Subtract 346 from 1000: Vertical Format Solution

Q: Why can't I just borrow from the tens place when it's zero?

You cannot borrow from zero! When the tens place is 0, you must first borrow from the hundreds place to make the tens place become 10, then borrow 1 from that to help the units place.

Q: What happens to all those zeros when I borrow?

Each zero becomes 9 after borrowing. Think of it like this: when you borrow 1 from 10, you get 9 remaining. The same happens with place values!

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

Work systematically from right to left. Cross out each digit as you change it, and write the new digit above. This helps you visualize each borrowing step.

Q: Is there a faster way to do this problem?

You could think of it as 1000 - 346 = 1000 - 300 - 46 = 700 - 46 = 654. But learning the standard borrowing method helps with more complex problems!

Q: How can I check if my borrowing was done correctly?

After borrowing, make sure your top number still represents the same value. For example, 1000 should still equal your modified digits when you add up their place values.

Q: What if I make a mistake while borrowing?

Start over with fresh numbers! Borrowing mistakes compound quickly, so it's better to restart than try to fix errors mid-problem. Practice makes perfect!

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 place

00:06 0 is less than 6

00:09 The tens digit is also equal to 0 so we cannot borrow from it

00:12 The hundreds digit is also equal to 0 so we cannot borrow from it

00:15 We'll borrow a thousand from the thousands place for the hundreds

00:18 So now instead of 0 we'll have 10, in hundreds!

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

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

00:28 So now instead of 0 we'll have 10, in tens!

00:31 And now we'll borrow ten from the tens for the ones

00:34 Which will turn the tens from 10 to 9

00:37 So now instead of 0 we'll have 10, in ones!

00:43 Now we subtract ones from ones, and place in ones

00:46 Subtract tens from tens, and place in tens

00:52 Subtract hundreds from hundreds, and place in hundreds

00:58 Place 0 in the missing digits

01:01 Subtract thousands from thousands, and place in thousands

01:04 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

$\begin{aligned} &1000 \\ -& \\ &~~346 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Write the numbers vertically aligning by their respective place values:
$\begin{array}{c} 1000 \\ - \phantom{0}346~~~ \\ \hline \\ \end{array}$
Step 2: Start subtracting from the units column: - Units column: $0 - 6$ , since $0 < 6$ , we need to borrow. Notice that all digits to the left are zeros, so multiple steps of borrowing are required.
Step 3: Borrowing Process: - First, borrow from the hundreds place: Borrow 1, making the hundreds column $9$ (since $10 - 1 = 9$ ), leaving the ten column as $9$ (from borrowing). - Borrow again to the tens column, reducing hundreds column further, ultimately making tens column $9$ and units column $10$ .
Step 4: Perform the subtractions: - Units Column: $10 - 6 = 4$ - Tens Column: $9 - 4 = 5$ - Hundreds Column: $9 - 3 = 6$ - Thousands Column: Remains $0$ .

Therefore, putting it all together, we get: $\begin{array}{c} 1000 \\ - \phantom{0}346 ~~~ \\ \hline \phantom{0}654 \\ \end{array}$

Thus, the solution to the problem is $654$ .

3

Final Answer

654

Key Points to Remember

Essential concepts to master this topic

Borrowing Rule: When subtracting larger digit from smaller, borrow from left
Multiple Borrowing: From 1000, borrow makes 0→10, then 9→19 for tens
Check: Add answer to subtrahend: 654 + 346 = 1000 ✓

Common Mistakes

Avoid these frequent errors

Not borrowing through consecutive zeros
Don't just borrow from the immediate left digit when it's zero = impossible borrowing! This creates confusion and wrong calculations. Always trace borrowing all the way to the first non-zero digit on the left.

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 from the tens place when it's zero?

+

You cannot borrow from zero! When the tens place is 0, you must first borrow from the hundreds place to make the tens place become 10, then borrow 1 from that to help the units place.

What happens to all those zeros when I borrow?

+

Each zero becomes 9 after borrowing. Think of it like this: when you borrow 1 from 10, you get 9 remaining. The same happens with place values!

How do I keep track of all the borrowing steps?

+

Work systematically from right to left. Cross out each digit as you change it, and write the new digit above. This helps you visualize each borrowing step.

Is there a faster way to do this problem?

+

You could think of it as 1000 - 346 = 1000 - 300 - 46 = 700 - 46 = 654. But learning the standard borrowing method helps with more complex problems!

How can I check if my borrowing was done correctly?

+

After borrowing, make sure your top number still represents the same value. For example, 1000 should still equal your modified digits when you add up their place values.

What if I make a mistake while borrowing?

+

Start over with fresh numbers! Borrowing mistakes compound quickly, so it's better to restart than try to fix errors mid-problem. Practice makes perfect!

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Subtract 346 from 1000: Vertical Format Solution

Multi-Digit Subtraction with Extensive Borrowing

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