How to Divide a Three Digit Number


Division is a mathematical process in which you determine how many times a certain value will fit into another value. Division is the opposite of multiplication. Some students are frustrated by division, especially when dividing values into larger numbers, such as three-digit numbers. You can divide three-digit numbers once you understand the processes of estimating, multiplying and borrowing. With a little practice, you should have no trouble handling three digit-numbers in division problems.

  • Write a given three-digit number underneath a division bracket. This is called the "dividend."

  • Write the number that will be divided into the three-digit number on the left side of the bracket. This is called the "divisor."

  • Make an estimate as to how many times the divisor will fit into the dividend based on rounded numbers. For instance, if you have 309 as your divisor and 675 as your dividend, you could round 309 to 300 and 675 to 700 mentally. The number 300 will fit into 700 twice, so you could try 2 as your first estimate.

  • Multiply your estimate times your actual divisor off to the side of your problem or on a scratch piece of paper. In this example, you would multiply 2 times 309, which gives a product of 618. If you were to use 3 as the first digit of your quotient, your answer would be over 900, which is too large. Therefore, you know that 2 will be the first digit of your quotient.

  • Write the first digit of your quotient over the ones column of your dividend. Write this number on top of the division bracket. In this case, you would write a 2.

  • Multiply the first digit of your quotient times your divisor and write the answer underneath your dividend and draw a line underneath the product. In this example, you would multiply 2 by 309 to get 618.

  • Subtract your answer from Step 6 from your dividend. In this example, you would subtract 618 from 675. Since the 8 in the ones column is larger than the 5, you must "borrow" a 1 from the tens place, which makes the 5 a 15. Subtract 8 from 15 to get 7 in the ones place. Moving to the tens column, you must subtract 1 from the 7 since you borrowed previously. This makes the tens digit a 6. Therefore, you will subtract 1 from 6 to get 5. Finally, in the hundreds position, you will subtract 6 from 6, which leaves zero. Therefore, your answer from this step will be 57, which you would write under the line that you drew in Step 6.

  • Add a decimal to your divided, making it 675.0 in this case. Drop the zero down to your previous difference of 57, creating 570. Then divide your divisor into this number. In this example, you would divide 309 into 570, which will only fit 1 time. Therefore you would write a decimal after the first digit of your quotient (which was a 2), followed by the number 1.

  • Multiply the second digit of your quotient times your divisor and write the product at the bottom of the problem, with a line underneath it. In this case, you would multiply 1 times 309 to get 309. You would write 309 underneath 570 and subtract to get 261.

  • Continue the process of adding a zero to the dividend, dropping the zero down, dividing the divisor into the new number, multiplying and subtracting until you carry out the problem to the place value that you desire.

Tips & Warnings

  • If you are dividing a three-digit number by a one- or two-digit number, the first digit of your quotient will go over the digit in the dividend that represents the ones place of the first value that is divisible by the divisor. For instance, if you were to divide 3 into 675, you would write a 2 over the 6 in the dividend. If you were dividing 30 into 675, you would write a 2 over the 7 in the dividend, since 30 goes into 67 twice.


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