Of course, primary school children do not use either method in the above forms with brackets; instead they have the

subtrahend directly under the minuend and use crossing out and pre-indices to denote the trading used in Example 1.

For subtractions, each number of the pair became the

subtrahend. To enable testing of the problem size effect, problems composed from pairs with a product [less than or equal to] 25 were classified as small, whereas those with a product [greater than or equal to] 25 were classified as large.

The structure of each trial was as follows: (1) a fixation point was presented for 500 ms; (2) the minuend was presented for 1500 ms; (3) the subtraction sign was presented for 300 ms; (4) the

subtrahend was presented for 2500 ms; (5) the proposed solution was presented for 2500 ms or until the response; and (6) a question about strategy use was presented and remained on the screen until the participant gave an answer.

The red blocks, placed on the right side of the minus sign, represented the

subtrahend, the number to be taken away.

Do all your students know words such as minuend,

subtrahend, quotient, remainder; product and partial product?

This is also true for any combination of any two designs since the absolute difference between them is the same irrespective of which is the minuend or

subtrahend. Table 1 explicitly shows this for some of the designs in Fig 4 and Fig 5.

By utilizing the Gain Basis as the

subtrahend in the gain computation formula, the Basis Reduction Tax Trap would be eliminated as no gain attributable to useless depreciation deductions would ever be triggered.

Difference of rates--ternary relation containing three roles: difference, minuend and

subtrahend;

The number removed from the minuend is called the

subtrahend. Finally, the amount left over or remaining after the problem is completed is called the difference.

In a vertical format, a zero in the ones or tens place of the

subtrahend, or bottom number, means that there is nothing to take away and leaves some students wondering what to do.

teachers give an explanation of "subtraction with regrouping" that is not "a real mathematical explanation."20 She gives an example of a situation in which teachers said that "because the digit at the ones column of the minuend is smaller than that of the

subtrahend, the former should borrow a ten from the tens column and turn it into ten ones." Does that mean "borrowing" (interest free, of course!) is not "a real mathematical explanation"?

As soon as the remainder (5 in this case) is smaller than the

subtrahend, multiply that remainder by 60 and add it to the fractional part of the complement (42 in this case):

P(v) is complete because [P.sub.e](v) is complete and the

subtrahend removes all the nonimmediate supertypes of v resulting in a complete set of direct supertypes P(v).