Subtract 667 - 89: Vertical Format Solution Guide

Q: What does 'borrowing' actually mean in subtraction?

Borrowing means taking 10 from the next column to the left. When you can't subtract (like 7 - 9), you borrow 10 from the tens place, making 7 become 17.

Q: Why do I change 6 to 5 when I borrow?

When you borrow 10 from the tens place, you're actually taking away 1 ten. So 6 tens becomes 5 tens, and that's why you reduce the digit by 1.

Q: What if I need to borrow from zero?

You can't borrow from 0! Instead, look to the left until you find a non-zero digit. Borrow from there, turning all the zeros into 9s along the way.

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

Add your answer to the number you subtracted. If you get the original number, you're right! For example: $578 + 89 = 667$ ✓

Q: Can I subtract from right to left or left to right?

Always work from right to left (ones, tens, hundreds). This ensures borrowing works correctly because you need to know if borrowing happened before moving to the next column.

Subtraction with Borrowing

$\begin{aligned} &667 \\ -& \\ &~~89 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve a math problem together.

00:07 First, think about subtracting two digits each time.

00:11 We see that 7 is less than 9.

00:14 So, let's borrow 1 from the tens, adding it to the ones.

00:18 This means, instead of 7, we now have 17.

00:24 Subtract the ones from 17.

00:27 Place your answer in the ones position.

00:31 Next, we see 5 is less than 8.

00:35 Again, borrow 1 from the hundreds and add it to the tens.

00:41 Now, instead of 5, we have 15.

00:45 Subtract from 15 and put the answer in tens.

00:49 Use 0 where there's no number to subtract.

00:53 Subtract hundreds from hundreds, and place the result.

00:57 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &667 \\ -& \\ &~~89 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve $667 - 89$ , we perform vertical subtraction by aligning the numbers by place value:

Step 1: Start with the units column. Subtract $9$ from $7$ . Since $7 < 9$ , we need to borrow from the tens column. Change $6$ in the tens column to $5$ and add $10$ to the units column, making it $17$ . Now, subtract: $17 - 9 = 8$ .
Step 2: Move to the tens column, where we borrowed from $6$ , changing it to $5$ . Now subtract $8$ from $5$ . Since $5 < 8$ , we need to borrow from the hundreds column. Change $6$ in the hundreds column to $5$ and add $10$ to the tens column, making it $15$ . Now, subtract: $15 - 8 = 7$ .
Step 3: Finally, in the hundreds column: Subtract $0$ from $5$ , leaving $5$ .

Therefore, the solution to $667 - 89$ is $\mathbf{578}$ .

Given the multiple-choice options, the correct choice is option 2: $578$ .

Final Answer

578

Key Points to Remember

Essential concepts to master this topic

Borrowing Rule: When top digit is smaller, borrow from left column
Technique: Change 7 to 17, reduce 6 to 5: $17 - 9 = 8$
Check: Add your answer to subtrahend: $578 + 89 = 667$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to reduce the borrowed-from digit
Don't borrow 10 from the tens place but forget to change 6 to 5 = wrong calculation! This leaves you with the wrong digit for the next column. Always reduce the digit you borrowed from by 1.

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

What does 'borrowing' actually mean in subtraction?

Borrowing means taking 10 from the next column to the left. When you can't subtract (like 7 - 9), you borrow 10 from the tens place, making 7 become 17.

Why do I change 6 to 5 when I borrow?

When you borrow 10 from the tens place, you're actually taking away 1 ten. So 6 tens becomes 5 tens, and that's why you reduce the digit by 1.

What if I need to borrow from zero?

You can't borrow from 0! Instead, look to the left until you find a non-zero digit. Borrow from there, turning all the zeros into 9s along the way.

How can I check if my subtraction is correct?

Add your answer to the number you subtracted. If you get the original number, you're right! For example: $578 + 89 = 667$ ✓

Can I subtract from right to left or left to right?

Always work from right to left (ones, tens, hundreds). This ensures borrowing works correctly because you need to know if borrowing happened before moving to the next column.

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