Solve Vertical Subtraction: 97 minus 68 Step-by-Step

Q: Why can't I just do 8 - 7 = 1 in the units column?

Because we're subtracting 8 from 7, not 7 from 8! In $97 - 68$, the units calculation is $7 - 8$, which requires borrowing since 7 is smaller than 8.

Q: How do I remember which number to subtract from which?

In vertical subtraction, always subtract the bottom number from the top number in each column. If the top digit is smaller, you need to borrow first.

Q: How can 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 correct: $29 + 68 = 97$ ✓

Q: Is there a way to do this without borrowing?

For this specific problem, no. Since \(7 in the units place, borrowing is required. Some subtraction problems don't need borrowing when each top digit is larger than the corresponding bottom digit.

Vertical Subtraction with Borrowing Technique

$\begin{aligned} &97 \\ -& \\ &68 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 7 is less than 8

00:09 Therefore we subtract 1 from the tens and add this amount to the ones

00:13 Which means now instead of 7 we will have 17

00:17 We subtract the ones from the ones plus the ten

00:21 We place in the ones

00:25 We subtract tens from tens, and place in the tens

00:29 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

$\begin{aligned} &97 \\ -& \\ &68 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve the subtraction problem $97 - 68$ , we'll follow these steps:

Step 1: Set up the numbers vertically, aligning the digits by place value.
Step 2: Subtract the digits in the units column. Here, $7 - 8$ is not possible without borrowing.
Step 3: Borrow 1 from the tens column of 97, changing it to 8, and making the units column 17 (since 7 becomes 17 after borrowing).
Step 4: Subtract the units: $17 - 8 = 9$ .
Step 5: Move on to the tens column: $8 - 6 = 2$ .

Now, let's work through the subtraction:

Starting with the units: Borrow from the tens column, so the number in the tens becomes 8 and the units digit becomes 17.

Calculate the units: $17 - 8 = 9$ .

Then, calculate the tens: $8 - 6 = 2$ .

Putting it all together, the subtraction $97 - 68$ results in $29$ .

Therefore, the solution to the subtraction problem is $29$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Borrowing Rule: When units digit is smaller, borrow from tens place
Technique: Change 97 to 8|17, then calculate $17 - 8 = 9$
Check: Add your answer to subtrahend: $29 + 68 = 97$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting smaller from larger in wrong order
Don't calculate $8 - 7 = 1$ in units place = wrong answer 31! This ignores place value rules and borrowing. Always borrow from tens when units digit is too small, making it $17 - 8$ instead.

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 do 8 - 7 = 1 in the units column?

Because we're subtracting 8 from 7, not 7 from 8! In $97 - 68$ , the units calculation is $7 - 8$ , which requires borrowing since 7 is smaller than 8.

What exactly happens when I borrow?

When you borrow 1 from the tens place, you're actually borrowing 10 ones! So 7 becomes 17, and the 9 in tens place becomes 8. Think of it as trading one ten for ten ones.

How do I remember which number to subtract from which?

In vertical subtraction, always subtract the bottom number from the top number in each column. If the top digit is smaller, you need to borrow first.

What if I forget to reduce the tens digit after borrowing?

You'll get the wrong answer! After borrowing 1 from the tens place, you must reduce that digit by 1. In this problem, 9 becomes 8 after lending 1 to the units place.

How can 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 correct: $29 + 68 = 97$ ✓

Is there a way to do this without borrowing?

For this specific problem, no. Since $7 < 8$ in the units place, borrowing is required. Some subtraction problems don't need borrowing when each top digit is larger than the corresponding bottom digit.

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