In order to solve vertical subtraction, we follow these rules: First rule - write the problem in the correct order! Ones digits under ones digits, tens digits under tens digits, and so on. Second rule - when the upper digit is smaller than the lower digit - we borrow 1 from the next digit. Third rule - a 0 that cannot be borrowed from becomes 9 until we reach a digit that is not 0 from which we can borrow 1. Note! If there is a third 0 right after, it will become 8, if there is a fourth 0 right after, it will become 7, and so on.
Vertical subtraction is a way of writing a subtraction problem where the second number is written below the first number vertically and in the correct order - ones under ones, tens under tens, and so on.
Why do we need vertical subtraction?
Sometimes you'll encounter relatively complex subtraction exercises that look like this: 431−278= By writing them vertically we can easily solve them.
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The First Rule - writing the problem in the correct order!
ones digits under ones digits, tens digits under tens digits, hundreds digits under hundreds digits, and thousands digits under thousands digits. Pay attention! It is extremely important that the first number in the exercise is the first and top number. For example: 87−54= We will write it as follows:
Write the (minus) – sign in order to indicate that this is a subtraction exercise. Draw a line underneath to separate the exercise from the results line. We'll start by subtracting the ones digits as follows:
7−4=3
Let's continue to subtract the tens digits to obtain the following : 8−5=3
We're done! The result is 33. Now let's learn the next rule using the following example:
The Second Rule -
When the upper digit is smaller than the lower digit - we borrow 1 from the next digit.
Here's a more advanced exercise! 45−29=
Solution:
Given that we cannot subtract 5 minus 9 we need to borrow a digit from the next number! That means: 5 will become 15 given that we'll place one in front of it and 4 will become 3.
We will write it in the following way:
Now we can proceed to solve the problem: 15−9=6 3−2=1 As seen below:
The result is 16!
What do we do when we need to subtract a number from the digit 0? For example in the exercise 40−29= Here too we'll need to borrow 1 from the digit 4 resulting in the exercise seen below.
We can proceed to solve the problem : 10−9=1 3−2=1 As seen below:
We're done! The result is 11. Now let's see what happens when we can't borrow from the next digit given that it's also 0: For example in the following exercise: 500−365=
The third rule -0 that cannot be borrowed from becomes 9 until we reach a digit that is not 0 from which we can borrow 1.
Note! If there is a third 0 immediately after, it becomes 8, if there is a fourth 0 immediately after, it becomes 7 and so on..
Let's learn the following rule through an example:
We want to borrow 1 for the first 0 making it 10. The second 0 will be 9 because we can't borrow from it and the digit 5 will become 4 given that we borrowed one from it. As seen below:
We can proceed to solve the exercise: 10−5=5 9−6=3 4−3=1 Let's write the solution as follows:
We're done! The result is 135 Now let's move on to a very advanced exercise!
Let's solve this problem together – 5700−3786=
Solution: Let's write it correctly:
Let's begin to solve the problem: 0 The first will become 10 since we borrow 1. 0 The second will become 9 because we can't borrow from it and the 7 will become 6 because we borrowed 1 from it. As seen below:
Hi! We've encountered a problem! 6 is less than 7 thus we need to borrow 1 . So 6 will become 16 and 5 will become 4 because already borrowed 1from it. We'll obtain the following:
Let's solve the basic vertical subtraction problem where we subtract 4 from 157 step by step:
Step 1: Write the numbers in a vertical format, ensuring to align them by place values. 157−4776
Step 2: Perform subtraction starting from the rightmost digit (the ones place). - Subtract 4 from 7 in the ones column, resulting in 3.
Step 3: Since the number being subtracted, 4, has no digit in the tens and hundreds places, bring down the remaining digits from 157. These are 5 in the tens place and 1 in the hundreds place.
Thus, the result of subtracting 4 from 157 is 153.
Among the options provided, choice 2 is the correct answer, which states 153.
Therefore, the solution to the problem is 153.
Answer
153
Exercise #2
−amp;478amp;amp;2amp;776amp;
Video Solution
Step-by-Step Solution
Let's solve the subtraction problem by following these steps:
First, align the numbers vertically:
−4782776
Starting with the rightmost digits:
In the units place, subtract 2 from 8: 8−2=6.
Since there are no other digits from the subtrahend, bring down the remaining digits as they are.
This results in:
476
Therefore, the solution to the problem is 476.
Answer
476
Exercise #3
−amp;105amp;amp;3amp;776amp;
Video Solution
Step-by-Step Solution
Let's solve the subtraction problem 105−3:
Align the numbers vertically to ensure each digit is in the correct place value position:
Write 105 as: 1amp;0amp;5
Place 3 beneath 105 such that it aligns with the rightmost digit (units place): −amp;amp;3
Subtract each column starting from the rightmost side (units digit) to the left:
Step-by-step subtraction:
Units column: 5−3=2
Tens column: There is nothing to subtract with 0, so it remains 0.
Hundreds column: Similarly, there is nothing to subtract, so it remains 1.
Combine the results of these steps to find the answer:
The result of the subtraction 105−3=102.
Therefore, the correct answer is 102.
Answer
102
Exercise #4
−amp;37amp;amp;25amp;776amp;
Video Solution
Step-by-Step Solution
Let's solve the subtraction problem 37−25 using vertical subtraction:
Step 1: Align the numbers vertically:
37−25
Step 2: Start with the rightmost column (units place):
7−5=2
Write 2 under the line in the units place.
Step 3: Move to the left column (tens place):
3−2=1
Write 1 under the line in the tens place. This gives us 12 as the result.
Therefore, the solution to the problem is 12.
Answer
12
Exercise #5
−amp;578amp;amp;6amp;776amp;
Video Solution
Step-by-Step Solution
Let's solve this subtraction problem step-by-step:
Step 1: Align the numbers vertically by place value, ensuring units are aligned under units.
Step 2: Start subtraction from the rightmost column (units column). Here, subtract 6 from 8 in the units place: 8−6=2.
Step 3: Since we have dealt with the units place, move one step to the left to the tens place. Here, subtract 0 (since nothing is being subtracted from this place after borrowing) from 7 in the tens place: 7−0=7.
Step 4: Finally, move to the hundreds place. Subtract 0 from 5 (again, no borrowing affects this place): 5−0=5.
After completing the steps, the subtraction gives us the result.