Dividing Decimals by Whole Numbers: Fifth Grade Mathematics

Dividing a decimal by a whole number uses the standard long division algorithm, with the decimal point placed directly in the quotient above the dividend.

The Decimal Placement Rule

When dividing a decimal dividend by a whole number divisor, place the decimal point in the quotient directly above the decimal point in the dividend before calculating. Then divide as if both numbers were whole numbers.

   Standard Algorithm:  14.76 / 4

           3 . 6 9
       +----------
     4 | 1 4 . 7 6
       - 1 2
       -----
           2   7
         - 2   4
         -------
               3 6
             - 3 6
             -----
                 0

   1. Place decimal point directly above 14.76 into quotient.
   2. 4 goes into 14 three times (3 * 4 = 12). Remainder 2.
   3. Bring down 7 tenths. 4 goes into 27 six times (6 * 4 = 24). Remainder 3.
   4. Bring down 6 hundredths. 4 goes into 36 nine times (9 * 4 = 36). Remainder 0.
   Quotient: 3.69.

Adding Trailing Zeros to Complete Division

In whole number division, leftover amounts are written as remainders (e.g., 5 R2). In decimal division, you do not write remainders. Instead, annex trailing zeros to the dividend and continue the division cycle until the remainder becomes zero or forms a repeating pattern.

Dividing 7.5 by 6:

           1 . 2 5
       +----------
     6 | 7 . 5 0   <--- Annexed a 0 to continue dividing!
       - 6
       ---
         1   5
       - 1   2
       -------
             3 0   <--- Brought down annexed 0.
           - 3 0
           -----
               0   <--- Remainder is 0. Quotient: 1.25.

Leading Zeros in the Quotient

If the divisor does not go into the whole number portion of the dividend, place a 0 in the ones place of the quotient before the decimal point. For example, in 0.84 / 4: 4 goes into 0 zero times. Write 0, place the decimal point, and then divide 8 tenths to get 0.21.

Exercises and Solutions

Exercise 1: Standard Decimal Division with Annexed Zero. Divide 9.3 by 4. Show the long division steps, including placing the decimal point and annexing zeros until the remainder is zero.

Solution 1: Set up 4 into 9.3. Place the decimal point directly above the decimal point in 9.3. Divide: 4 goes into 9 two times (2 * 4 = 8; 9 - 8 = 1). Bring down 3 tenths to make 13. 4 goes into 13 three times (3 * 4 = 12; 13 - 12 = 1). Since there is a remainder of 1, annex a 0 to make 9.30 and bring down the 0 to make 10. 4 goes into 10 two times (2 * 4 = 8; 10 - 8 = 2). Annex another 0 to make 9.300 and bring down the 0 to make 20. 4 goes into 20 five times (5 * 4 = 20; 20 - 20 = 0). The final quotient is 2.325.

Exercise 2: Sharing Costs Equally. Four friends share the cost of a dinner bill totaling $58.60 equally. How much must each person contribute?

Solution 2: Divide $58.60 by 4. Place the decimal point directly above in the quotient. Divide 5 tens: 4 goes into 5 once (1 * 4 = 4; 5 - 4 = 1). Bring down 8 to make 18. 4 goes into 18 four times (4 * 4 = 16; 18 - 16 = 2). Place the decimal point after 14. Bring down 6 tenths to make 26. 4 goes into 26 six times (6 * 4 = 24; 26 - 24 = 2). Bring down 0 to make 20. 4 goes into 20 five times (5 * 4 = 20; 20 - 20 = 0). Each friend must contribute $14.65.