Solve: Finding the Difference Between 514941 and 221871

Q: When do I need to borrow in subtraction?

You need to borrow whenever the top digit is smaller than the bottom digit. Like when you see 4 - 7 or 1 - 2, you must borrow from the next column to the left.

Q: What happens to the digit I borrow from?

The digit you borrow from decreases by 1. So if you borrow from 9, it becomes 8. If you borrow from 5, it becomes 4. Always remember to write down the new smaller number!

Q: What if I need to borrow from a zero?

When borrowing from 0, you need to keep borrowing left until you find a non-zero digit. The 0 becomes 9, and you continue the borrowing chain.

Q: Why do we subtract from right to left?

We work from right to left because borrowing affects the next column. Starting with ones, then tens, then hundreds ensures we handle all borrowing correctly as we go.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's solve this problem step by step!

00:12 Imagine we need to borrow two digits.

00:16 We start by borrowing from the ones place to help out the ones.

00:20 Notice that four is less than seven.

00:23 So, we borrow one hundred from hundreds to help the tens.

00:28 This changes hundreds from nine to eight.

00:32 Now, we have fourteen in the tens, instead of four.

00:36 Let's borrow from tens, to place in tens.

00:39 Borrow from hundreds, to add to the hundreds.

00:43 Borrow thousands to help the thousands.

00:46 Notice, one is less than two.

00:49 So, borrow from hundred thousands, to help the ten thousands.

00:54 This changes hundred thousands from five to four.

00:59 And now, ten thousands change from one to eleven.

01:04 We keep borrowing from ten thousands to place there.

01:08 Borrow from hundred thousands and place it back.

01:12 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\begin{aligned} &514941 \\ -& \\ &221871 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

2

Step-by-step solution

To solve this subtraction problem, follow these steps:

Step 1: Write down the numbers in vertically aligned format, placing the bigger number (514941) on top and the smaller number (221871) underneath it, ensuring digits are aligned according to their place value.
Step 2: Begin with the rightmost digits. Subtract the units place: $1 - 1 = 0$ .
Step 3: Move to the tens place. Subtract: $4 - 7$ . Since 4 is less than 7, we need to borrow 1 from the next left column (hundreds place). The 9 becomes 8, and the 4 becomes 14. Now, subtract: $14 - 7 = 7$ .
Step 4: Hundreds place. Subtract $8 - 8 = 0$ .
Step 5: Thousands place. Subtract $4 - 1 = 3$ .
Step 6: Ten-thousands place. Subtract $1 - 2$ . Borrow 1 from the hundred-thousands place, which makes 5 become 4. Now, $11 - 2 = 9$ .
Step 7: Hundred-thousands place. Subtract $4 - 2 = 2$ .

Upon performing these steps, the calculated difference of the two numbers is:

The answer is $\boldsymbol{293070}$ .

Therefore, the solution to the subtraction is $293070$ , which matches choice 4.

3

Final Answer

293070

Key Points to Remember

Essential concepts to master this topic

Alignment: Line up digits by place value vertically
Borrowing: When 4 - 7, borrow from 9 to make 14 - 7 = 7
Check: Add answer 293070 + 221871 = 514941 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to adjust borrowed digits
Don't borrow 1 from the hundreds place and forget to change 9 to 8 = wrong calculation throughout! This creates errors in multiple columns. Always reduce the lending digit by 1 after borrowing.

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

When do I need to borrow in subtraction?

+

You need to borrow whenever the top digit is smaller than the bottom digit. Like when you see 4 - 7 or 1 - 2, you must borrow from the next column to the left.

What happens to the digit I borrow from?

+

The digit you borrow from decreases by 1. So if you borrow from 9, it becomes 8. If you borrow from 5, it becomes 4. Always remember to write down the new smaller number!

How do I check if my subtraction is correct?

+

Add your answer to the smaller number. If you get the original larger number, you're correct! For example: $293070 + 221871 = 514941$ ✓

What if I need to borrow from a zero?

+

When borrowing from 0, you need to keep borrowing left until you find a non-zero digit. The 0 becomes 9, and you continue the borrowing chain.

Why do we subtract from right to left?

+

We work from right to left because borrowing affects the next column. Starting with ones, then tens, then hundreds ensures we handle all borrowing correctly as we go.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Arithmetic Operations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Solve: Finding the Difference Between 514941 and 221871

Multi-Digit Subtraction with Borrowing

❤️ Continue Your Math Journey!