Column Division for Decimals
Column division for whole numbers can easily be applied to the division
of decimals. When this algorithm is applied to decimals, the student must
first think of a power of 10 that, when multiplied by the divisor, will
change the divisor into a whole number. Once both divisor and dividend
have been adjusted by the same power of 10, division can take place as it
does with whole numbers.
Build Understanding
If students need to review the whole-number version of this algorithm, refer
them to page 71. Review multiplying decimals by powers of 10. Then give
students numbers like 0.5, 0.03, and 0.0008, and ask them by what power of
10 they would multiply each number to make it a whole number.
Using page 73, tell students to begin multiplying both the divisor and the
dividend by the power of 10 that makes the divisor a whole number. Explain
to students that this process creates an equivalent problem. Fractional
equivalents might help students see that this is true: 0.324 0.04 (multiplied
by 10) = 3.24 0.4 (multiplied by 10) = 32.4 4. Use questions like the
following to guide students through the example:
• By which power of 10 would you multiply 0.04 to make it a whole number?
(100)
• Which number do you place to the left of the division bracket? (4)
• Will you need to make any trades before you share? (Yes. Trade 3 tens
for 30 ones.)
• Where do you place the decimal point in your answer? (above the decimal
point in the dividend; 8.1)
Error Alert Watch for students who multiply the divisor and the dividend
by different powers of 10. Make sure that students select the power of 10 based
on the divisor and that they multiply both the divisor and the dividend by that
power of 10.
Check Understanding
1. 120.1
Have a volunteer go to the board and model the column algorithm for decimal
division for the problem 6.74 ÷ 0.5. Encourage the student to explain what he
or she is doing while working so that the class can follow along. Have students
direct their questions to the volunteer, and guide that student in answering
as necessary. If many students are confused about a particular aspect of
the algorithm, do another problem on the board. When you are reasonably
certain that most students understand the algorithm, assign the “Check Your
Understanding” exercises at the bottom of page 73. Notice that Exercise 7
involves a 2-digit divisor. Exercise 8 requires students to insert a zero between
the decimal point and the first digit in the quotient. (See answers in margin.)
2. 0.15
3. 0.87
4. 1,490
Division
5. 61
Copyright © Wright Group/McGraw-Hill
Page 73
Answer Key
6. 1.62
7. 21.5
8. 0.0182
72
Teacher Notes
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Name
Date
Time
Column Division for Decimals
Think of a power of 10 that will make the divisor a whole number.
Multiply both the divisor and the dividend by the same power of
ten. Then divide as you would for whole numbers. Remember to
correctly place the decimal point in the quotient.
(dividend)
Example
0.324 ÷ 0.04
Multiply both the divisor and the
dividend by a power of 10 to make
the divisor a whole number.
0.324 ∗ 100 = 32.4
0.04 ∗ 100 = 4
Write the new problem.
4
3
2.
4⎯
Trade the 3 tens for 30 ones.
That makes 30 + 2 ones in all.
Record 32 in the ones column.
4
3
2.
4⎯
32
Place a decimal point in the quotient
directly above the one in the dividend.
There are 8[4s] in 32. Record 8 in the
answer space. Record 32 in the
ones column. Subtract.
There is 1[4] in 4. Record 1 in the
answer space. Record 4 in the
tenths column. Subtract.
8.
4
4⎯
3
2.
32
- 32
8.
1
4
3
2.
4⎯
32 - 4
- 32
0
0
0.324 ÷ 0.04 = 8.1
Division
Copyright © Wright Group/McGraw-Hill
(divisor)
Check Your Understanding
Solve the following problems.
1. 36.03 ÷ 0.3
2. 0.0075 ÷ 0.05
3. 0.0261 0.03
5. 2.44 0.04
6. 0.0486 ÷ 0.03
7. 40.85 1.9
Write your answers on a separate sheet of paper.
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_____
4. 0.006 8.94
________
8. 0.3 0.00546
Student Practice
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