yes! You can solve it mentally or horizontally, but the vertical format helps you organize your work and avoid mistakes, especially with larger numbers.

Q: What if there's nothing to borrow from?

If the tens place were 0, you'd need to borrow from the hundreds place first. Keep moving left until you find a digit greater than 0 to borrow from.

Q: How can I check my answer is correct?

Add your answer to the number you subtracted: 468 + 5 = 473. If you get back the original number, your subtraction is correct!

Vertical Subtraction with Borrowing

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

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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 consider a shortage of 2 digits, and then we'll place

00:06 3 is less than 5

00:09 So we'll subtract 1 from the tens and add this amount to the ones

00:15 In other words, instead of 3 we'll now have 13

00:18 We'll subtract the ones from the ones plus the carried ten

00:23 Place in ones

00:26 Place 0 in the missing digits

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

00:35 Subtract hundreds from hundreds, and place in hundreds

00:38 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

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

Step-by-step solution

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:

\begin{aligned} & 473 \\ -& \\ &~~~5 \\ \underline{~~~~~} & \\ & 468 \\ \end{aligned}

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

Final Answer

468

Key Points to Remember

Essential concepts to master this topic

Alignment Rule: Always align digits by place value from right to left
Borrowing Technique: When 3 < 5, borrow 1 ten making 13 - 5 = 8
Verification: Check by addition: 468 + 5 = 473 ✓

Common Mistakes

Avoid these frequent errors

Subtracting the smaller number from the larger in each column
Don't switch and do 5 - 3 = 2 in the units column = wrong answer 472! This ignores the subtraction direction and place value. Always subtract the bottom number from the top number, borrowing when needed.

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 subtracting 5 from 473?

You need to borrow because in the units column, 3 is smaller than 5. You can't subtract a larger digit from a smaller one, so you borrow 1 ten from the tens place, making it 13 - 5 = 8.

What happens to the tens digit when I borrow?

When you borrow 1 ten, the tens digit decreases by 1. In this problem, 7 becomes 6 after borrowing. This is crucial to get the right answer!

How do I know if I set up the problem correctly?

Make sure digits are aligned by place value: units under units, tens under tens, etc. The 5 should be directly under the 3 in 473.

Can I just do 473 - 5 without the vertical format?

Yes! You can solve it mentally or horizontally, but the vertical format helps you organize your work and avoid mistakes, especially with larger numbers.

What if there's nothing to borrow from?

If the tens place were 0, you'd need to borrow from the hundreds place first. Keep moving left until you find a digit greater than 0 to borrow from.

How can I check my answer is correct?

Add your answer to the number you subtracted: 468 + 5 = 473. If you get back the original number, your subtraction is correct!

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