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:
To solve this problem, we'll perform simple vertical subtraction for the numbers given, 15 and 4:
Step-by-step solution:
Step 1: Write the numbers in a column, aligning the digits according to place value.
Step 2: Start subtracting from the rightmost column (the ones column). In the ones column, subtract 4 from 5:5−4=1.
Step 3: Move to the tens column. There is no subtraction to perform here since it's only 1−0, which leaves the digit as is.
Thus, there is no borrowing needed because the digits in the minuend are sufficient to carry out the subtraction.
The result of the subtraction 15−4 is 11.
Therefore, the solution to the problem is 11.
The correct multiple-choice answer is option 1: 11.
Answer
11
Exercise #2
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Video Solution
Step-by-Step Solution
To solve this problem, we'll perform vertical subtraction:
Step 1: Write down the numbers vertically with the larger number (the minuend) on top:
−273776
Step 2: Subtract the digits in the ones place: 7 (from 27) minus 3 (from 3) equals 4.
Step 3: Subtract the digits in the tens place: 2 (from 27) minus 0 (no tens in 3) equals 2.
Therefore, the difference is 24.
The solution to the problem is 24, which corresponds to choice 2.
Answer
24
Exercise #3
−amp;39amp;amp;6amp;776amp;
Video Solution
Step-by-Step Solution
To solve this problem, we'll follow these steps:
Step 1: Write the numbers vertically, with each digit aligned in their respective place value.
Step 2: Begin subtracting starting from the rightmost column.
Step 3: Move to the left, repeating the process for each subsequent column until finished.
Now, let's work through each step: Step 1: Arrange the numbers vertically, aligning according to the decimal place. 39 - 6 ----- Step 2: Start subtracting from the right. Subtract the ones place: 9−6=3. 39 - 6 ----- 3 Step 3: Since there is no need to borrow, move to the tens place: The tens place comprises '3' from '39', as there is no corresponding digit above '6' to subtract from: 3−0=3. 39 - 6 ----- 33
Therefore, the solution to the problem is 33.
Answer
33
Exercise #4
−amp;48amp;amp;7amp;776amp;
Video Solution
Step-by-Step Solution
To solve this problem, we'll follow these steps:
Step 1: Align the numbers vertically by place value.
Step 2: Subtract the units place.
Step 3: Subtract the tens place if necessary.
Now, let's work through each step: Step 1: Write the numbers 48 and 7 in columns where the digits (ones place) are aligned: 48−7 Step 2: Subtract the units (8 - 7 = 1) and write the result in the units position. Step 3: The tens place after subtraction is unchanged because there is no borrowing needed, so the 4 from 48 stays as 4. Thus, we have: 48−741
Therefore, the solution to the problem is 41.
Answer
41
Exercise #5
−amp;56amp;amp;5amp;776amp;
Video Solution
Step-by-Step Solution
To solve this problem, let's use a methodical approach as follows:
Step 1: Write the numbers in a vertical format, aligning the digits by place value.
Step 2: Subtract the ones digit: 6 (from 56) minus 5 equals 1.
Step 3: Bring down the tens digit since we are not subtracting anything from it: 5.
In detail:
Align the numbers vertically, with the larger number on top: 56−4005
Subtract the digits in the ones column. The ones digit in 56 is 6 and the ones digit in 5 is 5. Subtract 5 from 6 to get 1.
Since there are no numbers to subtract from the tens column of the first number, write down the 5 from 56.
The result of the vertical subtraction is thus: 56−400551