More Related Content More from Mosab Qasem (8) رياضيات سابع دليل المعلم1. á©LGôe
(115 , 114) äÉëØ°üdG
(h ( `g ( O ( `L (Ü ( CG (1
2( h
CG-6
270 ( `g 3( O 4 ( `L 96 ( Ü 90 ( CG ( 2
15 ( … 12-
2(• 1( ì 480 ( R
8
13
Ü 9CG 2- ( `L 6
¢S 4 ( Ü ¢U 3¢S 125- ( CG (3
3
1 + ¢S ( h 7
¢S 10 (`g `L 8Ü 3CG 7- ( O
3
8 8
( )
3
72 27 - = 72 - 27 - = 2(6-) 2 - 2- ( Ü 2916 = 6(3) * 2(2-) ( CG (4
3
256 8
(2-) 8
¢S
= 6 = 6 ( O 8- = (3) 2 - 2- = ¢U 2 - ¢S ( `L
729 3 ¢U
18 = 5832 3
(Ü 60 = 10 * 6 = 100 * 36 = 3600 ( CG (5
8 64 15
= = 1 ( O 1^4- = 1-10 * 14- = 3-
10 * 2744- 3
= 744^2- 3
( `L
7 49 49
25 > 19 > 16 ( CG (6
5 > 19 > 4 ⇐ 25 > 19 > 16
. 19 Oó©∏d ájôjó≤J º«b »g 4^4 , 4^3 , 4^2 , 4^1 OGóYC’G ¿EÉa 25 ≈dEG É¡æe 16 ≈dEG ÜôbCG 19 ¿CG ɪHh
75 75 75
= =
10 100 100 = 0^75 ( Ü
81 > 75 > 64
9 > 75 >8⇐ 81 > 75 > 64
.75 Oó©∏d ájôjó≤J º«b »g 8^9 , 8^8 , 8^7 , 8^6 OGóYC’G ¿EÉa 64 ≈dEG É¡æe 81 ≈dEG ÜôbCG 75 ¿CG ɪHh
0^75 Oó©∏d ájôjó≤J º«b 0^89 , 0^88 , 0^87 , 0^86 ¿CG èàæj 10 ≈∏Y OGóYC’G √òg ᪰ù≤Hh
q
132651 > 125010 > 125000 ( `L
132651 3
> 125010 3
> 125000 3
51 > 125010 3
> 50
º«b »g 50^4 , 50^3 , 50^2 , 50^1 ¿EÉa 132651 ≈dEG ¬æe 125000 ≈dEG ÜôbCG125010 ¿CG ɪHh
125010 Oó©∏d ájôjó≤J
261
2. »JGP QÉÑàNG
(117 - 116) áëØ°U
35 2
CG ( Ü 4
(Ü-) CG ( CG (1
10 * 5 + 510 + 6 + 410 * 8 + 310 * 7 + 210 * 1 + 110 * 2 + 010 * 3 = 5687123 ( CG (2
6
2
10 * 5 + 110 * 4 + 010 * 2 + 1-10 * 3 + 2-10 * 8 + 3-10 * 7 = 542^387 (Ü
12
¢S = 4*3¢S = 6(2¢S) ( Ü ¢U = 1+5¢U ( CG (3
6
6
( 3- ) ( `L
4
4
3 * 62 ( Ü 2 ( CG (4
14
24 6
( h 2 ( `g 3
( 5 )( O
9
3
¢U ¢S 24- ( `L 1 (Ü ¢S 12- ( CG (5
3
4
`L 16
¢S 72-
7
( h 5
¢U 10¢S 108- ( `g Ü2( O
2
9
¢U
2
Ü + CG ( • ¢U ¢S
(¢U + ¢S) ( ì (¢U + ¢S) ( R
5
2 2
Ü * CG
45 2025 2025
0^45 = = = ( CG (6
100 10000 10000
35- = 42875- 3
(Ü
3 9
1^5 = = ( `L
2 4
49 > 46 > 36 ( CG (7
7> 46 >6
64 Oó©∏d ájôjó≤J º«b »g 6^9 , 6^8 , 6^7 , 6^6 ¿EÉa 36 ≈dEG É¡æe 49 ≈dEG ÜôbCG ¿CG ɪHh
q
53 53 53 (Ü
= = 100 = 0^53
10 100
64 > 53> 49
64 > 53 > 49
8 > 53 >7
262
3. »JGP QÉÑàNG ™HÉJ
(117 - 116) äÉëØ°üdG
º«≤dG √òg ᪰ù≤Hh ,Oó©∏d ájôjó≤J º«b »g 7^4 , 7^3 , 7^2 , 7^1 ¿EÉa 64 ≈dEG É¡æe 49 ≈dEG ÜôbCG 53 ¿CG ɪHh
q
0^53 Oó©∏d ájôjó≤J º«b »g 0^74 , 0^73 , 0^72 , 0^71 ≈∏Y π°üëf 10 ≈∏Y
27 > 21 > 8 ( `L
3> 21 3
> 2 ¿PEG 27 3
> 21 3
> 8 3
.Oó©∏d ájôjó≤J º«b »g 2^9 , 2^8 , 2^7 , 2^6 ¿EÉa 8 ≈dEG É¡æe 27 ≈dEG ÜôbCG 21 ¿CG ɪHh
q
14 10 ( CG ( 8
2 8= 2 5+ 2 3= 2 5+ 9*2 (Ü
7 7= 7 14 - 7 21 = 7 * 4 7- 7 21 ( 9
º°S 150 = ¥hóæ°üdG í£°ùd á«∏µdG áMÉ°ùªdG (10
2
¢S = ¥hóæ°üdG ™∏°V ∫ƒW ¿CG ¢VôØf
q
2
¢S 6 = Ö©µªdG í£°ùd á«∏µdG áMÉ°ùªdG ¿CG ɪH
q
150 = 2¢S 6 ¿PEG
º°S 5 = ¢S ⇐ 25 = 2¢S
263
4. ∂JÉeƒ∏©e ÈàNG
( 1
6
5
(4 , 1-) 4
3
(2 , 5)
(2 , 3-) 2
1
(0 , 0)
6- 5- 4- 3- 2- 1- 1 2 3 4 5 6
(1- , 2-) 1-
2-
3- (3- , 0)
4-
5-
6-
{ ..... , 4 , 3 , 2 , 1 } = • ( 2
( 3
6- 5- 4- 3- 2- 1- ôØ°U 1 2 3 4 5 6
¢S
2
¢S §ªædG IóYÉb ¿PEG 23 3 , 22 2 , 21 1 ¿CG ɪH ( CG ( 4
1 + ¢S * 2 ¢S §ªædG IóYÉb ¿PEG7=1 + 3 * 2 3 ,5 = 1 + 2 * 2 2 ,3 = 1 + 1 * 2 1 ¿CG ɪH ( Ü
9,8,7,6,5,4,3,2,1,0( 5
26 , 24 ( 6
15 , 13 , 11 , 7 , 5 , 3 , 2 ( 7
2,3,5,4,7( 8
.... , 12 , 9 , 6 , 3 ( 9
3 , 2 ( 10
`L
... 8 , 7 , 6 , 5 ( 11
Ü Ü Ü Ü ( 12
CG CG CG CG CG
264
5. (1 - 3) πFÉ°ùeh øjQÉ“ πFÉ°ùeh øjQÉ“ πM
125 áëØ°U áãdÉãdG IóMƒdG
¥ , O , CG , ¢U ( CG (1
AÉà°ûdG , ∞jôîdG , ™«HôdG , ∞«°üdG ( Ü
19 , 17 , 13 , 11 , 7 , 5 ( `L
( CG (2
(Ü
( `L
( CG (3
(Ü
( `L
( CG (4
(Ü
( `L
( O
{12 , 6 , 4 , 3 , 2 , 1} = ´ ( CG (5
{`L ,Ü , CG }=Ω(Ü
{21 , 18 , 15 , 12 , 9 , 6 , 3} = ∑ ( `L
{5 , 3 , 2} = h ( O
265
6. (2 - 3) πFÉ°ùeh øjQÉ“
129 áëØ°U
{™HÉ°ùdG ∞°üdG »a É¡°SQóJ »àdG åMÉѪdG øe åëÑe ¢S : ¢S} ( CG (1
{22 øY π≤j »dhCG OóY ´ : ´} ( Ü
{»©«ÑW OóY CG : CG } ( `L
{26 øY π≤J »àdG 5 äÉØYÉ°†e øe OóY Q : Q} ( O
¢S
{8 , 4 , 2 , 1} = ¢S ( CG (2
¥
{4 , 2 , 5 , 3} = ¥ ( Ü
ø`" ∫ɵ°TCÉH É¡∏«ãªJ øµªj ’ {.... , 104 , 102 , 100} = `g ( `L
{5 , 3 , 2 , 1} = ´ ( CG (3
{4 , 3 , 2 , 1} = ∫
{10 , 8 , 6 , 4 , 2} = Ω
{5 øe πbCG »©«ÑW OóY P : P} = ∫ ( Ü
{11 øe πbCG »LhR »©«ÑW OóY O : O} = Ω
á«¡àæe ( CG (4
á«¡àæe ô«Z ( Ü
á«¡àæe ô«Z ( `L
á«¡àæe ô«Z ( O
266
7. (3 - 3) πFÉ°ùeh øjQÉ“
134 áëØ°U
{7 , 5 , 3 , 2} = ¢S (1
{7 , 5 , 3 , 2} = ¢U
.¢S ¢U ∂dòch ¢U ¢S ¿CG …CG iôNC’G øe á«FõL áYƒªée ɪ¡æe kÓc ¿C’ ,º©f
.Ø hCG { } õeôdÉH É¡d õeôjh á«dÉîdG áYƒªéªdG (2
.á«fÉãdG áYƒªéªdG »a IOƒLƒe ≈dhC’G áYƒªéª∏d É¡©«ªL ô°UÉæ©dG ¿PEG ¿ÉàjhÉ°ùàe ø«àYƒªéªdG ¿CG ɪH (3
q
10 = Ü ¿CG …CG
q
( CG (4
(Ü
( `L
=( O
{5 , 1 , 3} = ¢S ( CG (5
{7 , 4 , 5 , 3 , 1} = ∫ ( Ü
.(∫ ≈dEG »ªàæj) ∫ »a OƒLƒe ¢S »a ô°üæY πc ¿C’ ;º©f ( `L
( CG (6
(Ü
( `L
( O
( `g
( h
=( R
(ì
(•
267
8. (4 - 3) πFÉ°ùeh øjQÉ“
138 áëØ°U
(1
{8 , 7 , 6 , 5 , 4} = CG (2
{9 , 7 , 5 , 3} = Ü
{7 , 5} = Ü CG
{8 , 6 , 4 , 2} = CG (3
{3 , 0 , 4 , 6} = Ü
{1 , 3 , 5 , 4 , 6} = `L
{6 , 4} = Ü CG
{6 , 4} = CG Ü
{6 , 4} = {3 , 4 , 6} CG = (`L Ü) CG
{6 , 4} = `L {6 , 4} = `L (Ü CG)
á«©«ªéJ á«∏ªY ™WÉ≤àdG
Ω á£≤ædG ( CG (4
Ω á£≤ædG ( Ü
¢U ¢S ( `L
Ω á£≤ædG ( O
´ Ω ( `g
{¢U , ¢S} (h
Ø= (R
268
9. (5 - 3) πFÉ°ùeh øjQÉ“
143 áëØ°U
{2 , 9 , 7 , 5} = Ω ∫ (1
{5 , 9 , 7 , 2} = ∫ Ω
´ (Ω ∫) = {9 , 7 , 5 , 4 , 2} = (´ Ω)
∫
{7} = (´ Ω) ∫
{7 ,5} {9 , 7} = (´ ∫) (Ω ∫)
{9 , 7 , 5} =
{ O , Ω , ì , CG} = ´ (2
{ O , ì , CG} = ∫
{ O , Ω , ì, CG} = ∫ ´
{ 25 , 20 , 15 , 10 , 5} = CG (3
{ 27 , 18 ,9} = Ü
{ 27 , 18 , 9 , 25 , 20 , 15 , 10 , 5} = Ü CG
Ω ¢S ( CG (4
Ω ¢S ( Ü
´ (Ω ¢S) ( `L
´ ¢S ( O
{9 , 4 , 7 , 5 , 1} = CG (5
{ 10 , 8 , 9 ,4} = Ü
{ 10 , 9 , 8 , 7 , 5 , 4 , 1} = Ü CG , { 9 , 4} = Ü CG
( CG (6
25 = 13 + 12 = ÜÓ£dG OóY = Ü CG á∏°ùdG Iôc hCG Ωó≤dG Iôc ¿ƒ∏°†Øj øjòdG ( Ü
15 = 25 - 40 ( `L
269
10. (6 - 3) πFÉ°ùeh øjQÉ“
147 áëØ°U
(1
{ 5 , 3} = Ü - CG ( CG (2
{ 4 , 2} = CG - Ü ( Ü
{ 7 , 5 , 3} = ´ - CG ( `L
{ 6 , 9 , 4} = CG -´ ( O
{ } = Ü - Ü ( `g
{ 7 } = ´ - (Ü CG) ( h
{ 5 , 3 } = Ü - (Ü CG) ( R
∫ Ω
( CG (3
{º°UÉY , óªëe} ( Ü
{≈«ëj , óªMCG} ( `L
{Ö©°üe , IõªM} ( O
270
11. (7 - 3) πFÉ°ùeh øjQÉ“
151 áëØ°U
{ 15 , 11 , 3 , 1} = ¢S ( CG (1
{ 9 , 3 , 2} = ´ ( Ü
{ } = ∑ ( `L
{ 15 , 11 , 9 , 5 , 3 , 2 , 1} = ∑ = ¢S ¢S ( O
{ } = ´ ´ ( `g
{ 15 , 11 , 1 } = ´ - ¢S ( h
{ 7 , 9 , 4 , 2} = ´ ( CG (2
{ 5 , 3 , 1 , 7 , 9} = ∫ ( Ü
{ 8 , 6} = ∫ ´ ( `L
{ 7 , 9 , 5 , 4 , 3 , 2 , 1} = ∫ ´ ( O
{8 , 6 , 5 , 4 , 3 , 2 , 1} = ∫ ´ ( `g
{9 , 7} = ∫ ´( h
{8,6,3,5,1}=´=(´)( R
.¿ƒàjõdG áYGQR ¿ƒ∏°†Øj 37 ( CG (3
.¿ƒª«∏dG áYGQR ¿ƒ∏°†Øj 48 ( Ü
. kÉ©e ø«Øæ°üdG áYGQR ¿ƒ∏°†Øj 12 ( `L
.ø«Øæ°üdG øe …CG áYGQR ¿ƒ∏°†Øj ’ ø«YQGõe 3 ( O
271
12. (8 - 3) πFÉ°ùeh øjQÉ“
155 áëØ°U
{(2 , 1) , (5 , 1) , (2 , 3) , (5 , 3) , (2 , 8) , (5 , 8)} = ¿ * Ω ( CG (1
{(1 , 2) , (3 , 2) , (8 , 2) , (1 , 5) , (3 , 5) , (8 , 5)} = Ω * ¿ ( Ü
{(2 , 2) , (5 , 2) , (2 , 5) , (5 , 5)} = ¿ * ¿ ( `L
{(3 , 1) , (8 , 1) , (1 , 1) , (1 , 3) , (8 , 3) , (3 , 3) , (1 , 8) , (3 , 8) , (8 , 8)} = Ω * Ω ( O
{ } = Ω * ¿ * ¿ * Ω ( `g
{ }=Ω*¿*¿*¿( h
{3 , 1} = Ω , { `L , Ü , CG} = ¢S (2
{(3 , 3) , (3 , 2) , (3 , 0) , (3 , 5) , (3 , 1)} (3
{(3 , 3) , (2 , 2) , (0 , 0) , (5 , 5) , (1 , 1)} (4
Gô°üæY 18 = 3 * 6 = ô°UÉæ©dG OóY (5
k
5 = CG (6
4=Ü
{(3 , 3) , (2 , 3) , (1 , 3) (3 , 2) , (2 , 2) , (1 , 2) (3 , 1) , (2 , 1) , (1 , 1)} = CG * CG (7
272
13. (9 - 3) πFÉ°ùeh øjQÉ“
163 áëØ°U
¢S Ω ¢S ¢S Ω ¢S
(`L) (Ü) ( CG )
{(4 , 2)} ( `L {(4 , 2) , (2 , 1)} ( Ü {(6 , 3) , (4 , 2) , (2 , 1)} ( CG (1
ábÓY â°ù«d ( O ábÓY â°ù«d ( `L ábÓY â°ù«d ( Ü ábÓY ( CG (2
{(3 , 1) , (2 , 1)} = 1´ ( CG (3
{(4 , 3) , (4 , 2) , (4 , 1)} = 2´
{(4 , 3) , (3 , 2) , (2 , 1)} = 3´
{(3 , 4) , (2 , 3) , (1 , 2)} = 1´( Ü
n
{(3 , 3) , (2 , 3) , (1 , 3)} = 2´
n
{(2 , 4)} = 3´
n
{(á«FGƒg áLGQO , IôFÉW) , (IQÉ«°S , IôFÉW) , (á«FGƒg áLGQO , IQÉ«°S)} (4
{4 , 3 , 2 , 1 , 0} = ∫ÉéªdG (5
{12 , 9 , 6 , 3 , 0} = ióªdG
¢S * 3 = ¢U
¢S 2 = ¢U (6
{100 , 95 , 90 , 85 , 80 , 75 , 70} = ∫ÉéªdG
{200 , 190 , 180 , 170 , 160 , 150 , 140} = ióªdG
273
14. á©LGôŸG
164 áëØ°U
{ 15 , 11 , 10 , 9 , 8 , 7 , 6 , 4 , 2 , 1} = Ω ¢S ( CG (1
{ 9 , 7} = Ω ¢S ( Ü
{11 , 10 , 8 , 6} = Ω - ¢S ( `L
.ÜÓW 10 §≤a äÉ«°VÉjôdG »a Gƒëéf øjòdG ÜÓ£dG OóY ( CG (2
.ÜÓW 9 §≤a AÉjõ«ØdG »a Gƒëéf øjòdG ÜÓ£dG OóY ( Ü
.ÜÓW 6 É©e AÉjõ«ØdGh äÉ«°VÉjôdG »a GƒÑ°SQ øjòdG ÜÓ£dG OóY ( `L
k
. kÉÑdÉW 39 AÉjõ«ØdG hCG äÉ«°VÉjôdG »a Gƒëéf øjòdG ÜÓ£dG OóY ( O
{ ¿ , O , Q , ∫ , CG} = ¢S ( CG (3
.´ áYƒªéª∏d »ªàæj ’h ¢S áYƒªéª∏d »ªàæj Q ±ôëdG ¿C’ , ’ ( Ü
( `L
{¿ , ∫ , CG} = ´ ¢S ( O
{9 , 7 ,5} = øªjC’G ±ô£dG ( CG (4
{9 , 7 ,5} = ô°ùjC’G ±ô£dG
{9 , 8 , 7 , 6 , 5 , 2 ,1} = øªjC’G ±ô£dG (Ü
{9 , 8 , 7 , 6 , 5 , 2 ,1} = ô°ùjC’G ±ô£dG
{(5 , 8) , (3 , 8) (5 , 7) , (3 , 7) , (5 , 6) , (3 , 6)} = ´ (5
{(3 , 2) (2 , 1) , (0 , 0) , (1 , 1-) , (1- , 1-)} = ´ (6
á«¡àæe ( `L á«¡àæe ( Ü á«¡àæe ( CG (7
{ }( O Ü CG ( `L Ü CG ( Ü {Ü} ( CG (8
{O , `L , Ü ,CG} ( ì { }( R Ü CG ( h O `L ( `g
¢U Ω ( h ¢U Ω ( `g ´ Ω ¢S ( O ´ Ω ¢S ( `L Ω ¢S ( Ü ¢U ¢S ( CG (9
274
15. »JGòdG QÉÑàN’G
166 áëØ°U
`L ( 1 ) (1
Ü(2)
CG ( 3 )
`L ( 4 )
Ü(5)
{7 , 6 , 4 ,2} = ∫ ( CG (2
{6 , 5 , 3 ,2} = Ω ( Ü
{ } = ∑ ( `L
∫ = {7 , 6 , 4 ,2} = ∫ - ∑ ( O
{ (12 , 6) (16 , 4) (12 , 4) (4 , 4) (16 , 2) (12 , 2) (4 , 2)} = ´ ( CG (3
{6 , 4 ,2} = ∫ÉéªdG
{16 , 12 ,4} = ióªdG
275
16. ∂JÉeƒ∏©e ÈàNG á∏Ä°SCG äÉHÉLEG
170 áëØ°U
¢U + 6
¢S (Ü 4 + ¢S 5 ( CG (1
:»JCÉj ɪe πµd É¡∏ãªj …òdG …ôÑédG QGó≤ªdGh á∏ªédG ø«H π°U (2
¢S - 4 Ée OóY ≈dEG 4 ™ªL èJÉf ( CG
¢S + 4 4 ≈∏Y OóY ᪰ùb èJÉf ( Ü
4 _ ¢S 4 øe Ée OóY ìôW èJÉf ( `L
4 - ¢S Ée OóY øe 4 ìôW èJÉf ( O
3 2 1 Iô≤ØdG ºbQ (3
Ü O O áHÉL’G õeQ
Ée OóY ≈dEG 3 ™ªL èJÉf ( CG (4
Ée OóY ≈∏Y 27 ᪰ùb èJÉf ( Ü
Ée OóY »a 15 Oó©dG Üô°V π°UÉM ( `L
276
17. (1 - 4) πFÉ°ùeh øjQÉ“ á©HGôdG IóMƒdG
176 áëØ°U È÷G
6 = πeÉ©ªdG ⇐ óMGh óM ⇐ ¢U ¢S 6 (1
5- = »fÉãdG óëdG πeÉ©e , 1- = ∫hC’G óëdG πeÉ©e ⇐ ¿GóM ⇐ ¢U 5 - ¢S 1-
3 3
5- 5-
6
= πeÉ©ªdG ⇐ óMGh óM ⇐ ´ ¢U ¢S 6
1- = ∫hC’G óëdG πeÉ©e ⇐ OhóM áKÓK ⇐ ∫ + ´ + ¢U-
1 = ådÉãdG óëdG πeÉ©e , 1 = »fÉãdG óëdG πeÉ©e
24- = 4 * 3- * 2 = ¢U ¢S 2 ( CG (2
1 1
9- = 6 - 3- = 3- * 2 + 4 * 3- * 4 = ¢S 2 + ¢U ¢S 4 ( Ü
6 = 6 - 12 = 6 - 4 * 3 = 6 - ¢U 3 ( `L
¢S = IQhóæÑdG øe ≠c 1 øªK :¿CG ¢VôØf (3
q
¢U = QÉ«îdG øe ≠c 1 øªK
´ = ¿ƒª«∏dG øe ≠c 1 øªK
´ + ¢U 3 + ¢S 5 = óªëe ¬©aO …òdG ≠∏ѪdG
¢U 2 + ¢S 2 = êÉ«°ùdG ∫ƒW ( CG (4
kGôàe 220 = 50 * 2 + 60 * 2 = êÉ«°ùdG ∫ƒW ( Ü
.ÜÉàc (8 - ¢S) = ódÉN óæY â«≤H »àdG ÖàµdG OóY (5
.(1 + ´2) * 3 = ™∏°†ªdG ∫ƒW * 3 = ´Ó°VC’G ≥HÉ£àªdG å∏ãªdG §«ëe (6
.(ôàe 3 + ´6) =
2
º°S 6 = 2 * 3 = áMÉ°ùªdG ( CG (7
2
º°S 180 = 12 * 15 = áMÉ°ùªdG ( Ü
277
18. (2 - 4) πFÉ°ùeh øjQÉ“
180 áëØ°U
CÉ£N ( O CÉ£N ( `L áMƒàØe ( Ü áë«ë°U ( CG (1
CÉ£N ( R áMƒàØe ( h áMƒàØe ( `g
{13 , 15 , 11 , 9 , 7 , 5 , 3 , 1} ( CG (2
{10 , 9 , 8 , 7 , 6 , 5 , 4 , 3 , 2 , 1} ( Ü
{13 , 11 , 7 , 5 , 3 , 2} ( `L
{15 , 12 , 9 , 6 , 3} ( O
{8 , 1} ( `g
{3 , 2 , 1} ( h
{ }( R
{9 , 8 , 7 , 6} ( ì
{4 , 3 , 2 ,1} ( CG (3
{... , 3- , 2- , 1- , 0 , 1 , 2 , 3 , 4} ( Ü
É¡∏M áYƒªée ɪæ«H ,Ø »g á«©«Ñ£dG OGóYC’G áYƒªée »a 1 = 2 + ¢S áMƒàتdG á∏ªédG πM áYƒªée kÓãe , º©f (4
.{1-} »g áë«ë°üdG OGóYC’G »a
(2-) + 8 = (2-) + 2 + ¢S 3 (5
6 = ¢S 3
3 _ 6 = 3 _ ¢S 3
2 = ¢S
{2} = qπëdG áYƒªée
{2 , 1 ,0} = qπëdG áYƒªée (6
278
19. (3 - 4) πFÉ°ùeh øjQÉ“
185 áëØ°U
15- = Ü , 5 = CG Gk ôØ°U = (15-) + ¢S 5 ( CG (1
15 = Ü , 5- = CG Gk ôØ°U = ¢S 5- 15 hCG
11 = Ü , 1- = CG Gk ôØ°U = 11 + ¢S- ( Ü
11- = Ü , 1 = CG Gk ôØ°U = 11 - ¢S hCG
12- = Ü , 3- = CG Gk ôØ°U = 12 - ¢S 3- ( `L
12 = Ü , 3 = CG Gk ôØ°U = 12 + ¢S3 hCG
4- = Ü , 2 = CG Gk ôØ°U = 4 - ¢S 2 ( O
4 = Ü , 2- = CG Gk ôØ°U = 4 + ¢S2- hCG
7 _ 21 = 7 _ ¢S 7 ⇐ 21 = ¢S 7 ⇐ (5-) + 26 = (5-) + 5 + ¢S 7 ( CG (2
3 = ¢S ⇐
26 = 5 + 21 = 5 + 3 * 7 : ≥≤ëàdG q
¢S ¢S ¢S
10 * 4 = 4 * 4 ⇐ 10 = 4 ⇐ 7 + 3 = 7 + 7 - 4 ( Ü
40 = ¢S ⇐
3 = 7 - 10 = 7 - 40 : ≥≤ëàdG q
4
4 _ 12 = 4 _ ¢S 4 ⇐ 12 = ¢S 4 ⇐ (5-) + 17 = (5-) + 5 + ¢S 4 ( `L
3 = ¢S ⇐
17 = 5 + 12 = 5 + 3 * 4: ≥≤ëàdG q
2- _ 12 = 2- _ ¢S 2- ⇐ 12 = ¢S 2- ⇐ 18 + (6-) = ¢S 2 - 6 + (6-) ( O
6- = ¢S
18 = 6- * 2 - 6: ≥≤ëàdG q
{5} ( O {0} ( `L {6 2 } ( Ü {0^6} ( CG (3
3
.¢Vô©dG * 2 + ∫ƒ£dG * 2 = π«£à°ùªdG §«ëe (4
¢S = ¢Vô©dG ¿CG ¢VôØf
80 = ¢S 2 + 50 ⇐ 80 = ¢S 2 + 25 * 2 ¿PEG
80 + (50-) = ¢S2 + 50 + (50-) ⇐
2 _ 30 = 2 _ ¢S2 ⇐ 30= ¢S 2 ⇐
kGôàe 15 = ¢S ⇐
5 _ 21- = ¢S ⇐ 21- = ¢S 5 ⇐ (3-) + 18- = (3-) + 3 + ¢S5 ( CG (5
4^2- = ¢S ⇐
18- = 3 + 21- = 3 + 4^2- * 5 : ≥≤ëàdG q
4 = ¢S ⇐ 6 _ 24 = 6 _ ¢S 6 ⇐ 24 = ¢S 6 ( Ü
24 = 8 + 16 = 4 * 2 + 4 * 4 : ≥≤ëàdG
q
279
20. (4 - 4) πFÉ°ùeh øjQÉ“
189 áëØ°U
25- = 6 + ¢S 4 ( CG (1
15- = 7 - ¢U 2 ( Ü
6 = 5 - ¢U 4 ( `L
72 = 8 - ¢S ( O
45 = ¢S6 ( `g
64 = 4 - ¢S ⇐ ¢S Oó©dG ¢VôØf ( CG (2
70 = 15 + ´ 2 ⇐ ´ Oó©dG ¢VôØf( Ü
101 = 1 + ¿2 ⇐ 1 + ¿ »fÉãdG Oó©dG ⇐ ¿ ∫hC’G Oó©dG ¢VôØf ( `L
10 = (7 - ¢S) * 2 ⇐ ¢S Oó©dG ¢VôØf ( O
20 = 7 + ¢U ⇐ ¢U ôª©dG ¢VôØf ( `g
12 + ¢S = ¢S 5 ⇐ ¢S Oó©dG ¢VôØf (3
215 = 120 - ´ ⇐ ´ »∏°UC’G ´ÉØJQ’G ¢VôØf (4
280
21. (5 - 4) πFÉ°ùeh øjQÉ“
192 áëØ°U
Gôàe (3 - ¢S2) = ∫ƒ£dG ⇐ Gôàe ¢S = ¢Vô©dG ¿CG ¢VôØf (1
k k
(¢Vô©dG + ∫ƒ£dG) * 2 = á≤jóëdG §«ëe
174 = (3 - ¢S 2 + ¢S) * 2 ¿PEG
174 = 6 - ¢S6 ⇐ 174 = (3 - ¢S3) * 2
Gôàe 30 = ¢S ⇐ 180 = ¢S6 ⇐
k
Gôàe 57 = 3 - 30 * 2 = ∫ƒ£dG ,Gôàe 30 = ¢Vô©dG ¿PEG
k k
¿ = ´Ó°VC’G óMCG ∫ƒW ¿CG ¢VôØf (2
q
2 + ¿ = ådÉãdG ™∏°†dGh 1 + ¿ = »fÉãdG ™∏°†dG ¿PEG
¬YÓ°VCG ∫GƒWCG ´ƒªée = å∏ãªdG §«ëe
39 = 3 + ¿3 ⇐ 39 = (2 + ¿) + (1 + ¿) + ¿
3 - 39 = 3 - 3 + ¿3 ⇐
3 _ 36 = 3 _ ¿3 ⇐ 36 = ¿3 ⇐
12 = ¿ ⇐
Gôàe 13 = »fÉãdG ™∏°†dG ∫ƒW ,Gôàe 12 = ∫hC’G ™∏°†dG ∫ƒW
k k
Gôàe 14 = ådÉãdG ™∏°†dG ∫ƒW
k
¢S 78^5 = ¢S * 2(5) 3^14 = ì (3
´ÉØJQ’G »a IOÉjõdG ó©H ºéëdG
(2 + ¢S) 2(5) 3^14 = ì
(2 + ¢S) 78^5 =
157 + ¢S 78^5 =
º°S 157 = (¢S78^5) - (157 + ¢S78^5) = ì - ì :ºéëdG »a IOÉjõdG
3
äÉeÓ©dG OóY _ äÉeÓ©dG ´ƒªée = ∫ó©ªdG (4
¢S = É¡«∏Y π°üëj ¿CG Öéj »àdG áeÓ©dG ¿CG ¢VôØf
q
85 = 5 _ (¢S + 71 + 94 + 82 + 80) ¿PEG
425 = ¢S + 327 ⇐ 85 * 5 = ¢S + 327
327 - 425 = ¢S ⇐
98 = ¢S ⇐
281
22. (5 - 4) πFÉ°ùeh øjQÉ“
192 áëØ°U
1 + ¢S = »fÉãdG Oó©dG ⇐ ¢S ∫hC’G Oó©dG ¢VôØf (5
196 = ¢S2 ⇐ 197 = 1 + ¢S2 ⇐ 197 = 1 + ¢S + ¢S
98 = ¢S ⇐
99 = »fÉãdG Oó©dG , 98 = ∫hC’G Oó©dG
5 - ¢S = äGƒæ°S 5 πÑb √ôªY ⇐ áæ°S ¢S = ¿B’G º°TÉg ôªY ¿CG ¢VôØf (6
q
15 - ¢S3 = (5 - ¢S)3 = äGƒæ°S 5 πÑb √ôªY ∫ÉãeCG áKÓK ⇐
17 = ¢S ⇐ 51 = ¢S3 ⇐ 36 = 15 - ¢S 3 ⇐
áæ°S 17 = ¿B’G º°TÉg ôªY
¿ = ∫hC’G Oó©dG ¿CG ¢VôØf (7
2 + ¿ = ådÉãdG Oó©dGh 1 + ¿ = »fÉãdG Oó©dG ¿PEG
138 = áKÓãdG OGóYC’G ´ƒªée
138 = 3 + ¿3 ⇐ 138 = (2 + ¿) + (1 + ¿) + ¿
3 - 138 = 3 - 3 + ¿3 ⇐
3 _ 135 = 3 _ ¿3 ⇐135 = ¿3 ⇐
45 = ¿ ⇐
Gôàe 47 = ådÉãdG Oó©dG ,Gôàe 46 = »fÉãdG Oó©dG , 45 = ∫hC’G Oó©dG
k k
5 + ¢S = ôÑcC’G Oó©dG ⇐ ¢S = ô¨°UC’G Oó©dG ¢VôØf (8
4 = ¢S3 - 10 + ¢S2 ⇐ 4 = ¢S3 - (5 + ¢S) 2
10 - 4 = ¢S- ⇐
6 = ¢S ⇐ 6- = ¢S- ⇐
11 = ôÑcC’G Oó©dG , 6 = ô¨°UC’G Oó©dG
282
23. á©LGôe
193 áëØ°U
`L (9) CG (8) `L (7) Ü (6) CG (5) O (4) `L (3) `L (2) O (1) (1
2 - = ¢S ⇐ 5 _ 2- = 5 _¢S 5 ( CG (2
5
2- = 10 - = 2 - * 5 ≥≤ëàdG
5 5 q
11- = ¢S- ⇐ 4 - 7- = ¢S- ⇐ 7- = 4 + ¢S- ( Ü
11 = ¢S ¿PEG
7- = 4 + 11- ≥≤ëàdG
q
41 = ¢S ⇐ 40 = 1 - ¢S ⇐ 10 * 4 = (1 - ¢S) 1 * 4 ( `L
4
10 = 40 * 1 = (1 - 41) 1 ≥≤ëàdG
4 4 q
3^6- = ¢U ⇐ 0^5 + 4^1- = ¢U ( CG (3
25- = ¢S7- ⇐ 21 - 4- = ¢S7- ⇐ 4- = 21 + ¢S7- ( Ü
4 25
3 7 = 7 = ¢S ⇐ 7- _ 25- = 7- _ ¢S7- ⇐
ôNBG πM
4- = (3 - ¢S) 7-
4 = 3- ¢S
7
3 4 = 3 + 4 = ¢S
7 7
øµªe ô«Z Gògh GôØ°U = 8- ⇐ ¢S4 = 8 - ¢S 4 ( `L
k
πM É¡d ¢ù«d ádOÉ©ªdG ⇐
3 - ¢S3 = 1 - ¢S2 ⇐ 3 - ¢S3 = 5 + 6 - ¢S2 ( O
2 = 3 + 1 - = ¢S ⇐
6 ¢S 2 ¢S ¢S ¢S
1 = 6 + 6 ⇐ 6 = 3 + 6 ( `g
1 ¢S 3
6 = ¢S 2 ⇐ 6 = 6
12 = ¢S
¢S = π«£à°ùªdG ¢VôY ¢VôØf (4
3 + ¢S2 = π«£à°ùªdG ∫ƒW ¿PEG
¢Vô©dG + 2 + ∫ƒ£dG * 2 = π«£à°ùªdG §«ëe
30 = ¢S2 + (3 + ¢S2) 2
30 = ¢S2 + 6 + ¢S4
24 = ¢S6
4 = ¢S
3 + 4 * 2 = π«£à°ùªdG ∫ƒW , QÉàeCG 4 = π«£à°ùªdG ¢VôY
Gôàe 11 =
k
283
24. »JGòdG QÉÑàN’G ™HÉJ
(195) áëØ°U
10 + ¢S7 + ¢S7- = ¢S2 + ¢S 7- ( CG (1
10 =¢S5-
5- _ 10 = 5- _ ¢S5-
2- = ¢S
3^6 - 4^2 = ¢U 1^5 + ¢U 0^5 ( Ü
0^3 = ¢U ⇐ 0^6 = ¢U2
0 = ´ ⇐ 0 = ´6 ⇐ 4 - 4 = ´2 + ´4 ( `L
1- = ∫ ⇐ 1- = ∫3 ⇐ 6 - 5 = ∫3 - ∫6 ⇐ 6 + ∫6 = 5 + ∫3 ( O
3
18 =¢S ⇐ 3 + 15 = 3 + 3- ¢S ( CG (2
15 = 3 - 18 ≥≤ëàdGq
9 4 9
162- = ¢S ⇐ 72 - * 4 = ¢S 9 * 4 ( Ü
18- 4
72- = 18- * 4 = 162- * 9 :≥≤ëàdG q
1
¢U = 6 - ¢U- ⇐ ¢U = 6 - ¢U2 - ¢U ( `L
3 - = ¢U ⇐
3- = 0 + 3- = 0 * 2 - 3- = (3 + 3-) 2 - 3- :≥≤ëàdG q
3 =¢S ⇐ 3 - 6 = ¢S3 - ¢S4 ( CG (3
16- = ¢S ⇐ 144- = ¢S9 ⇐ 81 - = 63 + ¢S9 ( Ü
ôNBG πM
81- = (7 + ¢S) 9
9- = 7 + ¢S
16- = 7 - 9- = ¢S
9 = ¢S ⇐ 9- = ¢S- ⇐ 14 - = 5 - ¢S - ( `L
ôNBG πM
9 = ¢S ⇐ 14 = 5 + ¢S ⇐ 14- = (5 + ¢S) -
5- = ¢S ⇐ 5 = ¢S- ⇐ ¢S7 = 5 -¢S5 + ¢S ( O
1^5 = ¢S ⇐ ¢S16 = 24 ⇐ 24 + ¢S16 = 48 ( `g
.¿ÉàjhÉ°ùàe ø«àjhGõdG ¿C’ 13 - ¢S8 = 7 + ¢S6 (4
7 - 13- = ¢S8 - ¢S 6
20- = ¢S2-
10 = ¢S
284
25. ∂JÉeƒ∏©e ÈàNG øjQɪàdGh á∏Ä°SC’G πM
198 áëØ°U á°ùeÉÿG IóMƒ∏d
áªFÉb ( O IOÉM ( `L áLôØæe ( Ü áª«≤à°ùe ( CG (1
IOó©àe ∫ƒ∏M (2
. Ü CG ᪫≤à°ùe á©£b º°SQG ( CG (3
.Ü CG á©£≤dG »aôW óMCG ≈∏Y Égõcôe ≥Ñ£æj å«ëH á∏≤æªdG ™°V ( Ü
( Ü CG ™∏°†dG óæY CGóÑj …òdG èjQóàdG ôàNG) `L á£≤ædG øµàdh á∏≤æªdG ≈∏Y 580 èjQóàdG óæY á£≤f ™°V ( `L
.580 ¢SÉ«≤dG äGP `L Ü CG ájhGõdG ≈∏Y π°üëàd Ü ™e `L π°U ( O
.590 , 5120 ájhGõdG º°Sôd É¡°ùØf äGAGôLE’G Qôc :á¶MÓe
q
º°S 6 º°S 6 .º°S 18 = 6 + 6 + 6 = ¬YÓ°VCG ∫GƒWCG ´ƒªée = ™∏°†ªdG §«ëe (4
º°S 6
´Ó°VC’G OóY ¢ShDhôdG OóY ÉjGhõdG OóY πµ°ûdG (5
6 6 6 »°SGó°ùdG
5 5 5 »°SɪÿG
4 4 4 ™HôŸG
3 3 3 å∏ãŸG
.º°S 5 É¡dƒW O `L á«≤à°ùe á©£b º°SQG ( CG (6
.É¡YÓ°VCG óMCG O `L , O á£≤ædG É¡°SCGQ , 5105 É¡°SÉ«b ájhGR º°SQG ( Ü
.º°S 3 = O CG ¿ƒµj å«ëH ôNB’G ™∏°†dG ≈∏Y CG á£≤f OóM ( `L
q
. º°S 5 É¡dƒW áëàa QÉLôØdG íàaG ( O
.É°Sƒb º°SQGh CG á£≤ædG »a QÉLôØdG ¢SCGQ õ qcQ ( `g
k
.Ü »a ∫hC’G ¢Sƒ≤dG ™£≤j É°Sƒb º°SQGh ,`L á£≤ædG »a QÉLôØdG ¢SCGQ õcQCGh , º°S 3 É¡dƒW áëàa QÉLôØdG íàaG ( h
k
.O `L Ü CG ´Ó°VC’G …RGƒàe ≈∏Y π°üëàd `L , CG ™e Ü π°U ( R
285
26. (1 - 5) πFÉ°ùeh øjQÉ“
203 áëØ°U
.`L á£≤ædG ƒg 4 ájhGõdG ¢SCGQ ( CG (1
O `L , h `L ( Ü
.Ω Ü `g ( `L
`g Ü ( O
(O `L h , Ω `L h ) , (Ω Ü `g , `g Ü CG ) ( `g
(Ü Ω O , O Ω CG ) , (`L Ω Ü , `L Ω CG ) ( CG (2
(`L Ω CG , O Ω Ü ) , (Ü Ω `L , O Ω CG ) ( Ü
.550 = `L Ω Ü > ¥ (3
.550 = O Ω CG > ¥
.5130 = Ü Ω O > ¥
.(¢SCGôdÉH ¿Éà∏HÉ≤àe) 573 = 543 + ¢S (4
.530 = 543 - 573 = ¢S
5 = á©°TC’G OóY 4 = á©°TC’G OóY 3 = á©°TC’G OóY 2 = á©°TC’G OóY (5
10 = ÉjGhõdG OóY 6 = ÉjGhõdG OóY 3 = ÉjGhõdG OóY 1 = ÉjGhõdG OóY
15 = É¡°ùØf ájGóÑdG á£≤f É¡d á©°TCG (6) áà°S øY áéJÉædG ÉjGhõdG OóY ( CG
21 = É¡°ùØf ájGóÑdG á£≤f É¡d á©°TCG (7) á©Ñ°S øY áéJÉædG ÉjGhõdG OóY ( Ü
28 = É¡°ùØf ájGóÑdG á£≤f É¡d á©°TCG (8) á«fɪK øY áéJÉædG ÉjGhõdG OóY ( `L
.á©°TC’G OóY º∏Y GPEG ÉjGhõdG OóY ójóëJ ¬H ™«£à°ùf §ªf óLƒj º©f ( O
.2_ {(1 - á©°TC’G OóY) * á©°TC’G OóY} = ÉjGhõdG OóY :ƒg §ªædG Gòg ( `g
286
27. (2 - 5) πFÉ°ùeh øjQÉ“
208 áëØ°U
(`L Ü O , O Ü CG ) , (O CG `L , Ü CG `L ) ( CG (1
(`L Ω Ü , Ü Ω CG ) , (`L Ω O , O Ω CG ) ( Ü
(`L Ω Ü , O Ω CG ) , (`L Ω O , Ü Ω CG ) ( `L
(`L Ω Ü , Ü Ω CG ) , (`L Ω O , O Ω CG ) ( O
.(áªFÉb) 590 = 2 ¥ (2
¿CG »æ©j Gògh ¿Éà∏eɵàe º«≤à°ùe ≈∏Y ¿ÉJQhÉéàe 545 ,3
5
135 = 545 - 5180 = 3 ¥ ⇐ 5180 = 545 + 3 ¥
.545 = 1 ¥ ¿CG »æ©j Gòg , (¢SCGôdÉH ¿Éà∏HÉ≤àe 545 , 1 )
πëdG (3
(᪫≤à°ùe ájhGR πµ°ûJ) 180 = `L Ü `g ¥ + `g Ü O ¥ + O Ü CG ¥
180 = 530 + `g Ü O
5
¥ + 550
5
100 = 580 - 5180 + `g Ü O ¥
50 ƒg CG ájhGõdG ᪪àe ¢SÉ«b (4
5
q
.5110 É¡°SÉ«b »àdG ájhGõdG »g 570 É¡°SÉ«b »àdG ájhGõdG á∏ªµeh , 520 É¡°SÉ«b »àdG ájhGõdG »g 570 ájhGõdG ᪪àe (5
q q
.570 É¡°SÉ«b »àdG ájhGõdG »g 5110 É¡°SÉ«b »àdG ájhGõdG á∏ªµe (6
q
5
70 = ¢S ⇐ 5140 = ¢S2 ⇐ 550 + (¢S - 590) = ¢S ájhGõdG ¢SÉ«b ¿CG ¢VôØf (7
20 ɡપàeh 570 ájhGõdG ¢SÉ«b ¿PEG
5
¢U - 5180 = ¢U3 ⇐ (¢U - 5180) 1 = ¢U ⇐ ¢U ájhGõdG ¢SÉ«b ¿CG ¢VôØf (8
3
180 = ¢U4 ⇐
5
180
5
45 = 4 = ¢U ⇐
.5135 = 545 - 5180 = É¡à∏ªµe 545 ájhGõdG ¿PEG
.(590 = 543 + 547 ¿C’ , ¿ÉàeÉààe 543 , 547) ( CG (9
(5180 = 540 + 5140 ¿C’ , ¿Éà∏eɵàe 540 , 5140) ( Ü
.( ∂dP ô«Z 546 , 545) ( `L
.(590 = 555 + 535 ¿C’ , ¿ÉàeÉààe 555 , 535) ( O
.(∂dP ô«Z 580 , 5110) ( `g
.(∂dP ô«Z 552 , 5122) ( h
287
28. (3 - 5) πFÉ°ùeh øjQÉ“
212 áëØ°U
.¿GóeÉ©àe ¿Éª«≤à°ùe (1
.¿ÉjRGƒàe ¿Éª«≤à°ùe (2
.¿GóeÉ©àe ¿Éª«≤à°ùe h `g , ¿ Ω , ¿GóeÉ©àe ¿Éª«≤à°ùe h `g , `L Ü (3
.¿ÉjRGƒàe ¿Éª«≤à°ùe ¿ Ω , `L Ü
.ɪ¡©WÉ≤J á£≤f »a áªFÉb ÉjGhR Óµ°û«d ¿É«≤à∏j ¿GóeÉ©àªdG ¿Éª«≤à°ùªdG ( CG (4
.âHÉK kɪFGO ájRGƒàªdG äɪ«≤à°ùªdG ø«H …Oƒª©dG ó©ÑdG ( Ü
.ájRGƒàªdG äɪ«≤à°ùª∏d êPƒªf ójóëdG áµ°S ÉaôW ( `L
.øjóeÉ©àe ø«ª«≤à°ùªd êPƒªf …õ«∏éfE’G ±ôëdG ( O
.ájRGƒàe äɪ«≤à°ùe ( `L O , Ü CG) , ( `L Ü , O CG ) (5
.IóeÉ©àe äɪ«≤à°ùe ( `L Ü , Ü CG ) , ( Ü CG , O CG )
.IóeÉ©àe äɪ«≤à°ùe ( `L O , CG O ) , ( Ü `L , O `L )
������
288
������
29. (4 - 5) πFÉ°ùeh øjQÉ“
217 áëØ°U
.¿ÉJôXÉæàe ¿ÉàjhÉ°ùàe ¿ÉàjhGR (5 , 1 ) ( CG (1
.(¿ÉàØdÉëàe ¿ÉàjhGR) ¿Éà∏eɵàe (5 ,3 )(Ü
(¿ÉàdOÉÑàe ¿ÉàjhGR) ¿ÉàjhÉ°ùàe (6 ,3 ) ( `L
.(¿ÉàØdÉëàe ¿ÉàjhGR) ¿Éà∏eɵàe (6 ,4 )( O
������ .(¿ÉJôXÉæàe ¿ÉàjhGR) ¿ÉàjhÉ°ùàe (8 ,4 ) ( `g
.(¢SCGôdÉH ¿Éà∏HÉ≤àe ¿ÉàjhGR) ¿ÉàjhÉ°ùàe (7 ,6 )( h
.(28 - 5) πµ°ûdG øe 5122 = Ü Ω h ¥ • (2
.¢SCGôdÉH πHÉ≤àdÉH 5122 = ¿ Ω CG ¥•
¿ÉJQhÉéàe ¿ÉàjhGR 558 = 5122 - 5180 = CG Ω h ¥•
.¢SCGôdÉH πHÉ≤àdÉH 558 = ¿ Ω Ü ¥•
.ôXÉæàdÉH 558 = `L ¿ Ω ¥•
������ .ôXÉæàdÉH 5122 = O ¿ Ω ¥•
������ ¢SCGôdÉH πHÉ≤àdÉH 558 = O ¿ `g ¥•
¢SCGôdÉH πHÉ≤àdÉH 5122 = `L ¿ `g ¥•
.(29-5) πµ°T) 5110 = O `L CG ¥ , 538 = O CG Ü ¥ (3
.¿ÉàØdÉëàe ɪ¡fC’ 5180 = Ü CG `L ¥ + CG `L O ¥ ( CG
O CG Ü ¥ + `L CG O ¥ = Ü CG `L ¥ øµd
180 = O CG Ü
5
¥ + `L CG O ¥ + CG `L O ¥ ¿PEG
5
180 = 538 + `L CG O ¥ + 5110
������ .532 = (538 + 5110) - 5180 = `L CG O ¥ ¿PEG
.`L CG O ™e ∫OÉÑàdÉH 532 = Ü O CG ¥(Ü
������
.O CG Ü ™e ∫OÉÑàdÉH 538 = CG O `L ¥ ( `L
…RGƒàe »a O `L CG ájhGõdG πHÉ≤J É¡fCG ÖÑ°ùH hCG) 5180 = O Ü CG å∏ãªdG ÉjGhR ´ƒªée 5110 = O Ü CG ¥( O
(´Ó°VC’G
5
24^5 = ¢S É¡æeh 598 = ¢S4 É¡æeh ôXÉæàdÉH 597 = 1 - ¢S4 : k’hCG (4
5
13 = ¢U É¡æeh 591 = ¢U7 É¡æeh ôXÉæàdÉH 590 = 1 - ¢U7 :Év«fÉK
289
������
30. (5 - 5) πFÉ°ùeh øjQÉ“
221 áëØ°U
(1
ÖÑ°ùdG AGôLE’G ºbôdG
äÉ«£©e k
Ω , ∫ øe Óc ™£≤j ¿ CG
¢SCGôdÉH ¿Éà∏HÉ≤àe ¿ÉàjhGR 3 ¥=1 ¥ Ü
äÉ«£©e 2 ¥=1 ¥ `L
ôXÉæJ ™°Vh ‘ ɪgh 3 , 2 Iƒ£N øe 3 ¥=2 ¥ O
¿ÉàjhÉ°ùàe ¿ÉJôXÉæàe ¿ÉàjhGR ¬æY ódƒJ Ω , ∫ Úª«≤à°ùª∏d ™WÉ≤àdG ¿C’ Ω // ∫ `g
(2 ájô¶f)
∫OÉÑJ ™°Vh »a ɪ¡fC’ 6 ¥ = 2 ¥ (2
(1) ..................... 550 = 2 ¥ É¡æeh
∫OÉÑJ ™°Vh »a ɪ¡fC’ 7 ¥ = 3 ¥
(2) ..................... 570 = 3 ¥ É¡æeh
º«≤à°ùe ≈∏Y IQhÉéàe ÉjGhR 5180 = 7 ¥ + 6 ¥ + 1 ¥
180 = 570 + 550 + 1 ¥ É¡æeh
5
(2) ..................... 560 = 5120 - 5180 = 1 ¥ ¿PEG
(3
(3) (2) (1)
.∫OÉÑàdÉH 5100 = ¢S ,¢SCGôdÉH πHÉ≤àdÉH 5100 = ¢U :(1) πµ°ûdG »a
.º«≤à°ùe ≈∏Y ¿ÉJQhÉéàe 552 = 5128 - 5180 =¢S ,ôXÉæàdÉH 5128 = ¢U :(2) πµ°ûdG »a
.¢SCGôdÉH πHÉ≤àdÉH 552 =¢U ,∫OÉÑàdÉH 552 = ¢S :(3) πµ°ûdG »a
290
31. (6 - 5) πFÉ°ùeh øjQÉ“
227 áëØ°U
(1
.¿ÉàjhÉ°ùàe ¬«a ¿ÉJOÉëdG ¿ÉàjhGõdG ,ájhGõdG ºFÉbh ø«©∏°†dG ≥HÉ£àe å∏ãe ( CG
.ÉjGhõdG OÉMh ´Ó°VC’G ∞∏àîe å∏ãe (Ü
.ájhGõdG êôØæeh ø«©∏°†dG ≥HÉ£àe å∏ãe ( `L
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.ÉjGhõdG OÉM å∏ãe ¬fCÉH √ÉjGhR ¢SÉ«b Ö°ùM ¬Ø°Uh øµªj ɪc
`L CG = Ü CG , 2- ¢S2 = `L CG , ¢S3 = `L Ü ,3 +¢S = Ü CG (3
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.8 = 2 - 5 × 2 = CG `L ,15 = 5× 3 = `L Ü , 8 = 3 + 5 = Ü CG ¿CG »æ©j Gògh
.ájhGõdG êôØæeh ø«©∏°†dG ≥HÉ£àe å∏ãe ƒg `L Ü CG å∏ãªdÉa ∂dòd
.....O Ω Ü å∏ãªdG ,O Ω `L å∏ãªdG ,O `L Ü å∏ãªdG ,`L Ü CG å∏ãªdG ,`L Ω CG å∏ãªdG ,Ü Ω CG å∏ãªdG (4
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32. (7 - 5) πFÉ°ùeh øjQÉ“
230 áëØ°U
5
180 = å∏ãªdG ÉjGhR ´ƒªée (1
5
78= 5102 - 5180= (520 + 582) - 5180=¢S É¡æeh 5180= ¢S + 520 + 582 Gòd •
112 = 568 - 5180= ( 556 + 512) - 5180=¢U É¡æeh 5180= ¢U + 556 + 512 •
5
.575 = ∫ É¡æeh 5150= (530) - 5180= ∫2 É¡æeh 5180= ∫ + ∫ + 530 •
å∏ãª∏d á«LQÉîdG ájhGõdG = IQhÉéªdG GóY á«∏NGódG ájhGõdG ´ƒªée •
5
135 = 5´ + 590
5
45 = 590 - 5135= 5´
5
60 = 53 _ 5180= 5´ É¡æeh 5180= 5h + 5h + 5h •
5
45 = 590 - 5135= 5´
(1).................. 5180 = 4 ¥ + 1 ¥ (2
(2).................... 5180 = 5 ¥+2 ¥
(3).................... 5180 = 6 ¥+3 ¥
540 = 6
5
¥ + 3 ¥ + 5 ¥ + 2 ¥ 4+ ¥ 1+ ¥ ¿CG èàæj (3) , (2) ,(1) ™ªéH
å∏ãe ÉjGhR ´ƒªée 5180 =6¥ 5+ ¥ + 4 ¥ øµd
.(™ªédG èJÉf »aôW øe 5180 ìô£H ) 5360 = 3 ¥ + 2 ¥ 1+ ¥ ¿PEG
. 5180 = 580+¢S3 + ¢S : k’hCG (3
. 5180 = 580 + ¢S4
. 5100 = ¢S4
.575 ,525 : »g ÉjGhõdG äÉ°SÉ«b É¡æeh 525 = ¢S É¡æeh
.1 ájhGõdG »g 5150 ájhGõ∏d IQhÉéªdG ájhGõdG øµàd :É«fÉK
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5
30 = 1 ¥ É¡æeh (º«≤à°ùe ≈∏Y ¿ÉJQhÉéàe ¿ÉàjhGR ) 5180 = 5150 +1 ¥ ¿ƒµ«a
IQhÉéªdG GóY ø«à∏NGódG ø«àjhGõdG ´ƒªée = å∏ãª∏d áLQÉN ¢S ájhGõdG
5
55 = 525 + 530 =
.(1)..........................(º«≤à°ùe ≈∏Y ¿ÉJQhÉéàe ¿ÉàjhGR) 5180 = 4 ¥+1 (4
.(2)............................( å∏ãe ÉjGhR ´ƒªée ) 5180 = 3 ¥ +2 ¥ +1 ¥
.3 ¥ +2 ¥ =4 ¿CG èàæj QÉ°üàN’Gh (2) , (1) ø«àdOÉ©ªdG IGhÉ°ùªH
292