Whole numbers are the first step into the world of math, and subtracting them is one of the primary manipulations. Subtracting whole numbers requires practice before moving on to more complicated topics that may turn up on your exam.
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Depending on the problem, you may need the following skills. However, it’s unlikely you will need it on the actual math GED® exam.
The Idea of Borrowing
The problematic concept for subtracting numbers involves borrowing. During this process, you can take a group from the next column to the left of a number. This process drops the number you borrowed from drop by one (most people put a slash through it), and the original column that necessitated borrowing gain 10. Most people denote this with a small 1 above the number.
The borrowing process can be repeated as many times as necessary throughout a problem. It’s important to note that borrowing is only required if you cannot complete a column without going into negative numbers. Additionally, you cannot borrow from a 0, and must perform further steps.
Steps for Subtracting Whole Numbers
The first step in subtraction is lining up the numbers. Unlike addition, the order of the problem does matter, and mixing them up will give you the wrong answer. As you’re reading from left to right, the value on the left goes on top of the problem. The value to the right goes underneath.
The subtraction process for whole numbers begins on the right side with the values in the ones column. Your first step is asking if the number at the top of that column is bigger than the number below it. If it is, great, you don’t need to borrow. If it is not, you need to borrow from the tens column. Then you can subtract. Write the answer under that column. Then move to the next column to the left.
You can continue this process until you run out of columns to move to. At that point, you have your answer. If there is no value under a number, it is assumed to be a 0.
If you have three or more values in a subtraction problem, it’s best to separate into separate operations. Begin with the two values in the problem furthest left. Once you solve those, subtract the third number from the answer. You can repeat this as needed.
Example Problems for Subtracting Whole Numbers
Let’s start with a simple problem, 19-5. When we line up the problem, the 5 goes underneath the 9. We first ask ourselves if 9 is bigger than 5, which it is. Then we can take 5 from 9, leaving us to write 4 under that column. Since there is nothing under the 1, we just drag it down. Therefore, the final answer is 14.
For our next example of subtracting whole numbers, let’s look at 29-13. When we’re lining up the numbers, the 3 goes under the 9 and the 1 goes under the two. We start with the ones column by asking ourselves if 9 is bigger than 3, which it is. We can subtract without borrowing, and we would write 6 under that column. Then we repeat the process with the tens column, writing 1 under there. The final answer is 16.
Now let’s talk about borrowing with 23-19. The 9 goes under the 3 and the 1 goes under the 2 when you set it up. We begin with the ones column by asking ourselves if 3 is bigger than 9, which it is not so we need to borrow. The borrowing makes the ones column 13-9, which is 4. Now we examine our new tens column post-borrow, which is 1-1. That makes 4 our final answer.
Let’s talk about the next complication with 112-35. The 5 goes under the 2 and the 3 goes under 1. We ask our question, and 2 is not bigger than 5. That means we must borrow from the 1 in the tens column. That makes the ones column, 12 minus 5, so we write 7 under that. Then we look at our new tend column, 0 minus 3. After asking our question, we find we must borrow from the 1 in the hundreds column. The new tens problem is 10 minus 3, which is 7. Since the borrowing made the hundreds column a 0, our final answer is 77.
For our final example, let’s look at 101-54. After we line up, we ask if 1 is bigger than 4, which tells us we need to borrow from the tens column. Unfortunately, we can’t borrow from zero. So, we must borrow from the hundred spot for the tens column, and then we can borrow from the newly created ten in the tens column.
So, after this borrowing, we can subtract 4 from 11. We write that 7 under the ones column before moving on to the tens column. That now looks like 9 minus 5, which is 4. Since we borrowed from the 1 in the hundreds column, it became a 0. That makes the final answer 47.