???????? (??????)

百度用户如发现商家违规售卖香烟，可通过饿了么开设的电话投诉热线、app一键举报功能进行反馈，平台收到相关信息后将第一时间进行处理。

???????? ??????, ?????? ??????????? ?????? ?????????? ?????????. ??? ??????????? ????????????. ???????? ????????, ???????? (?) ?????????? ?????????????????. ????????????????: 5 - 3 ?????? ????????????? ???????? ?????????? ??????????. ???? ????????????? ??????? ???? ???????????? ???????.

?.??:

5-3=2.

???, ????? ?? ?????? ???? ?????? ????? ???????????????????.

?????? ??????, ??????????, ????????? ??????, ??????????, ????????, ?????????, ?????? ????? ???????? ?????? ??????????? ??????, ????????? ??????? ????????? ????????? ????????? ??????? ?????????, ???????? ??????? ????? ???????????.

???????? ?? ??????? ?????????? ???????????. ??? ????????? ???????? ???????????; ?????? ????????? ???????? ??????? ?????????? ????? ???????? ????????? ??????????. ???????????? ?????????? ??????? ????????; ??????, ??????? ????????????? ????? ???? ?????????????? ????? ???? ??????????. ???????? ??????????????? ??? 0 ??? ????????? ??? ??????? ???????????????. ??????? (??????) ??????? ????????? (??????) ?????????? ?????????????? ??????? ???????? ?????? ????????. ?????????? ??????????? ????? ????????. ??????? ???? ???????? ?????? ??????, ??????? ???????? ??????? ???????? ??????????????????? ???????????? ?????????????? ????????. ??????? ?????????????? ??????? ??????????? ???????? ????? ????????????????.

?????????? ???????? ?????????

?????????????????? "?" ?????????? ???????? ??????????????. ???? ???? ???? ?????? ??????????????.

??????????????????:

2-1=1

4-2=2

6-3=3

4-6=-2

"?" ??????????????? ???????? ????? ??????????? ?????????? ?????:

?????? ???? ?????? ?????????? ??? ???????? ??????? ??? ??????? ?????????? ???????????????????, ????????? ??? ?????????? ??????? ??? ???? ???????????. ????????? ??????????? ???? ??? ????????????, ???????? ???? ???????????? ???????????? ??????.

??????????, ????????????? ??? "??????????" ?????? "???????????????" (subtrahend) ??????,^[1]^[2] ???? ????????????? ???????????????? ??????? ?????????? (minuend) ??????.^[1]^[2] ???????? ?????????? ???? ??????????? (difference) ?????? ?????????????????.^[1]^[2]

"????????" ????????? ?????? ?????? ???????? "Subtraction" , ???????? ???????? ?????????? subtrahere ?????????????? ???????????. ???? ???????? ????, sub ("from under") ??????? trahere ("to pull") ???? ??? ??????????????? ????????? ??????????????????.^[3]^[4]

??????????? ??????? ????????????? ????????

???????????

????????, b ???????? ??? ???????????????? ???? ???? a ??????? ???? ???? c ??????? ????????????????.

a ????????? ??????? ????? b ?????? ???????? c ? ????????.

????????? ??????????? ???? ??????? ???????? ???? ??????:

a + b = c.

c ????????? ???????, ?????????? b ?????? ???????? ???????? a ??? ????????????.

?????????? ??????????? ???? ??????? ???????? ???? ??????:

c ? b = a.

????????, 1, 2, 3 ?????? ??? ???????????????????? ???????????????????.

3 ??? ?????????????? 3 ??? ?????????? ??????????? ?????????? ???????????? ?????. ????,

3 ? 0 = 3.

3 ??? ?????????????? 1 ??? ?????????? ????? ?????????? ?????????? ?????? 2. ????,

3 ? 2 = 1.

3 ??? ?????????????? ?????????? ?????? ?????? ?????????? ??????? ???????? ????? ??????? ?????????? ?????. ?????? ???????????????? ?????????? ????????? ????????.

???? ??????

???? ???????? ????????????, ??????? ???? ???????? (0, 1, 2, 3, 4, 5, 6, ...) ????????????? ??????? ????????. ???????????, 4 ????????? ?????? ?????? ?????????? ?????????? 0 ? ????????. ?????? 4 ? 4 = 0. ????? 4 ????????? 5 ?????? ?????????? ??????? ???? ???? ??????????? ??????. (3 ? 4)

??????????????? ?????? ???????? ???????????? ?????.

3 ? 4 = ?1, ??? ????????.

???? ???? ??????, ???????????? ??????? ????? ?????????. ??? ???? ???????? ???????? ????, ???? ???????? ?????? ???????????? ??????????, ????????????????? ???????? ?????? ????????.

26 ? 11 ????????? ???????? ????????. ??????????? ?????? ???????? ?????????:

26 ? 11 ????????? ?????? ????????; ???? ???????? ????? ??? ??????? ?????? ??????.
?????? ???? ???????? (?????? ???) ???????. ??????,

11 - 26 = ?15.

???????????

????????????? ????????, ????????????? ???????? ???????? ???????????????????. ??? ???????????? ????????????? ?????? ???? ???????????? ??????? ???????? ???????????????.

3 ? π = 3 + (?π).

??????? ?????????????, ????????????? ??????????, ???????? ??? ????? ???????? ?????????????? ??????? ??????????????? ????????????. ??????? ??? ?????? ?????? ?????????? ??????????????. ???????? ?????????? ??????? ?????????? ????????? ???????????????. ?????????? ??????? ??????? ???????? ???? ??????? ??????; ????? ???????? ???? ????? ????? ?????. ???? ????????????? ???????? ?????????? ?????????? ?????????, ?????????? ?????????? ?????????????? ?????????? ?????????

????????

?????-????????????????

???????? ???????????????? ????? ???????. ?????? ?????????? ???????????? ????? ?????????????? ?????????? ????, ??? ???????? ?????? ?????? ?????????.

a , b ??? ?????? ?????,

a ? b = ?(b ? a).

?????????????????????

???????????? ?????????? ????? ?????

"a ? b ? c" ???? ???????? (a ? b) ? c ??????? a ? (b ? c) ?? ????????????????? ???????? ???????? ????????? ?????. ???? ???????????? ????????, ??????? ????????????? ????? ???? ????????? ?????????????? ????????.

??????

?????????????, ???????? ?????????????????????? (a) ??? 1 ??? ????????? ?????????? ????????, (a ? 1), ??? ?????????? ????? ??????????????? ?????????? ??????????????. ?????? (a ? 1) ?????? a ??? ?????? (predecessor) ?????????.

????????? ???????

??????????, ???????, ???????? ????? ????????? ????? ??? ???? ???????? ????????? ????, ??? ???????? ??? ????????? ?????????????? ???????. ??????? ????? ???????? ???????????? ??? ???????? ???????????????.

100 ??.??. - 28 ??.??. = 72 ??.??.

54 ??? - 43 ??? = 11 ???

?????????????

??????????????? ??????????, ?????????? ??????????? ??????? ????? ???????????? ??????????? ?? ????????? ??????. ?????????? ??????????? ?????? ??? ??????????? ??????????????? ??????????????. ????? ???????????? ??????????? ?????? ??? ??????????????? ??????????? ?????.^[5]^[6]^[7]

???????????????: ??? ?????????????? ???????? ??????????? ??????????? 30% ?????????????; ????????????????? ??????? 20% ????????? ????????????? ????.

????? ???????????? ??????????? = 20% -30% = -10% = -10 ????????????????
?????????? ??????????? = (-10/30) x 100 = ?33 1/3%

???????? ???????

???????? ???????? ??????? ????????? ???????????????.

???????? ????

???????????????:

1 + ... = 3
???????????? ??????????? ??????????????.
9 + ... = 5
??????????? ???????????? (5) ????????????!
???? ??????? 10 ????????????, ?????????????? ?????? ???? ??????????? ???? 1 ??????????????.
9 + ... = 15
????????? ??????? ??????????? ???????.
(4 + 1) + ... = 7
?????????? ???????????? ???? ??????????????.
????? ???????????.

?????????? ??????? ????????

???????????????:

7 ? 4 = 3
??????? ?????????? ?????????????????.
?????? ??????? ?????? ??????? ?????? ??????? ?????????????? ???????? ????????, ?????????? ?????????? ????????????? 1 ????????????? ??????????? ?????????? ??????????? 10 ???????????????.
15 ? 9 = 6
?????????????? ?????? ??????? ????????? ?????????????? ???????? ???????? ???????? ?????????????? ??????????? ?????????????.
3 ? 1 = 2

???????? ????

??????????? ???????? ?????????? ??????? ???????????????.

???????? ??????? ???????? ??????? ?????? ??????? ???????? ????????? ????? ???????? ????????? ??????? 10 ???????????? ??????? ??????????? ?????????????. ????????????? ???? 10 ????, ???????? ??????? ????????????????? ?????????????? ????????????, ???? ????????????????? 1 ??????????????????????. ??????? ??????????? ???????? ?????????? ????????????? ???? ???????? ???????? ?????????????????.

???????????????:

3 ? 1 = ...
???????????? ??????????? ??????????????.
5 ? 9 = ...
?????? ???????? ??? (5) ???????? ??????!
??????? 10 ???????????????. ???? 10 ???? 5 ???? ???????? ???????? ???????? 7 ????????? 1 ????????????????? 7, 6 ???? ?????????????????.
15 ? 9 = ...
??????????? ??????????????????? ???????????? ???? ??????????????.
6 ? 4 = ...
??????????? ???????????? ???? ??????????????.
????? ???????????.

????????? ???????????

???????? ?????????????? ??????? ?????? ??????? ???????. ??????????? ???????? ?????????? ????????????? ?????????? ????????????? ???????, ???????? ????????????????.^[8]

Example:

1 ? 3 = ?????? ????????.
???????? 5 ???????? 1 ??????????????, 10 ?? 1 ???? ???????????????. ??????? 5, 4 ???? ?????????.
4 ? 9 = ?????? ????????.
???????? 7 ???????? 1 ??????????????, 10 ?? 4 ???? ???????????????. ??????? 7, 6 ???? ?????????.
?????????? ????? ???????? ???????????????:
11 ? 3 = 8
14 ? 9 = 5
6 ? 4 = 2

????? ???????????

???????????? ???????? ??????????????? ????? ????????? ???? ????????????????. ????? ??????????? ?????. ???????? ??????, ??????????, ?????????? ???????????? ????? ????????????? ????? ??? ????????????? ???????????? ??????????? ???????? ???? ???????/???????? ????????? ??????????????????????. ????? ???????????????? ?????????????? ??????? ????? ???????????? ?????????.^[9]

???????????????:

700 ? 400 = 300
???????? ???, ?????? ?????????? ??????? ???????? ????? ??????????? +700.
90 ? 50 = 40
?????? ???, ???????? ?????????? ??????? ???????? ????? ??????????? -40.
3 ? 1 = 2
???????? ???, ?????? ?????????? ??????? ???????? ????? ??????????? +2
+300 ? 40 + 2 = 262

???????????? ???????

??????? ???????? ??????????? ???????????? ??????, ?????? ??????????? ???????? ??????????? ????? ???? ???????? ????????????? ?????????? ?????????? ??????? ??????????????? ??????????.^[10]

???????????????: 1234 ? 567 = ? :

567 + 3 = 570
570 + 30 = 600
600 + 400 = 1000
1000 + 234 = 1234
3 + 30 + 400 + 234 = 667 = ????? ???????????.

???????? ????????? ?????????? ????????

????????????? ?????????? ?????????? ?????? ???????? ????????? ?????????? ???????? ???? ??????? ?????????.^[11]

???????????????: 1234 ? 567 = ? :

1234 ? 500 = 734
734 ? 60 = 674
674 ? 7 = 667

?? ???????

???????? ??? ??????? ?????? ??? ??????????? ??????????? ?????/?????? ????????????? ??????? ????????? ???? ????????? ???????????? ??????? ?????????????????????. ????????????? ??????????? ????????? ??????????? ??????? ??? ???????????????.^[12]

???????????????:

"1234 ? 567 = ?" :

1234 ? 567 = 1237 ? 570 = 1267 ? 600 = 667

???????????

↑ ^1.0 ^1.1 ^1.2 Schmid, Hermann (1974). Decimal Computation (1 ed.). Binghamton, New York, USA: ???? ?????? ??? ?????. ISBN 0-471-76180-X.
↑ ^2.0 ^2.1 ^2.2 Schmid, Hermann (1983) [1974]. Decimal Computation (1 (reprint) ed.). Malabar, Florida, USA: Robert E. Krieger Publishing Company. ISBN 0-89874-318-4.
↑ "Subtraction". (Online). ??????????? ????????????? ?????????. (Subscription or participating institution membership required.)
↑ "Subtrahend" is not a Latin word; in Latin it must be further conjugated, as in numerus subtrahendus "the number to be subtracted".
↑ Paul E. Peterson, Michael Henderson, Martin R. West (2014) Teachers Versus the Public: What Americans Think about Schools and How to Fix Them Brookings Institution Press, p.163
↑ Janet Kolodzy (2006) Convergence Journalism: Writing and Reporting across the News Media Rowman & Littlefield Publishers, p.180
↑ David Gillborn (2008) Racism and Education: Coincidence Or Conspiracy? Routledge p.46
↑ The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Trade First
↑ Partial-Differences Subtraction ????????????? 2025-08-06 at the ??????? ?????????; The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Partial Differences
↑ The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Counting Up
↑ The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Left to Right Subtraction
↑ The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Same Change Rule

???? ???????

Brownell, W. A. (1939). Learning as reorganization: An experimental study in third-grade arithmetic, Duke University Press.
Subtraction in the United States: An Historical Perspective, Susan Ross, Mary Pratt-Cotter, The Mathematics Educator, Vol. 8, No. 1 (original publication) and Vol. 10, No. 1 (reprint.) ????????????? 2025-08-06 at the ??????? ????????? ??.??.???

???????????????

Hazewinkel, Michiel, ed. (2001), "Subtraction", Encyclopedia of Mathematics, Springer, ISBN 978-1556080104
Printable Worksheets: Subtraction Worksheets ????????????? 2025-08-06 at the ??????? ?????????, One Digit Subtraction, Two Digit Subtraction, Four Digit Subtraction, and More Subtraction Worksheets
Subtraction Game at cut-the-knot
Subtraction on a Japanese abacus selected from Abacus: Mystery of the Bead

?????????? ???????????

[Schmid_1974-1] 1.0 ^1.1 ^1.2 Schmid, Hermann (1974). Decimal Computation (1 ed.). Binghamton, New York, USA: ???? ?????? ??? ?????. ISBN 0-471-76180-X.

[Schmid_1983-2] 2.0 ^2.1 ^2.2 Schmid, Hermann (1983) [1974]. Decimal Computation (1 (reprint) ed.). Malabar, Florida, USA: Robert E. Krieger Publishing Company. ISBN 0-89874-318-4.

[3] "Subtraction". (Online). ??????????? ????????????? ?????????. (Subscription or participating institution membership required.)

[4] "Subtrahend" is not a Latin word; in Latin it must be further conjugated, as in numerus subtrahendus "the number to be subtracted".

[5] Paul E. Peterson, Michael Henderson, Martin R. West (2014) Teachers Versus the Public: What Americans Think about Schools and How to Fix Them Brookings Institution Press, p.163

[6] Janet Kolodzy (2006) Convergence Journalism: Writing and Reporting across the News Media Rowman & Littlefield Publishers, p.180

[7] David Gillborn (2008) Racism and Education: Coincidence Or Conspiracy? Routledge p.46

[8] The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Trade First

[9] Partial-Differences Subtraction ????????????? 2025-08-06 at the ??????? ?????????; The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Partial Differences

[10] The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Counting Up

[11] The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Left to Right Subtraction

[12] The Many Ways of Arithmetic in UCSMP Everyday Mathematics Subtraction: Same Change Rule

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