2026七年级数学举一反三系列(沪科)专题1.1 正数和负数(讲义)(原卷版)

专题1.1正数和负数（举一反三讲义）

2024



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知识点1正数和负数的概念

1.





0

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3

1.8%

3.5

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5

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@8

.

知识点2具有相反意义的量

1.

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LM

@.

2.

NO

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LM

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PH+,QRF<S

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U89

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知识点3有理数

1.

dI0Idefd644ef46d+,0g4

hi6+,0

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j.

2.

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j

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【题型1认识正负数】

13

=

>?@ABCDEFGHIIIIIIIJIK/>G

124-25··92012%47

AL6MBL5M−18CL4M−7.2D−L3Mπ

NO1-1

>24-25P@AC·QRST·EFGUVWXYE"

Z[\H,]^_`abcIdef

ghi"12I$Vjkhl800@L[\9Tmn'opIqn'opI

rstqn'op"u>G

AL+3BLCL0DL||

NO1-2

>24-25P@AC−3·vWwx·EFGByz{

|}“~−3”"u€‚ƒ

①②

C“~”"Šu€|‹HŒ|uI|u"€0℃Ž/I‘Je"/

()③④

AL0MBL1MCL2MDL3M

NO1-3

>24-25P@AC·’“”·EJG•B–I`—uUV˜™"š`›œžIŸ

/¡O

i¢O£¤I¢Oi¡O…†¥žMI˜¦HM§C¨C©ª†L•“”

Ir“”–"uL

−723

【题型2用正负数表示相反意义的量】

=2

>24-25P@AC·«”¬­·®¯°±G²³´µ†B¶·#

¸¹º8sº€»¼½3

8»¾€¿À3ÁÂ8ÃÄ3Á€£ÅÆÇ$ÈIÉÊË£Ì"$44;①65

②60860

℃

65L‘Jœ/−3℃③!"#/>ÎÎG④

AL1·BL2·CL3·DL4·

NO2-1

>24-25P@AC·ÏÐÑÒ·EJGHÓÔÕÖJI7×"ØÙu4.00ÚIÛKÓgh4.12ÚI

ܾ+0.12ÚIÝÞÓgh3.95ÚIÜß>G

AL+3.95ÚBLÚCL+0.05ÚDLÚ

NO2-2

>2025·àá&â−3.95·¹ãGäåV+æç"èéiVêˆëæç×ì„íî"ïðI−0.0592ñæ"

ç׍äNòL•óô¼92ñæ"ç×Cõ0.2ÂIÜß+0.2ÂIö÷Âô¼92ñæ"ç

×>G−0.1

ALCõ0.1ÂBLCõ0.3ÂCLBø0.1ÂDLBø0.3Â

NO2-3

>24-25P@AC·RùDú·EJG•û¾'düýLþÿmĀ3.71Âā“+3.71”I

rĂ㥹7.35ÂIHĆćĈā"uL

【题型3正负数比较大小】

=3

>24-25P@AC·vWĉĊ·EFGYJċČČ¾hčĎIďu|ĐđĒēĔĕLĖĖ9T€ôė

Ęę»H0°C†BĚěĘ½»H8°C†BIĜĝĒSĞĔLğĠġĢė»ģĤIĥžÿĥĦČČ/ħėĜ

ĝĨĒSĞĔĩ4ÍuĪħėĩ

ĥžĥ¹ĥsĥīĥĬĥ?ĥĦ

Ę½»>°CG18963279

Ęę»>°CG8201

NO3-1

>24-25P@AC·vWĉĊ−3·EFGH−5−1I0I3IĭīMJIĘ'"u€Œ|u

|u"uL−0.5−1

NO3-2

>24-25?@AB·xWĮį·EJGHI8II0JIĘꏐuIĘ½

uI‘JIİß−2℃℃€ıB−32℃18Üß℃L

NO3-3

>24-25P@AC−32℃·áIJijĴ·EJGBuĵ@ĶķĸĹĺ'ĻÕ#"ĸļQ"žĥê"Ľ§N℃

òľĿ

>“+”Ľ§$žėC¼I“”Ľ§$žėBøIý§uÚG

ŀEž¹s−īĬ?Ħ

Ľ§Nò/Ú+0.25+0.52+0.06+0.1

(1)CĥF"Ľ§u73.07ÚIġĥŀEž"Ľ§uŁłĩ−0.18−0.13−0.49

(2)H>1G"ļŃBIġĥĪžėQń"Ľ§Ę½ĩġĥĪžėĽ§ĘęĩŅņ§ŇňʼnĽ§CŊuBĩ

(3)8CĥF$IġĥF"QńĽ§uC¼hŊuBøhIC¼hĚBøhŁłÚĩ

【题型4借助正负数的实际意义解决实际问题】

=4

>24-25P@AC·Qįŋ”·®¯°±GĸŌ

ō<I†454Ŏ¾1Mcŏý§IŐÜôėCő

10:00cŏ¾0I10c†Ü¾I10c†ŒÜ¾I=•

9:15ܾI10:45ܾ1IœŔ5ŕICő6:15

−1

ܾ>G

ALBLCLDL6.15

NO4-1−4

>24-25P@AC−5·xŖŗŘ·EJG•ûIƒ›ž¤řcIřŚśH−3.45299.5ŜÚÿ300.2Ŝڝŏ

.

"ŝëu7×ëIHûŞCşŠ300.šĭ¤ř"ƒ›ĨŢIĭţŚśu300ŜÚI

+02

+0.2Ę&Ť…†$300ŜÚŁ휑0.2ŜÚI−05Ę&Ť…†$300ŜÚł휑3000.5ŜÚLťƒ›īt

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řIřŚś"ƒ›ĨŢu50.IIByŦuƒ›ˆ"řŚśI‘J|7×"u>ÎÎG−0.5

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AL50.02BL50.01CL49.99DL49.88

NO4-2

>24-25P@AC·àáŧx·®¯°±G•ûuƒ›ıŃ"ŨũĨŢIť/ByŚśŨũ"ŝë

>ý§

ŜÚG

44.9€45.02€44.99€45.01L‘J|7×"uL>Ū‡ūG

①Φ②Φ③Φ④Φ

NO4-3

>24-25P@AC·Ŭ\7ŭ·EJGŮlÊůŰ8Rù"cű•B>¥žcŲ$Rù

k"cI¥žcŲ$Rùų"cG

ŴRù10ŵ8Ħ15cIůŰÊŮl"cŏ4Íu>G

ŶŷůŰŮl

cű/c+2

AL10ŵ8Ħ−1313c€10ŵ9Ħ4cBL10ŵ8Ħ17c€10ŵ8Ħ2c

CL10ŵ8Ħ17c€10ŵ9Ħ4cDL10ŵ8Ħ13c€10ŵ8Ħ2c

【题型5有理数的概念及分类】

=5

>24-25P@AC·’“Ÿ”·®¯°±GByŹ

J

>1GžM„|uŠu€>2GĘ

'"„uı€>3GJŽ/Ę&"€>4GźŻžTu„€>5G/0Āż/0Êıi

/0€>6G„Šu„i„€>7Gıu„Ž|u€>8GÊžſ¾/0€

>9GK/0uƀ/0i0Le"M/ML

NO5-1

>24-25P@AC·ƁRƂX·EFGByŇ“0”"ƃƄJI|e"u>G

AL“Ž/”IŽ/*+!Iu“”8“”"4ƅ

BLŒ|uI|u

CLu„IuĘ'"źŻ

DL|Ɔ‡ˆ4"‰OI|u/0

22

NO

>P@AC“ƇŠ”EJGBy¶

IIIII

5-224-25··0.51.264850349070.2121121112…

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1

NO

>P@ACƋƌƍƎEJGťƏg•B/0

IIIIL‘J/0

5-324-25··035

"Mu>G−1.1−0.8−3

AL4MBL3MCL2MDL1M

【题型6数的集合】

=6

>24-25P@AC·xWĮá·EJGƐBy¶ŪHƑ"żţL

1

I2I0II0.1010010001I%I6I3I3.14I2

327

휋

„67

−3{−…}−12−0.−

467

{…}

K/067

{…}

NO6-1

>24-25P@AC·QRƒƓ·EJGHJƔ7ļŃ"ƕ×ţƖC“√”.

NO6-2

>24-25P@AC·Ŭ\?Ŭ·EFGƐBy¶ŪƗûJƑ"§ƘIŐŪ‡

ƙƚ4"ƛſL

2

IIIII

03+32

−16−−4−3.6

NO6-3

>24-25P@AC·vWĉĊ·EJGƜBy¶ŪƗƝŴ"żê

36

5III8.9IIIII0I23

4π75

(1)/067

−3{−−3.14−9…}

(2)/067

{…}

(3)„67

{…}

(4)467

{…}

【题型7有理数与规律探究】

=7

>24-25P@AC·vW