Trade-First Subtraction

Contributed by:

Diego Tue, Mar 15, 2022 07:47 AM UTC

Trade-first subtraction involves:
• Figuring out the place value of digits,
• Making decisions about where trades are necessary,
• Trading first before doing any subtraction, and
• Focusing on the subtraction in one place-value column at a time

1. Everyday Mathematics
Trade-First Subtraction
Left-to-Right Subtraction
(Focus Algorithm)Algorithm

2. Trade-First Subtraction Algorithm
Trade-first subtraction involves:
• Figuring out the place value of digits,
• Making decisions about where trades are necessary,
• Trading first before doing any subtraction, and
• Focusing on the subtraction in one place-value column at a time.
Everyday Mathematics

3. Trade-First Subtraction Algorithm
The trade-first subtraction algorithm looks very similar to the “traditional”
method of subtracting. The key difference is that all trades are completed
before any subtracting.
You can perform the trades beginning from the right or the left. When first
introduced to the algorithm, children may prefer to draw vertical lines
separating the columns.
Solve 9,231 – 4,557 using the trade-first subtraction
Everyday Mathematics

4. Trade-First Subtraction Algorithm
Solve 9,231 – 4,557.
Set up the problem.
Write the numbers in their
place-value columns. 9, 2 3 1
− 4, 5 5 7
Everyday Mathematics

5. Trade-First Subtraction Algorithm
Solve 9,231 – 4,557.
Decide where trades need to
be made.
8 12
The hundreds require a trade.
9, 2 3 1
Go to the thousands place and
break one of the 9 [1000s] − 4, 5 5 7
into 10 [100s]. We now have
8 [1000s] and 12 [100s].
Everyday Mathematics

6. Trade-First Subtraction Algorithm
Solve 9,231 – 4,557.
Decide where trades need to
be made.
11
The tens require a trade.
8 12 13
Go to the hundreds place and 9, 2 3 1
break one of the 12 [100s]
into 10 [10s]. We now have − 4, 5 5 7
11 [100s] and 13 [10s].
Everyday Mathematics

7. Trade-First Subtraction Algorithm
Solve 9,231 – 4,557.
Decide where trades need
to be made.
11 12
The ones require a trade.
8 12 13 11
Go to the tens place and 9, 2 3 1
break one of the 13 [10s] −
into 10 [1s]. We now have 4, 5 5 7
12 [10s] and 11 [1s].
Everyday Mathematics

8. Trade-First Subtraction Algorithm
Solve 9,231 – 4,557
Now we’re ready to subtract.
At this point, the order in 11 12
which the steps are completed 8 12 13 11
will not matter.
9, 2 3 1
Subtract in the thousands, the
hundreds, the tens, and the − 4, 5 5 7
ones column. 4, 6 7 4
Everyday Mathematics

9. Trade-First Subtraction Algorithm
9,231 – 4,557 = 4,674
Note that when children use the trade-first subtraction algorithm to solve an
subtraction problem, they have an opportunity to practice a variety of skills
related to developing number sense and algebraic reasoning.
These skills include:
• Writing numbers according to the place value of the digits,
• Breaking a hundred as 10 [10s]; breaking a ten as 10 [1s], and
• Renaming numbers after shifting a group of 10 [10s] or a group of 10 [1s]
to the column on its right.
Everyday Mathematics

10. Trade-First Subtraction Algorithm
9,231 – 4,557 = 4,674
With the trade-first subtraction method, children easily talk
about the place-value columns within which they are working.
Because all trades are completed first, the procedure itself is
Finally, if children trade where it is not necessary, they can
adjust their final answer by regrouping. See the column-
addition method for more information about regrouping the
Everyday Mathematics

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