Double-digit divisions are pretty much like a single-digit long division, but they take a little more time and some practice. Since most people haven't memorized the 47 times table, you will have to guess a few things, but there is a useful trick you can learn to make it faster. This also gets easier and easier with practice, so don't get frustrated if you find yourself slowing down now.
Part 1 of 2: Divide by a two-digit number
Step 1. Look at only the first digit of the largest number
Write the problem as a long division problem. As in the simplest division problems, you can start by looking at the smallest number and asking yourself "Does it fit within the first digit of the largest number?"
Suppose you are going to solve 3472 ÷ 15. Ask yourself "Does 15 fit into 3?". Since 15 is definitely larger than 3, the answer is "no" and now proceed to the next step
Step 2. Look at the first two digits
Since you can't fit a two-digit number into a one-digit number, you now need to look at the first two digits just as you would a regular division problem. If you still have the problem that it is impossible to do the division, you should look at the first three digits, although for this example it is not necessary to do so:
Does 15 fit into 34? Yes, it does. So you can start calculating the answer (the first number doesn't have to fit perfectly, it just has to be smaller than the second number)
Step 3. Try to guess
Find out exactly how many times the first number fits inside the other. You may already know the answer, but if you don't, try to guess and check your answer with multiplication.
You need to solve 34 ÷ 15, or answer "how many times does 15 go into 34?". You should look for a number that you can multiply by 15 to get a number less than 34, but also quite close to it:
- Does 1 work? 15 x 1 = 15, which is less than 34, but you have to keep trying to guess.
- Does the 2 work? 15 x 2 = 30. This number is also less than 34, so 2 is a better answer than 1.
- Does the 3 work? 15 x 3 = 45, which is greater than 34. Too high! The answer should be 2.
Step 4. Write the answer above the last digit you used
If you ordered the numbers like in a long division problem, this should sound familiar.
Since you are going to calculate 34 ÷ 15, write the answer, which is 2, on the answer line above "4"
Step 5. Multiply your answer by the smallest number
This is the same as in a normal long division problem, except that you will now use a two-digit number.
Your answer was 2 and the smallest number in the problem is 15, so you must calculate 2 x 15 = 30. Write "30" under 34
Step 6. Subtract the two numbers
The last thing you wrote was under the original large number (or part of it). Treat it like a subtraction problem and write the answer on a new line below them.
Solve 34 - 30 and write the answer below them on a new line. The answer is 4. This 4 is still a "remainder" left after matching 15 to 34 twice, so you will need to use it in the next step
Step 7. Move down the next digit
As in a regular division problem, you should keep calculating the next digit of the answer until you finish.
Leave the 4 where it is and lower the "7" in "3472" to make a "47"
Step 8. Solve the following division problem
To get the next digit, just repeat the same steps you did, but now with the new problem. You can try guessing one more time to find the answer:
You must solve 47 ÷ 15:
- 47 is larger than the last number, so the answer will be a higher number. Try four: 15 x 4 = 60. No. It's too tall!
- Now try three: 15 x 3 = 45. Smaller than 47, but close to it. Perfect.
- The answer is 3, so you should write it over the "7" on the answer line.
- If you end up having a problem like 13 ÷ 15, with the first smallest number, you must lower a third digit before you can solve it.
Step 9. Continue using long division
Repeat the long division steps you used earlier to multiply the answer by the smallest number. Write the result under the largest number and subtract to get the next remainder.
- Remember that you just calculated 47 ÷ 15 = 3, and now you want to find out what the remainder is:
- 3 x 15 = 45, so write "45" under "47".
- Solve 47 - 45 = 2. Write "2" under 45.
Step 10. Find the last digit
Lower the next digit of the original problem as you did before so you can solve the next division problem. Repeat the steps above until you find all the digits of the answer.
- You have 2 ÷ 15 as your next problem, which doesn't make much sense.
- Lower one digit to make 22 ÷ 15 instead of 2 ÷ 15.
- 15 goes into 22 once, so write "1" at the end of the answer line.
- The answer now is 231.
Step 11. Find the remainder
You just need a subtraction problem to find the final remainder, and with this you are done. In fact, if the answer to the subtraction problem is 0, you won't even need to write the remainder.
- 1 x 15 = 15, so write 15 under 22.
- Find 22 - 15 = 7.
- You have no more digits to go down, so instead of dividing, just write "remainder 7" or "R7" at the end of the answer.
- The final answer is: 3472 ÷ 15 = 231 remainder 7.
Part 2 of 2: Follow These Tips to Guess Better
Step 1. Round to the nearest ten
It is not always easy to see how many times a two-digit number fits into a larger one. Use helpful tricks to round to the nearest multiple of 10 to make guessing easier. This is useful for smaller division problems or for solving parts of a long division problem.
For example, suppose you are going to solve 143 ÷ 27, but you have a hard time guessing how many times 27 goes into 143. Suppose you have to solve 143 ÷ 30 instead
Step 2. Count by the smallest number with your fingers
In the example, you can count by 30 instead of counting by 27. Counting by 30 is pretty easy once you get the skill to do it: 30, 60, 90, 120, 150.
- If you find it difficult, just count by three and add a 0 at the end.
- Count to a number higher than the large number in the problem (143), then stop.
Step 3. Find the two most likely answers
You didn't get exactly 143, but you got two close numbers: 120 and 150. Now see how many fingers you counted to get them:
- 30 (one finger), 60 (two fingers), 90 (three fingers), 120 (four fingers). So 30 x four = 120.
- 150 (five fingers), so 30 x five = 150.
- 4 and 5 are the two most likely answers to the problem.
Step 4. Test the two numbers in the real problem
Now that you have found two possible estimates, test them with the original problem, which was 143 ÷ 27:
- 27 x 4 = 108
- 27 x 5 = 135
Step 5. Make sure you can't get any closer
Since the two numbers ended up being less than 143, it is necessary to try to get even closer by trying one more multiplication problem:
- 27 x 6 = 162. This number is higher than 143, so it cannot be the correct answer.
27 x 5 is the closest without going over, so 143 ÷ 27 =
Step 5. (plus a remainder of 8, since 143 - 135 = 8).
If you don't want to multiply by hand during long division, try breaking the problem down into digits and solving each part in your head. For example, 14 x 16 = (14 x 10) + (14 x 6). Write 14 x 10 = 140 so you don't forget. Then think: 14 x 6 = (10 x 6) + (4 x 6). Well, 10 x 6 = 60 and 4 x 6 = 24. Add 140 + 60 + 24 = 224 and there you have the answer
- If, at any point, the subtraction results in a number greater than your divisor, the number you guessed is not large enough. Delete the entire step and try guessing with a larger number.
- If, at any point, the subtraction results in a negative number, the number you guessed was too large. Delete the entire step and try guessing with a smaller number.