Dividing by 1-Digit Divisors: Fifth Grade Mathematics

Long division by 1-digit divisors follows a repeatable four-step cycle: Divide, Multiply, Subtract, and Bring Down.

The Long Division Cycle

The standard division algorithm is a cyclical process that works through the dividend place by place, from left to right.

+--------------------------------------------------------------------------+
|                     THE FOUR-STEP DIVISION CYCLE                         |
|                                                                          |
|       [ D ] --> DIVIDE    : How many times does divisor go into digits?  |
|       [ M ] --> MULTIPLY  : Multiply that quotient digit by the divisor. |
|       [ S ] --> SUBTRACT  : Subtract the product from the working digits.|
|       [ B ] --> BRING DOWN: Bring down the next digit of the dividend.   |
|                                                                          |
|       Remember: "Does McDonalds Sell Burgers?" (Divide, Multiply,        |
|                 Subtract, Bring down).                                   |
+--------------------------------------------------------------------------+

Step-by-Step Worked Example

Let us divide 738 by 6 using the standard cycle.

       1  2  3
     +--------
   6 | 7  3  8
     - 6         <--- Divide 7 by 6 = 1. Multiply 1 * 6 = 6. Subtract 7 - 6 = 1.
     ---
       1  3      <--- Bring down 3.
     - 1  2      <--- Divide 13 by 6 = 2. Multiply 2 * 6 = 12. Subtract 13 - 12 = 1.
     ------
          1  8   <--- Bring down 8.
        - 1  8   <--- Divide 18 by 6 = 3. Multiply 3 * 6 = 18. Subtract 18 - 18 = 0.
        ------
             0   <--- Remainder is 0. Quotient is 123.

The Check Step: Subtract Must Be Less Than Divisor

After performing the subtraction step in any cycle, compare the difference to the divisor. The difference must always be less than the divisor. If your difference is equal to or greater than the divisor, your quotient digit was too small and must be increased.

Handling Zeros in the Quotient

When a brought-down digit creates a number that the divisor cannot divide into (it goes 0 times), you must record a 0 in the quotient before bringing down the next digit.

Dividing 816 by 4:
       2  0  4
     +--------
   4 | 8  1  6
     - 8
     ---
       0  1      <--- Bring down 1. 4 goes into 1 ZERO times!
     -    0      <--- Must write 0 in quotient!
     ------
          1  6   <--- Bring down 6.
        - 1  6   <--- 4 goes into 16 four times.
        ------
             0   <--- Quotient is 204 (NOT 24!).

Exercises and Solutions

Exercise 1: Standard Algorithm with Internal Zero. Divide 924 by 3. Show every step of the division cycle, including the handling of any zeros in the quotient.

Solution 1: Set up 924 divided by 3. First cycle: 3 divides into 9 three times. Multiply 3 * 3 = 9. Subtract 9 - 9 = 0. Bring down 2. Second cycle: 3 divides into 2 zero times. You must record 0 in the tens place of the quotient. Multiply 0 * 3 = 0. Subtract 2 - 0 = 2. Bring down 4 to form 24. Third cycle: 3 divides into 24 eight times. Multiply 8 * 3 = 24. Subtract 24 - 24 = 0. There are no more digits to bring down, and the remainder is 0. The final quotient is 308.

Exercise 2: Division with a Remainder. Solve 1,483 / 5. State the quotient and remainder, and verify the answer using multiplication and addition.

Solution 2: Set up 1,483 divided by 5. 5 does not go into 1; 5 goes into 14 two times (2 * 5 = 10; 14 - 10 = 4). Bring down 8 to get 48. 5 goes into 48 nine times (9 * 5 = 45; 48 - 45 = 3). Bring down 3 to get 33. 5 goes into 33 six times (6 * 5 = 30; 33 - 30 = 3). The remainder is 3. The quotient is 296 with a remainder of 3 (296 R3). To verify: multiply 296 * 5 = 1,480. Add the remainder 3: 1,480 + 3 = 1,483. The answer is verified.