Trade-First Subtraction for Decimals
FOCUS
ALGORITHM
Trade-first subtraction for whole numbers can easily be applied to the
subtraction of decimals. It looks just like the standard algorithm for
decimal subtraction (pages 36–37) when it is completed. The difference is
that with the trade-first algorithm, all trading is carried out before any
subtracting begins.
Build Understanding
If students need to review the whole-number version of this algorithm, refer
them to pages 25–27.
Using page 35, explain that with this method of subtracting decimals, students
will begin by writing the problem so that the decimal points are aligned
vertically. If the subtrahend and the minuend do not have the same number
of decimal places, students will add one or more zeros to the end of one of the
numbers so that both numbers have the same number of decimal places.
Subtraction
Students then carry out all necessary trading until the top number in each
column is at least as large as the bottom number. Finally, students will
subtract the numbers in each column. Use questions like the following to guide
students through the examples:
• In the example, which numbers are in the tenths place? (2 and 7) Can
you remove 7 tenths from 2 tenths? (no) What trade can you make so that
you will be able to remove the 7 tenths? (Trade 1 one for 10 tenths. After
trading, there will be 12 tenths, and you can then remove 7 tenths.)
• What do the 5 and 12 written above the 6 and 2 show? (They show that
1 of the 6 ones was traded for 10 tenths, decreasing the number of ones
to 5 and increasing the number of tenths to 12.)
• Does it matter whether you begin trading and subtracting on the left or
the right? (no)
1. 4.4
2. 1.2
Check Understanding
Have a volunteer go to the board and solve the problem 8 − 3.14. Ask the
volunteer to explain each step as he or she works. The class should direct
questions concerning the problem to the volunteer. When you are reasonably
certain that most of your students understand the algorithm, assign the
“Check Your Understanding” exercises at the bottom of page 35. (See answers
in margin.)
3. 1.82
4. 2.57
5. 0.87
Copyright © Wright Group/McGraw-Hill
Error Alert Watch for students who have difficulty subtracting a decimal
from a whole number. If it helps students, ask them to draw vertical lines to
separate the place-value columns and write place-value abbreviations (100s,
10s, 1s, 0.1s, 0.01s, 0.001s) above the columns. Making the line that separates
the ones (1s) and the tenths (0.1s) columns thicker might also help students
accurately place the decimal point in the answer.
Page 35
Answer Key
6. 5.449
7. 0.11
8. 8.992
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Teacher Notes
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Name
Date
Time
FOCUS
ALGORITHM
Trade-First Subtraction for Decimals
Use what you already know about subtracting whole numbers.
Pay attention to the place values of the minuend and subtrahend
when you place the decimal point in the difference.
Example
6.21 (minuend)
- 2.75 (subtrahend)
1s
Think: Can I remove 7 tenths from 2 tenths? (no)
Think: Can I remove 5 hundredths from
1 hundredth? (no)
Trade 1 tenth for 10 hundredths.
Copyright © Wright Group/McGraw-Hill
Subtract the numbers in each column.
0.01s
6. 2
− 2. 7
5
Trade 1 one for 10 tenths.
0.1s
1
5
12
6. 2
− 2. 7
1
5
11
12
11
6. 2
− 2. 7
1
5
3. 4
6
5
Subtraction
Write the problem in a place-value chart.
3.46
3.46 is the difference.
Check Your Understanding
Solve the following problems.
1. 6.3 − 1.9
2. 3.1 − 1.9
3. 6.82 − 5
4. 4.37 − 1.8
5. 2 − 1.13
6. 5.81 − 0.361
7. 1.1 − 0.99
8. 9 − 0.008
Write your answers on a separate sheet of paper.
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Student Practice
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