Doubling large numbers may seem intimidating at first, but the task becomes easier with practice. There are multiple methods you can use to double a number. Learn each of them and then use the one that is easiest for you the next time you have to double a number.
Method 1 of 3: Method One: Basic Addition
Step 1. Write the problem
For this method, you will need to write the problem as if it were any other addition problem. Write the number twice, placing the plus sign in the middle.
Example: Find the double of 357.
Write the problem as you would in any other addition problem: 357 + 357
Step 2. Add the numbers to the right
Add the right hand digits in both values. Basically, you will double the digit that is on that end.
Example: in the case of 357 + 357, the number to the right is
7 + 7 = 14
Step 3. Shift any digit greater than 10 to the left
If the sum of the digits to the right is 10 or more, you will need to move the value to the "tens" place over the next set of digits. Just write the number in the “ones” place as part of your answer.
Example: in this problem, 14 is greater than 10, so you must carry the 1 over the next number. The 4 will be the digit to the far right of the answer
Step 4. Add the following set of numbers
Add the next set of digits, moving to the left. If you carried a "1" from the previous position, you must also add it to the two digits.
Example: in the case of 357 + 357, the next digit to the left is
- Since you carried the 1 of the previous position, you must also add it to the duplicate value of this position.
- 5 + 5 + 1 = 11
Step 5. Repeat the process until you reach the end of the line
Keep solving the rest of the numbers in the same way, going from right to left until you reach the final set of digits on the left side of the total value.
Example: since 11 is greater than 10, you must carry the extra 1 to the next position. The 1 on the right will be in the middle of your answer.
- There is only one place left to resolve in this answer. You will need to add the values of that place together with the 1 that you took from the previous operation: 3 + 3 + 1 = 7
Step 7. it will be the digit that is in the extreme left of the answer.
Step 6. Write the final answer
If you haven't already, write the calculated sums of each position next to each other. This answer must be twice the original number.
Example: the leftmost digit is 7, the middle digit is 1, and the far right digit is 4. When we write them together we get the answer '714.
Therefore, the double of 357 is 714
Method 2 of 3: Method Two: Duplicate Each Row
Step 1. Double the digit on the left
Look at the first digit of the number (the one to the left with the highest place value). Mentally duplicate it and write it down. The result will be the first digit or two of the final answer.
Example: Find the double of 872.
- The digit to the left is 8.
The double of 8 is
Step 2. Look at the second digit
If the second digit to the right is 5 or more, you will need to add 1 to the value you calculated in the previous step.
- If the second digit is less than 5, you don't need to add anything else to the previous value.
- Doubling any digit between 5 and 9 will result in a two-digit number, which makes this step necessary. Doubling a digit between 0 and 4 will result in a single digit number.
Example: the second digit in 872 is 7. Since 7 is greater than 5, you will need to add 1 to the sum of the previous value.
- 16 + 1 = 17
- This means that the final answer will start with a
Step 3. Double the second digit
Go back to the second digit and double it. This value will be the next digit in the final answer.
- If the value calculated in this step has two digits, ignore the one in the tens and just type the one in the ones place.
Example: the second digit in 872 is 7.
The double of 7 is
- Ignore the number in the tens (1) and only keep the one in the ones (4) for the final answer.
Step 4. it will be the middle number in the final answer.
Step 4. Repeat the procedure to the right
Continue with the rest of the digits in the same way, moving from left to right until you have doubled the one in the ones place.
Example: For this problem, there is only one more place to solve.
- In 872 the final digit is 2. Since 2 is less than 5, you don't need to add anything else to the sum performed on the middle value.
The double of 2 is
Step 4.. This will be the last digit in the answer.
Step 5. Write the answer
Write all the values you calculated in each position next to each other. The result will be the final answer.
Example: the first part of the answer is 17, the middle digit is 4, and the last is 4. When we write them together we get the answer 1744.
Therefore, the double of 872 is 1744
Method 3 of 3: Method Three: Duplicate Partitions
Step 1. Separate the numbers into partitions
Divide or decompose the number into its separate values: units, tens, hundreds, etc. Write it in its extended form.
Example: Find the double of 453.
When decomposing the number, it will look like this: 453 = 400 + 50 + 3
Step 2. Duplicate each part
Look at each partition and duplicate it while it is detached.
- To double values larger than those in the ones place, double the zero, then add the same number of zeros to that calculated value.
Example: you will need to double the 400, 50 and 3 separately.
- Since double 4 is 8, double 400 will be 800.
- Since double 5 is 10, double 50 will be 100.
The double of 3 is
Step 3. Add the results
Add the duplicate values to get the answer in standard form.
Example: 800 + 100 + 6 = 906
Step 4. Write the answer
The answer you find when adding the duplicate values should be twice the original number and therefore the final answer.