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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

• 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

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

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

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

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

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

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

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

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

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

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