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)(解析版)

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

.



3

1.8%

3.5

3)*

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)*−−−−

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456

%2(0+,

“7

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%3(0+,89

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<=>

?:;

@8

A:;

@8

.

知识点2具有相反意义的量

1.

BCDEF

GHC8I9

<JK

LM

@.

2.

NO

<=>

JK

LM

@

PH+,QRF<S

@T

U89

QVWLM

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U89

.

X

YTZ[

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^_`ab?Z[8848.86m,c'+8848.86m.

知识点3有理数

1.

dI0Idefd644ef46d+,0g4

hi6+,0

g4hi

f

j.

2.

j

4k

l

j

4kl

j

mn#$4k

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0

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e4

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e

4

cfgh

4/0

4ij"

44



3.ok

p

qfrsqfrs

d0

ddt0

d

40

44t0

4

u0u0

udd0udd0

【题型1认识正负数】

13

=

>?@ABCDEFGHIIIIIIIJIK/>G

124-25··92012%47

AL6MBL5M−18CL4M−7.2D−L3Mπ

NO

B

4P

Q

RST"45IUVWX/0"12Y,

"ZL[\K"]!^_`ab

cL

13

d,

,

HIIIIIIIJI

92012%47

−18−7.2−π

1

K/IIIIkMI

92012%75

lm

BLπ

nj1-1

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xyzH,{|}~€I‚ƒ„

…T†"12I$t‡ˆT‰800@Lyz9]Š‹'ŒIŽ‹'ŒI

[Ž‹'Œ"Y>G

AL+3BLCL0DL||

NO

B−3−3

4P

[\"!,NbcL

Q

RST"!IU‘WX]!Y,

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d,

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I’[Ž‹'Œ"YI

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nj1-2

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C“›”"¡Y™¢H£™YI¤™Y"①0℃¥/¦§I¨Jƒ"/②

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−652

【题型2用正负数表示相反意义的量】

=2

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AL+3.95ċBLċCL+0.05ċDLċ

NO

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.−7.35

−7.35

【题型3正负数比较大小】

=3

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ōêè¦>°CG18963279

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nj∴3-1

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ĢŷŸ

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ŹE_æ−Şş?Ś

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(1)CřF"ŶÍY73.07ċIQřŹE_"ŶÍYźŻŜ−0.18−0.13−0.49

(2)H>1G"ŵżBIQřŝ_ŌpŽ"ŶÍōêŜQřŝ_ŌŶÍōŎŜ­žÍšſƀŶÍÄCƁYÄBŜ

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NO

(1)73.32ċ

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(3)CéT0.13ċ

4P

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řæŶÍ

73.32+0.52=73.84ċ

řŶÍ

=73.66ċ

řŞŶÍ

73.6673.84−0.18+0.06=73.72ċ

řşŶÍ

=73.59ċ

ř?ŶÍ

73.72−0.13=73.1ċ

řŚŶÍ

73.173.59−0.49+0.1=73.2ċI

ŶÍōê"Y

řæIÍšſƀŶÍfC

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CéT0.13ċL73.2−73.07

∴

【题型4借助正负数的实际意义解决实际问题】

=4

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10:00ƈ°0I10fžč°I10fƋč°I=½

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č°>G−1

ALBLCLDL6.15

NO

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【题型5有理数的概念及分类】

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【题型6数的集合】

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4π75

(1)/067

−3{−−3.14−9…}

(2)/067

{…}

(3)e67

{…}

(4)467

{…}

33

NO

IIIII

(1)548.9π25

6

IIII

(2)7

(3)5−3I−I−3.14I0I−9

363

I−3I−9III

(4)48.9725

4P

¶

RST/0"45I[\/0"45ǚÆīĠ,Nbc−−3.14.

>1G[\/0"!īĠ,Nbc

>2G[\/0"!īĠ,Nbc

>3G[\e"!īĠ,Nbc

>4G[\4"!īĠ,Nbc.

33

d,

>G,

/067

IIIII

1{548.9π25…}

6

>G,

/067

IIII

2{7…}

>3G,

e67

{5I−3I−I0−3.14I…}−9

363

>G,

467

I−3I−9III

4{48.9725…}

−−3.14

【题型7有理数与规律探究】

=7

>24-25o@AC·“uǛǗ·ÞߑàGǘ_ǜ/0ŔB–9:ǝ–IǞNB–.

(1)HAĻ"YƁYŜ

(2)ǝHAIBICIDJ"ǟħÍǕŜ

(3)Ǡ2028MYƁYŜǝHÖךAIBICIDJ"ǟħÍǕŜ

NO

(1);(2)B¹D;(3)IA.

4P

ĪÕǝ–9:cļ

AYIBYICYIDY.Ĥ4M_ǡǢ.

d,

,

(1)HAĻ"YL

(2)ǝHBID"ÍǕCL

(3)2028=4×507,©fǠ2028MYIǝHÖ×A"ÍǕCL

´µ

Q

Rǣļ´

–9:.,

Z´

ŃǤ9:IԅǡǢIþ.

5

nj7-1

>24-25o@AC·º»Ƹ¼·ÞߑàGŃǤB–ä

1,23,4II[\­ž"ǝ–9:

23456

g…Ǡ2024M°L−,−,−⋯

2024

NO

2025

4P

[\ÓJ©nj4"ǥǦIńŪ9:bc’,L

12345

d,

,

IIIIII

23456…

Ĥ_ü"þYǧÍǕ°IǨÍǕ°I4ŊY©HÍǕ"ƩI4ǩ$4Ŋ&∵−−−1IlǠ2024M

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