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How to Do Long Division

No calculator handy? Here's how to divide numbers the old-fashioned way.

Instructions

  • Step 1: Understand the terminology Recognize that when you have long division problems, you must divide a dividend by a divisor to obtain the answer, called a quotient.
  • TIP: The dividend is the number inside the division box, the divisor is the number on the outside of the box.
  • Step 2: Look at the first digit Decide whether the divisor is small enough to divide the first digit in the box -- the one farthest to the left.
  • TIP: If you are dividing 12 into 86, for example, note that 12 won't go into eight.
  • Step 3: Place a zero Place a zero above that first digit on the top of the division box if the divisor is too large to go into the first digit. Move one digit to the right and try dividing into that number. Keep doing this until you have found a number that the divisor can be divided into.
  • TIP: In the example, since 12 won't go into eight, consider the first two digits under the dividend -- or 86.
  • Step 4: Consider the next portion of the dividend Determine how may times the divisor will go into that that portion of the dividend, and place the quotient above it, on top of the division box. In the example, 12 will go into 86 seven times, so place a 7 above the 6 in 86.
  • TIP: Write the product of seven and 12 under the dividend in the box. Since seven times 12 equals 84, write 84.
  • Step 5: Subtract Subtract the product from the divided portion of the dividend and write the result underneath. In the example, you will place the difference between 86 and 84 -- the number two -- under the number four in 84.
  • Step 6: Bring down Bring down the next number in the dividend and continue the same process until there are no more numbers to bring down or until the final number is too small to divide into.
  • TIP: If the last number is too small, write it as the remainder. In the example the remainder is two.
  • Step 7: Check your result Clear any leading zeros on the left side of the quotient. Now check your result by multiplying the quotient by the divisor to see whether you get the dividend.
  • FACT: The Egyptians performed multiplication and division by doubling and halving.

You Will Need

  • Paper and pencil

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