Solve Vertical Subtraction: 577 minus 18 Step-by-Step

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

Because 7 is smaller than 8! You can't take away 8 things when you only have 7. That's why we need to borrow 10 from the tens column to make it 17 - 8 = 9.

Q: What happens to the number I borrow from?

When you borrow 10 from the tens column, that digit gets reduced by 1. So the 7 in the tens place becomes 6 after you borrow from it.

Q: How do I remember which direction to borrow from?

Always borrow from the column to the left (the bigger place value). Think of it like borrowing money from someone with more - you go to the tens to help the ones!

Q: What if I need to borrow from zero?

You'll need to keep borrowing leftward until you find a non-zero digit. Each 0 becomes 9, and you reduce the first non-zero digit by 1.

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 right: $ 559 + 18 = 577 $ ✓

Q: Is there an easier way than borrowing?

Borrowing is the standard method that always works! Some people use mental math tricks, but learning borrowing properly will help you with any subtraction problem.

Vertical Subtraction with Borrowing

$\begin{aligned} &577 \\ -& \\ &~~18 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem step by step.

00:08 First, we'll subtract two-digit numbers one by one.

00:12 Since 7 is less than 8, we have to adjust.

00:16 Let's borrow 1 from the tens place and add it to the ones.

00:21 Now, we have 17 instead of 7 in the ones place.

00:25 Subtract the smaller ones from the larger ones,

00:29 and place the result in the ones column.

00:33 Next, subtract tens from tens,

00:36 and put the result in the tens column.

00:40 Don't forget to fill in any missing digits with zero.

00:44 Finally, subtract hundreds from hundreds and record it.

00:48 And that's how we solve this subtraction problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &577 \\ -& \\ &~~18 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll use vertical subtraction, often referred to as column subtraction. The given problem is:

$\begin{aligned} &577 \\ -& \\ &~~18 \\ \underline{\phantom{776}} & \\ \end{aligned}$

We'll perform the subtraction step by step:

Step 1: Subtract the rightmost column (units):
- From 7, subtract 8. Since 8 is larger than 7, borrow 1 from the tens column of 577.
- Borrowing makes the 7 into 17 in the units column and the 7 in the tens column into 6.
Step 2: Subtract in the tens column:
- From the borrowed 6 in the tens column, subtract 1, giving us 5.
Step 3: Subtract the hundreds column:
- There is no borrowing needed here. Simply bring down the 5 as there is no corresponding number to subtract from the subtrahend, yielding 5.

Hence, the calculation becomes:

$\begin{aligned} &5 &\cancel{7}6 &&17 \\ - \\ &&1 &&8 \\ \overline{\phantom{2342}} \\ \end{aligned}$

Therefore, the solution to the subtraction problem is $559$ .

Final Answer

559

Key Points to Remember

Essential concepts to master this topic

Borrowing Rule: When top digit is smaller, borrow 10 from next column
Technique: 7 becomes 17, and 7 in tens becomes 6 after borrowing
Check: Add your answer to the subtracted number: 559 + 18 = 577 ✓

Common Mistakes

Avoid these frequent errors

Subtracting smaller number from larger number in each column
Don't subtract 7 - 8 = 1 by flipping to 8 - 7 = 1! This ignores place value and gives wrong answers like 561. Always borrow from the next column when the top digit is smaller than the bottom digit.

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 subtract 7 - 8 = 1 in the ones column?

Because 7 is smaller than 8! You can't take away 8 things when you only have 7. That's why we need to borrow 10 from the tens column to make it 17 - 8 = 9.

What happens to the number I borrow from?

When you borrow 10 from the tens column, that digit gets reduced by 1. So the 7 in the tens place becomes 6 after you borrow from it.

How do I remember which direction to borrow from?

Always borrow from the column to the left (the bigger place value). Think of it like borrowing money from someone with more - you go to the tens to help the ones!

What if I need to borrow from zero?

You'll need to keep borrowing leftward until you find a non-zero digit. Each 0 becomes 9, and you reduce the first non-zero digit by 1.

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 right: $559 + 18 = 577$ ✓

Is there an easier way than borrowing?

Borrowing is the standard method that always works! Some people use mental math tricks, but learning borrowing properly will help you with any subtraction problem.

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