Addition
In This Chapter
- Adding left to right
- Calculating addition problems with numbers near 10 or a multiple of 10
- Solving addition problems with number splitting
Addition is one of the first operations you learned as a child. And if you’re like me, you loved doing our 2 + 2’s. In this chapter, you’ll learn some simple addition methods that will make the process once again feel like child’s play. Once you know them, you’ll be able to do addition problems faster and without the aid of a calculator or even a pencil and paper.
Left-to-Right Addition
You can speed up your addition by adding the numbers in each column from left to right. In the following sections, I take you through how to use this method on two-digit and three-digit numbers.
For two-digit numbers, you first add the left column of numbers, followed by the right column of numbers. You then combine the digits in the middle, which gives you your answer.
Example 1
Solve the problem 78 + 45.
Step 1: Add the numbers in the first column: 7 + 4 = 11.
Step 2: Add the numbers in the second column: 8 + 5 = 13.
Step 3: Combine the middle digits: 1 + 1 = 2.
Solution: The answer is 123.
QUICK TIP
Make sure you’re not merely writing these examples down or plugging them into your calculator. Practice doing them in your head.
Solve the problem 87 + 69.
Step 1: Add the numbers in the first column: 8 + 6 = 14.
Step 2: Add the numbers in the second column: 7 + 9 = 16.
Step 3: Combine the middle digits: 4 + 1 = 5.
Solution: The answer is 156.
Example 3
Solve the problem 48 + 97.
Step 1: Add the numbers in the first column: 4 + 9 = 13.
Step 2: Add the numbers in the second column: 8 + 7 = 15.
Step 3: Combine the middle digits: 1 + 3 = 4.
Solution: The answer is 145.
Three-Digit Numbers
You can build on what you learned doing two-digit addition left to right by tackling three-digit addition. This involves another step of combining numbers in the middle.
Example 1
Solve the problem 582 + 759.
Step 1: Add the numbers in the first column: 5 + 7 = 12.
Step 2: Add the numbers in the second column: 8 + 5 = 13. Combine the middle digits: 2 + 1 = 3. This gives you a value of 133.
Step 3: Add the numbers in the third column: 2 + 9 = 11. Combine the middle digits for the values 133 and 11: 1 + 3 = 4.
Solution: The answer is 1,341.
Example 2
Solve the problem 834 + 786.
Step 1: Add the numbers in the first column: 8 + 7 = 15.
Step 2: Add the numbers in the second column: 3 + 8 = 15. Combine the middle digits: 5 + 1 = 6. This gives you a value of 161.
Step 3: Add the numbers in the third column: 4 + 6 = 10. Combine the middle digits for the values 161 and 10: 1 + 1 = 2.
Solution: The answer is 1,620.
QUICK TIP
It probably feels strange to add left to right instead of right to left, like most schools teach. However, you can probably see after doing a few problems how much faster it is not just marking off all the carryovers and then doing the addition. You’re dealing with the numbers individually and combining as needed, which is a better use of your time and energy.
Example 3
Solve the problem 983 + 694.
Step 1: Add the numbers in the first column: 9 + 6 = 15.
Step 2: Add the numbers in the second column: 8 + 9 = 17. Combine the middle digits: 5 + 1 = 6. This gives you a value of 167.
Step 3: Add the numbers in the third column: 3 + 4 = 7. Because this is a single digit, you simply bring down the 7 to the end of the answer—no addition is necessary.
Solution: The answer is 1,677.
Rapid Left-to-Right Columnar Addition
When doing addition, you won’t always be adding two short numbers. Sometimes, you’ll have to have many multiple-digit numbers at the same time. Using left-to-right addition, I’ll show you how to do it quickly and easily.
Example 1
Solve the problem 5,273 + 7,372 + 6,371 + 9,782.
Step 1: Add the numbers in the first column: 5 + 7 + 6 + 9 = 27.
Step 2: Add the numbers in the second column: 2 + 3 + 3 + 7 = 15. Combine the middle digits: 7 + 1 = 8. This gives you a value of 285.
Step 3: Add the numbers in the third column: 7 + 7 + 7 + 8 = 29. Combine the middle digits for the values 285 and 29: 5 + 2 = 7. This gives you a value of 2,879.
Step 4: Add the numbers in the fourth column: 3 + 2 + 1 + 2 = 8. Because this is a single-digit number, you bring it down to the end of the answer.
Solution: The answer is 28,798.
SPEED BUMP
Remember, because you’re bringing down a single digit, there will be no combining and adding. The answer will simply be 28,798.
Example 2
Solve the problem 8,336 + 4,283 + 3,428+ 9,373.
Step 1: Add the numbers in the first column: 8 + 4 + 3 + 9 = 24.
Step 2: Add the numbers in the second column: 3 + 2 + 4 + 3 = 12. Combine the middle digits: 4 + 1 = 5. This gives you a value of 252.
Step 3: Add the numbers in the third column: 3 + 8 + 2 + 7 = 20. Combine the middle digits for the values 252 and 20: 2 + 2 = 4. This gives you a value of 2,540.
Step 4: Add the numbers in the fourth column: 6 + 3 + 8 + 3 = 20. Combine the middle digits for the values 2,540 and 20: 0 + 2 = 2.
Solution: The answer is 25,420.
Addition with Numbers Near 10 or a Multiple of 10
Numbers near 10 or a multiple of 10—such as 9, 18, 27, 36, and so on—are very simple to add. To simplify addition problems which include these numbers, all you have to do is make the digit 10 or the multiple of 10 it’s closest to and then subtract how much you added in after you get your answer. These require no carryover and are possible to do just mentally!
Solve the problem 24 + 9.
Step 1: Change the 9 to a 10 by adding 1.
9 + 1 = 10
Step 2: Add the numbers.
24 + 10 = 34
Step 3: Because you had to add 1 to make the 9 a 10, you must now subtract 1 from the sum.
34 − 1 = 33
Solution: The answer is 33.
QUICK TIP
Don’t forget to subtract how much you had to add in to make the digit 10 or a multiple of 10.
Example 2
Solve the problem 46 + 18.
Step 1: Change the 18 to a 20 by adding 2.
18 + 2 = 20
Step 2: Add the numbers.
46 + 20 = 66
Step 3: Subtract 2 from the sum.
66 − 2 = 64
Solution: The answer is 64.
Example 3
Solve the problem 458 + 38.
Step 1: Change the 38 to a 40 by adding 2.
38 + 2 = 40
458 + 40 = 498
Step 3: Subtract 2 from the sum.
498 − 2 = 496
Solution: The answer is 496.
Number Splitting
Number splitting is a very useful method that allows you to split a big problem into two or three smaller parts. It reduces the number of steps you need to take to compute the answer.
The following examples may look slightly difficult because you’re adding two four-digit numbers. However, with number splitting, finding the answers is a piece of cake!
Example 1
Solve the problem 4,381 + 2,707.
Step 1: Split the problem into two parts by drawing or imagining a line down the middle.
Step 2: Add the numbers on the left side of the split: 43 + 27 = 70.
Step 3: Add the numbers on the right side of the split: 81 + 07 = 88. Bring the two parts together.
Solution: The answer is 7,088.
Solve the problem 1,762 + 3,519.
Step 1: Split the problem into two parts by drawing or imagining a line down the middle.
Step 2: Add the numbers on the left side of the split: 17 + 35 = 52.
Step 3: Add the numbers on the right side of the split: 62 + 19 = 81. Bring the two parts together.
Solution: The answer is 5,281.
Example 3
Solve the problem 5,235 + 8,997.
Step 1: Split the problem into two parts by drawing or imagining a line down the middle.
Step 2: Add the numbers on the left side of the split: 52 + 89 = 141.
Step 3: Add the numbers on the right side of the split: 35 + 97 = 132. Write or think of the 1 as smaller; this is the carryover.
Step 4: Carry over the 1 from the right to the left side of the split. Bring the two parts together.
Solution: The answer is 14,232.
QUICK TIP
As you gain confidence applying number splitting, try doing the problems in your head rather than on a piece of paper. It’s easier than you think!
The Least You Need to Know
- To find quick answers for problems with two- and three-digit numbers, you can add the columns from left to right and then combine the middle digits.
- Changing numbers to 10 or a multiple of 10 in a problem can help you get a sum much faster. You then simply subtract from the sum how much was needed to get to 10 or the multiple.
- You can break a problem down into more manageable parts through number splitting.