# GED Mathematical Reasoning: Addition and Subtraction

**Addition**

- To add numbers means to combine them.
- The addition operation is denoted by a plus sign “+”
- The answer to an addition problem is called a “sum.”
- When we add numbers, the order of the numbers doesn’t matter: 2 + 3 is the same as 3 + 2. The sum in each case is 5.

**Subtraction**

- Subtracting numbers means that we take one away from the other.
- We use a minus sign “-“ to denote subtraction.
- The result of a subtraction problem is called the “difference.”
- Order matters
- Unlike addition, the order in which we subtract numbers does matter: 10 – 7 and 7 – 10 have different results.
- For now, the general rule we will follow is to subtract the smaller number from the larger number.

**Example 1**

In its first month of business, a coffee shop served 1,367 cups of coffee. In its second month, the shop served 2,981 cups. How many total cups of coffee did the coffee shop serve during its first two months?

The word “total” in the question indicates that we should add the numbers 1,367 and 2,981.

We’ll stack the numbers vertically to begin the addition process. Pay special attention to your handwriting here – take the time to carefully line up the digits in corresponding place values.

We begin by adding the “ones” place value- working from right to left.

7 plus 1 equals 8. We place that result in the ones column.

Next, add 6 and 8. Note that the sum of 6 and 8 is 14, but we can only place one digit in the tens column.

This is when we use a technique called “carrying.” To “carry” means we will record the second digit of the sum in the current place value column and “carry” the first digit to the top of the column just to the left.

In this case, we will record a 4 in the tens column and write the number 1 on top of the hundreds column. That 1 will then be incorporated when we add the hundreds column, which we will do next.

Next is the hundreds column. We add 1, 3, and 9. The result is 13. Since the sum is two digit number, we will use the carrying technique again. A 3 goes in the hundreds column and a 1 is carried to the top of the thousands column.

Finally, we add the digits in the thousands column and record the result. 1 plus 1 plus 2 is equal to 4. Since this is our last place value, we record the result under the thousands column no matter how many digits it contains.

When we place our 4 in the thousands column, we see the final result of 4,348.

**Example 2**

One house measures 2,309 square feet. Another house measures 1,526 square feet. What is the difference in square footage between these two houses?

In this question, the word “difference” implies that we need to subtract 2,309 and 1,526. We will begin by stacking the numbers vertically – as we did with addition. As a reminder, take the time to carefully line up each place value.

When subtracting the numbers in this example, we will subtract the smaller number from the larger number. This means we will stack the larger number on top of the smaller one. As in addition, we work from right to left and subtract beginning with the “ones” place value. 9 minus 6 is equal to 3. We will place this result of 3 in the ones column.

Next, look at the tens column. Notice that we cannot subtract 2 from zero. We will use a technique called “borrowing.” To “borrow,” take a 1 from the column to the left and give it to the column you are working in. In other words, we’ll take a 1 from the hundreds column (crossing out the 3 to make it a 2) and “give” the 1 to the tens column, making the zero a 10.

Now we subtract 2 from 10, which is equal to 8, and place the 8 in the tens column. Move to the hundreds column. To subtract 5 from 2, we will need to borrow again. Take 1 from the thousands place (cross out the 2 and make it a 1) and give it to the hundreds place, making that 2 a 12.

Now subtract 5 from 12. The answer is 7. Place the 7 in the hundreds column.

Finally, we subtract the thousands column. 1 minus 1 is equal to zero. We place that zero in the thousands column and see our final answer of 0783.

We can drop the zero sitting in the thousands place, as it is simply a place-holder and there is no digit to the left. Our final answer is 783 square feet.

**Example 3**

Subtract 196 from 203.

Since 203 is the larger number, we’ll stack these numbers so that 203 is on top and 196 falls underneath.

We cannot subtract 6 from 3 so we must borrow. But notice that the digit we would borrow from is a zero – we cannot borrow from zero because it has nothing to offer. Therefore in this situation, we must first borrow from the hundreds column to make the number in the tens column larger. So, we’ll borrow one from the hundreds column and make that 2 a 1. Then give a 1 to the tens column to make that zero a 10.

Now, we can borrow a 1 from the 10. Cross out the 10 and make it a 9. Give the 1 to the 3 in the ones column, making it a 13. We can now subtract 6 from 13. The result is 7 and we will place that 7 in the ones column.

Next, move to the tens column and subtract 9 from 9. The result is zero, which will go in the tens column.

Finally, subtract 1 from 1 in the hundreds column. The result of zero will go in the hundreds column.

The final result showing is zero zero seven. We can drop the zeros sitting in the tens and hundreds places, as they are simply place-holders and there is no digit to the left of them. This makes our final answer 7.