Math Help: Algorithms for Elementary Students

Help with Algorithms

Adding Multi-Digit Numbers

Here's the algorithm for adding together numbers with more than 1 digit:

1. Add together the digits in the ones place. If the result is less than 10, it becomes the ones digit of the answer. If it's 10 or greater, the ones digit of the result becomes the ones digit of the answer, and you add 1 to the next column. For instance, in the problem 45 + 26, you would begin by adding 5 + 6, which equals 11. Write a 1 in the ones column and carry a 1 over.

2. Add together the digits in the tens place, plus the 1 carried over from the ones place, if necessary. Once again, if the answer is less than 10, it becomes the tens digit of the answer; if it's 10 or more, the ones digit becomes the tens digit of the answer and 1 is added to the next column. In the sample problem, add 4 + 2, which equals 6. Don't forget the 1 you carried over. The final answer is 71.

3. Repeat this process for any additional columns until they are all added.

Subtracting Multi-Digit Numbers

To subtract a multi-digit number from another multi-digit number, follow these steps:

1. Subtract the numbers in the ones places and write the answer directly below the ones digits. If the top number's ones digit is smaller than the bottom number's, add 10 to the top number and take away 1 from the top number in the next column. Then subtract the numbers in the ones column.

For instance, consider the problem 32 - 14. To subtract the numbers in the ones column, you'd have to subtract 2 - 4, which you can't do! So, add a 10 to the 2 in this problem to make it 12 - 4 = 8. Then, remember to subtract 1 from the 3 in the tens column.

2. Follow the same procedure for the column with the tens digits, and repeat until you've subtracted each column. In the sample problem above, the next step is to subtract the numbers in the tens column. Remember that you've subtracted 1 from the 3 in the tens place already. So, your new problem is 2 - 1, which equals 1. Your final answer is 18.

3. You can check your answer by adding in the opposite direction, up the columns. For each column, the digit in the answer plus the digit in the bottom number should add up to the corresponding digit in the top number (or the number you changed it to if you added 10).

Problem Solving with Algorithms

You might be asked to create your own algorithm, or apply one to a number. Since an algorithm is just a set of steps, all it takes is a little creativity to make one up. Here's an example:

1. Add 1.

2. Subtract 7.

3. Divide by 2.

You can apply this algorithm to any number, like 22. Completing the first step (22 + 1) gives you 23, and 23 - 7 = 16. Finally, 16 ÷ 2 = 8.

Another common problem-solving challenge you might face is creating an algorithm that produces a certain number or a certain type of number. For example, you might be asked to create an algorithm that always produces an even number. Here's one of many possibilities:

1. Add a zero to the end of the number.

2. Subtract 4.

3. Multiply by 2.

This algorithm will make any number even because any number that ends in zero is even. Additionally, multiplying any number by 2 will produce an even result.