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Topic outline
Umutwe wa 1: Imibare kuva kuri 0 1 kugera ku 2 000
1.1 Gusoma imibare kuva kuri 0 kugera ku 2 000
Igikorwa cya 1
Mwitegereze ishusho maze mwigane ibiri gukorwa.
Igikorwa cya 2
Mufate amakarita yanditseho iyi mibare:
Mukore imibare itandukanye iri hagati ya:
1) 1 000 na 1 030
2) 1 040 na 1 05
3) 1 060 na 1 070
4) 1 080 na 1 090
Buri mubarwa ukora inshuro imwe.
Igikorwa cya 3
Musome imibare muhereye ku muto mujya ku munini
Koresha amakarita y’imibare wahawe ukore imibare 3 iri hagati ya 1 000 na 2 000. Nurangiza uyisomere bagenzi bawe.
Mu gakarito karimo udupapuro twanditseho imibare 1234; 1908; 1567; 1324; 1110. Buri wese atombore agapapuro kamwe asome aranguruye ijwi umubare wanditseho.
1.2 Kwandika imibare kuva kuri 0 kugera ku 2 000
Igikorwa
Mukoreshe aya makarita y’imibare. Mukore imibare 4 iri hagati ya 1 000 na 2 000
Muyandike mu magambo hanyuma muyisomere bagenzi banyu. Buri mubarwa ukoreshwe inshuro imwe mu mubare.
Umwitozo
Shaka imibare ibura kuri uyu murongo w’ibara, uyisome unayandike mu magambo.
Shaka imibare iri hagati ya:
a) 1 990 na 2 000
b) 1 240 na 1 250
c) 1 590 na 1 600
d) 1 920 na 1 930
Uyandike mu mibare no mu magambo
Mukoresheje amakarita y’imibare:
Nimukore imibare 4 iri hagati ya 1 000 na 2 000. Nimurangiza muyandike mu magambo hanyuma muyisomere bagenzi banyu. Itegeko: Buri mubarwa ukora inshuro imwe mu mubare
1) Andika mu mibare cyangwa mu magambo
a) 1 924
b) Igihumbi magana atatu na cumi n’ikenda:
c) Igihumbi magana inani mirongo irindwi na kane:
d) 1 499
2) Koresha amakarita y’imibare akurikira
ukore imibare 6 iri hagati ya 1 000 na 2 000 uyisome, uyandike mu ikayi yawe y’imyitozo, mu mibare no mu magambo.
3) Soma imibare iri mu mbonerahamwe ikurikira
– Iyanditse mu magambo uyandike mu mibare
– Iyanditse mu mibare uyandike mu magambo
1.3 Gusesengura imibare kuva kuri 0 kugera ku 2 000
Igikorwa cya 1
Itegereze imbonerahamwe ikurikira usobanure ibyakozwe
Umubare 1 456 ugizwe n’ikinyagihumbi ---- ibinyajana---- ,
ibinyacumi---- n’ibinyabumwe -----
Igikorwa cya 2
Mwandike imibare ikurikira mu mbonerahamwe mukurikiza urugero rw’ibyakozwe mu gikorwa cya 1. Mugaragaze ibinyagihumbi, ibinyacumi, n’ibinyabumwe.
a) 1 456 b) 1 239
c) 1 699 d) 1 479
e) 1 953 f) 1 974
Reka nisuzume
Itegereze ibinyagihumbi (h), ibinyajana(j), ibinyacumi (c) n’ibinyabumwe(b) maze wandike umubare wasesenguwe.
a) h 1 c 9 b 5 j 7 c) j 6 b 9 c 4 h 1 e) b 7 c 5 h 1 j 9
b) b 9 j 9 h 1 c 9 d) c 9 j 3 h 1 b 5 f) c 9 h 1 b 5 j 2
Koresha imbonerahamwe y’ibara ushyire umubare mu mwanya wawo.
a) 1 456 = h _ j _ c _ b _ d) 1 239 = b _ j _ c _ h _
b) 1 996 = c _ h _ b _ j _ e) 1 197 = c _ j _ h _ b _
c) 1 759 = j _ b _ h _ c _ f) 1 597 = j _ b _ h _ c _
Nsobanukiwe ko:
– Agaciro k’ibinyagihumbi (h) ari umubare wabyo gukuba na 1 000
– Agaciro k’ibinyajana (j) ari umubare wabyo gukuba na 100
– Agaciro k’ibinyacumi (c) ari umubare wabyo gukuba na 10
– Agaciro k’ibinyabumwe (b) ari umubare wabyo gukuba na 1
Igikorwa cya 3
a) Itegereze usobanure ibyakozwe
1 675 = 1 000 + 600 + 70 + 5
1 675 = (1 × 1 000) + (6 × 100) + (7 × 10) + (1 × 5)
1 675 = Ikinyagihumbi , Ibinyajana , Ibinyacumi , Ibinyabumwe
b) Kora nk’ibyakozwe hejuru muri a)
1 874
Igikorwa cya 4
Musesengure imibare ikurikira mo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b) musobanure uburyo byakozwemo.
a) 1 265 = c) 1 645 = e) 1 997 =
b) 1 799 = d) 1 436 = f) 1 956 =
Mutahure kandi mwandike imibare yasesenguwe
a) (1 × 1 000) + (9 × 100) + (4 × 10) + (5 × 1) =
b) 1 000 + 900 + 50 + 9 bingana-----
c) Ikinyagihumbi 1 + Ibinyajana 9 + Ibinyacumi 7 + Ibinyabumwe 3 bingana---
1) Koresha imbonerahamwe y’ibara uvuge umwanya n’agaciro k’imibarwa iciyeho akarongo
a) 1 456 c) 1 324 e) 1 179
b) 1 795 d) 1 299 f) 1 975
2) Shaka umubare wasesenguwemo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b).
a) b 6 h 1 c 9 j 9 = c) c 9 h 1 b 9 j 7 =
b) b 7 c 9 h 1 j 9 = d) j 5 b 4 c 8 h 1 =
3) Sesengura imibare ikurikira mo ibinyagihumbi (h), ibinyajana (j), ibinyacumi (c) n’ibinyabumwe (b).
a) 1 765 = c) 1 956 = e) 1 564 =
b) 1 672 = d) 1 254 = f) 1 713 =
4) Shaka umubare wasesenguwe
a) (1 × 1 000) + (2 × 100) + (3 × 10)+ (4 × 1) =
b) 1 000 + 300 + 70 + 1 =
c) h 1 + j 7 + c 9 + b 6 =
1.4 Kugereranya imibare 2 itarenze 2 000
Igikorwa cya 1
Itegereze iyi shusho uvuge ibiri gukorwa:
Igikorwa cya 2
Mukurikize urugero mwahawe mugereranye imibare ikurikira mukoresha <, > na =
Igikorwa cya 3
Mukurikize urugero mwahawe mugereranye imibare ikurikira mukoresha <, > na =
Nsobanukiwe ko:
Iyo ugereranya imibare ibiri wita kuri ibi bikurikira:
1. Uhera ku binyagihumbi ujya ku binyabumwe ukagenda ugereranya buri mubarwa
2. Iyo ibinyagihumbi bingana uhita ugereranya ibinyajana
3. Iyo ibinyajana bingana uhita ugereranya ibinyacumi
4. Iyo ibinyacumi bingana ugereranya ibinyabumwe
5. Ibyo byose iyo birangiye wamenye umubare munini n’umuto cyangwa wabonye ko imibare ingana
ukoresha ibimenyetso by’igereranya ari byo: < (Birutwa), > (Biruta) na = (Bihwanye)
Ikitonderwa:
Ibimenyetso by’igereranya bya < na > bigomba kuba bireba buri gihe ahari umubare munini.
Igikorwa cya 4
Mukoreshe amakarita ariho imibare mugereranye imibare mushyiramo ikimenyetso k’igereranya gikwiye.
Gereranya abantu babarurirwa mu kagari kacu bari muri iyi mbonerahamwe
a) Umubare w’abagore n’uw’abagabo
b) Umubare w’abana n’uw’abagabo
c) Umubare w’abagore n’uw’abana
d) Umubare w’abagabo n’uw’urubyiruko
e) Umubare w’abagore n’uw’urubyiruko
f) Umubare w’abana n’uw’urubyiruko
Igikorwa cya 5
Mwitegereze iyi shusho maze mugereranye amajwi y’abana batorewe guhagararira abandi mu Kagari.
a) Muhizi afite amajwi--------
b) Mutesi afite amajwi--------
c) Kayitesi afite amajwi--------
d) Mutayomba afite amajwi----
e) Muri aba bakandida ni nde ufite amajwi make?
f) Muri aba bakandida ni nde ufite amajwi menshi?
g) Gereranya amajwi y’abakandida ukoresheje <, > na =
– Kayitesi na Mutayomba
– Kayitesi na Muhizi
– Kayitesi na Mutesi
– Mutayomba na Muhizi
– Mutayomba na Mutesi
– Muhizi na Mutesi
Mukoreshe <, > na = mugereranye imibare ikurikira:
1.5 Gutondeka imibare kuva kuri 0 kugera ku 2 000
A. Gutondeka imibare kuva ku muto ujya ku munini
Igikorwa
Kurikiza urugero utondeke imibare yo kuri (a) na (b) uva ku muto ujya ku munini.
Urugero: Tondeka imibare uhereye ku muto ujya ku munini,
1 649, 1 836, 1 598, 1 752
Igisubizo: 1 598, 1 649, 1 752, 1 836
a) 1 953, 1 395, 1 593 b) 1 613, 1 136, 1 479
Reka nisuzume
Ifashishe impapuro, wandike imibare 10, iri hagati ya 1 000 na 2 000 uyitondeke uva ku muto ujya ku munini.
Nsuzuma ngusuzume
Mukoreshe amakarita mwigane ibiri gukorwa ku ishusho mutondeke imibare iriho muhereye ku muto mujya ku munini
B. Gutondeka imibare uva ku mubare munini ujya ku mubare muto
Igikorwa
Mukurikize ingero mwahawe maze mutondeke imibare yo muri (a) n’iyo muri (b) muva ku munini mujya ku muto.
Urugero: Tondeka iyi mibare uva ku munini ujya ku mu
1 987, 1 897, 1 789
Igisubizo: 1 987, 1 897, 1 789
a) 1 048, 1 840, 1 084 b) 1 613, 1 136, 1 479
Reka nisuzume
Tondeka imibare iri ku makarita uva ku munini ujya ku muto
Nsuzuma ngusuzume
Mwifashishe impapuro, mwandike imibare 10, iri hagati ya 1 000 na 2 000 muyitondeke muva ku munini mujya ku muto.
Nsobanukiwe ko:
Iyo utondeka imibare ukoresha imbonerahamwe y’ibara.
– Ukabanza kugereranya ibinyagihumbi ureba uko birutana
– Ibinyajana na byo ukareba uko birutana
– Ibinyacumi na byo ukareba uko birutana
– Ibinyabumwe na byo ukareba uko birutana
– Ugatondeka ukurikije uko wabisabwe.
1.6 Guteranya imibare igiteranyo cyayo kitarenze 2 000
A. Iteranya ritabitsa ry’imibare ibiri igiteranyo cyayo kitarenze 2 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe
Urugero: 1 324 + 675 =
1 324 + 675 = 1 999
a) 1 156 + 823 = d) 972 + 1 017 =
b) 1 543 + 456 = e) 675 + 1 323 =
c) 1 235 + 704= f) 794 + 1 002 =
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho
ibimenyetso byo + na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo +
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo uteranya imibare ibiri ukora ibi bikurikira:
1. Wifashisha imbonerahamwe y’ibara
2. Umubare munini ukajya hejuru, umuto ukajya hasi.
3. Uteranya uhereye ku binyabumwe ugaherukira ku binyagihumbi.
4. Ukandukura igiteranyo
Reka nisuzume
Muteranye imibare ikurikira:
a) 1 234 + 763 =
b) 567 + 134 =
c) 990 + 1 009 =
d) 1 099 + 900 =
e) 765 + 1 213 =
f) 1 002 + 691 =
B. Iteranya ribitsa ry’imibare igiteranyo cyayo kitarenze 2 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe:
Urugero: 1 425 + 575 = 2 000
a) 934 + 799 =
b) 967 + 999 =
c) 999 + 1 001 =
d) 1 099 + 897 =
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso byo + na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo +
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo uteranya imibare ibiri:
1. Wifashisha imbonerahamwe y’ibara
2. Uteranya uhereye ku binyabumwe ugana ku binyagihumbi.
3. Umubare munini ujya hejuru, umuto ukajya hasi.
4. Iyo igiteranyo k’ibinyabumwe kigizwe n’imibarwa ibiri, wandika ikinyabumwe k’icyo giteranyo, ukabitsa
ikinyacumi hejuru y’ibinyacumi, ukabiteranya, ugakomeza utyo kugera ku binyagihumbi.
5. Ukandukura igiteranyo.
Reka nisuzume
Teranya imibare ikurikira:
a) 1 056 + 899 =
b) 797 + 1 197 =
c) 1 235 + 757 =
d) 972 + 969 =
e) 675 + 979 =
f) 1 239 + 476 =
1.7 Amahurizo yo guteranya imibare igiteranyo cyayo kitarenze 2 000
Urugero:
Umwaka ushize Muhizi yasaruye inanasi 799, uyu mwaka
asarura 967. Shaka igiteranyo k’inanasi yasaruye mu myaka
ibiri.
Nsuzuma ngusuzume
1) Mu Mujyi wa Kigali hubatse amagorofa 754 n’andi mazu y’ikitegererezo 969. Shaka umubare w’amazu yose yubatswe mu Mujyi wa Kigali?
2) Mu isoko hacururizamo abagore 1 006 n’abagabo 979. Shaka umubare w’abacuruzi bose hamwe.
3) Ishuri ryigamo abakobwa 997 n’abahungu 967. Shaka umubare w’abanyeshuri biga muri iryo shuri.
4) Mu bitaro byivurizamo abarwayi batandukanye, mu kwezi kumwe haje abagore 799, abana 356 n’abagabo 795.
Shaka umubare w’abivurije muri ibyo bitaro bose hamwe.
Reka nisuzume
1) Mu nzu y’imyidagaduro hari abagore 976 n’abagabo 779.
Muri iyo nzu harimo abantu bangahe?
2) Akagari kacu gatuwemo n’abagore 357, abana 656, abagabo 337 n’urubyiruko 731. Akagari kacu gatuwe n’abaturage bangahe?
3) Muri banki habikuza abantu batandukanye. Mu cyumweru kimwe habikuje abagore 969, abagabo 656 n’urubyiruko 245. Shaka umubare w’ababikuje muri icyo cyumweru.
4) Mu murenge wa Kicukiro harimo amazu y’ikitegererezo 675, amagorofa 199 n’amazu aciriritse 992. Muri uwo murenge harimo amazu angahe?
1.8 Gukuramo imibare itarenze 2 000
A. Ikuramo ridatira ry’imibare itarenze 2 000
Igikorwa cya 1
Itegereze urugero usobanure ibyakozwe
Urugero: 1 999 – 1 675 = 324
Igikorwa cya 2
Musubize ibibazo bikurikira mukurikije urugero mwahawe
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso byo – na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya –
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo ukuramo imibare ukora ibi bikurikira:
1. Wifashisha imbonerahamwe y’ibara
2. Wandika imibare mu mbonerahamwe y’ibara uhereye ku munini.
3. Uhera ku binyabumwe ukuramo ugaheruka ibinyagihumbi.
4. Wandukura ikinyuranyo ubonye.
Reka nisuzume
Kuramo imibare ikurikira:
a) 1 995 – 763 =
b) 1 567 – 1 341 =
c) 1 990 – 1 090 =
d) 1 999 – 979 =
e) 1 765 – 1 213 =
f) 1 956 – 923 =
B. Ikuramo ritira ry’imibare itarenze 2 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe
Urugero: 1 282 – 967 = 315
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso byo – na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo –
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo ukuramo imibare isaba gutira ukora ibi bikurikira:
1. Wifashisha imbonerahamwe y’ibara.
2. Wandika umubare munini hejuru y’umubare muto mu mbonerahamwe y’ibara.
3. Ukuramo uhereye ku binyabumwe ugana ku binyagihumbi.
4. Iyo gukuramo ibinyabumwe bidashoboka, utira ikinyacumi kimwe ukongera ku binyabumwe umubare
10 ugakuramo.
5. Ukomeza utyo aho bidashoboka hose, kugeza ukuyemo ibinyagihumbi.
Reka nisuzume
Kuramo imibare ikurikira
a) 1 034 – 799 =
b) 1 123 – 979 =
c) 1 234 – 1 196 =
d) 1 345 – 997 =
e) 1 456 – 1 299 =
f) 1 789 – 1 236 =
1.9 Amahurizo yo gukuramo imibare itarenze 2 000
Urugero:
Mu kigo cyacu higa abanyeshuri 1 791. Niba abahungu ari 999, shaka umubare w’abakobwa biga mu kigo cyacu
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo gukuramo imibare:
1. Ugaragaza ibyo baguhaye mu ihurizo.
2. Ugaragaza ibyo bagusaba mu ihurizo.
3. Wandika umubare munini wahawe mu ihurizo ukawuvanamo umubare muto, ukandika ikinyuranyo.
Nsuzuma ngusuzume
1) Kaneza yateye ibiti 1 917. Hashize iminsi hava izuba
ryinshi 769 muri byo biruma. Yasigaranye ibiti bingahe?
2) Mutoni yari afite inka 1 231, inka 523 muri zo yazigabiye abavandimwe n’inshuti. Yasigaranye inka zingahe?
3) Umurenge wacu utuwe n’abaturage 1 163. Niba abaturage 999 muri bo ari abagore n’abana, shaka umubare w’abagabo n’urubyiruko batuye mu murenge wacu.
4) Uruganda rukora imifuka rwakoze imifuka 1 721, imifuka 179 muri yo igurwa na Rukundo. Shaka umubare w’imifuka uruganda rwasigaranye.
Reka nisuzume
1) Ishuri ryacu ryahize kuzatera ibiti 2 000 uyu mwaka kugeza ubu tumaze gutera 1 099. Harabura ibiti bingahe ngo twese umuhigo?
2) Mu bitaro by’Akarere hari harwariye abarwayi 1 532
none hasezerewe abarwayi 799 bamaze gukira neza.
Hasigayemo abarwayi bangahe?
3) Abanyamuryango ba koperative babumbye amatafari
1 911, amatafari 975 muri yo bayubakisha ikiraro k’inkoko.
Shaka umubare w’amatafari yasigaye.
4) Mu kigo cyacu harimo abantu 1 921, muri bo 124 ni abakozi b’ikigo. Shaka umubare w’abanyeshuri biga muri iryo shuri.
1) Itegereze neza ibiri mu mbonerahamwe maze ukore ibyo wabajijwe
Shaka igiteranyo k’imibare ikurikira:
a) A 1 + B 1 =
b) A 1 + C 1 =
c) A 1 + D 1 =
d) A 2 + B 2 =
e) A 2 + C 2 =
f) A 2 + D 2 =
Shaka ikinyuranyo k’imibare ikurikira:
a) A 1 – B 1 =
b) A 1 – C 1 =
c) A 1 – D 1 =
d) A 2 – B 2 =
e) A 2 – C 2 =
f) A 2 – D 2 =
2) Mu kagari kacu harimo abantu 996 bemerewe gutora. Mu Kari duturanye, harimo abantu bemerewe gutora 999. Ubwo abantu bemerewe gutora muri utwo tugari twombi ni bangahe?
3) Mu ibarura riheruka, Akagari kacu kari gatuwe n’abantu 1 964 bose hamwe. Niba 1 324 muri bo ari abana, ubwo Akagari kacu kari gatuwe n’abantu bakuru bangahe?
1.10 Mara ya 7 n’ibikubo bya 7 bitarenze 70
Igikorwa
a) Mukore uturundo tw’utubarisho 7, 14, 21, 28, 35, 42,
49, 56, 63, 70.
b) Mubare ibiri muri buri karundo maze mwandike inshuro
uwo mubare ugaruka kuri buri murongo.
c) Ese witegereje ibikurikira hari isano iri hagati yo guteranya
no gukuba na 7?
3) Uzurisha umubare ukwiye
1.11 Mara ya 8 n’ibikubo bya 8 bitarenze 80
Igikorwa
a) Mukore uturundo tw’utubarisho 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.
b) Mubare ibiri muri buri karundo maze mwandike inshuro
uwo mubare ugaruka kuri buri murongo.
c) Ese witegereje ibikurikira hari isano iri hagati yo guteranya no gukuba na 8?
1) Uzurisha imibare ikwiye
1.12 Mara ya 9 n’ibikubo bya 9 bitarenze 90
Igikorwa
a) Mukore uturundo tw’utubarisho 9, 18 , 27, 36, 45, 54, 63, 72, 91, 90.
b) Mubare ibiri muri buri karundo maze mwandike inshuro
uwo mubare ugaruka kuri buri murongo.
c) Ese witegereje, ibikurikira hari isano iri hagati yo guteranya
no gukuba na 9?
1) Uzurisha imibare ikwiye
1.13 Gukuba imibare y’imibarwa ibiri cyangwa itatu na 7, 8 na 9 igikubo cyayo kitarenze 2 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe
Urugero: 237 × 7 = 1 659
7 × 7 = 49 Twandika 9 mu binyabumwe tukabitsa 4 mu binyacumi.
7 × 3 = 21 Twandika 1 + 4 mu binyacumi tukabitsa 2 mu binyajana.
7 × 2 = 14 Twandika 4 + 2 mu binyajana tukabitsa 1 mu binyagihumbi.
Nsobanukiwe ko:
Iyo ukuba imibare uhera ku binyabumwe. Iyo usanze
igikubo kigizwe n’imibarwa ibiri wandika ikinyabumwe
k’icyo gikubo hanyuma ukabitsa ikinyacumi mu binyacumi.
Ukomeza utyo kugeza ku binyagihumbi.
Nsuzuma ngusuzume
Shaka umubare ubura
Reka nisuzume
Igana urugero wahawe ushake ibikubo by’iyi mibare
Urugero:
1.14 Ikuba ry’umubare w’imibarwa 3 n’undi w’imibarwa 2 igikubo cyayo kitarenze 2 000
Igikorwa
Musubize ibibazo bikurikira mukurikije urugero mwahawe.
Urugero:
Nsuzuma ngusuzume
Mwifashishe amakarita yanditseho imibare n’andi ariho ibimenyetso byo × na =
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo ×
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
Nsobanukiwe ko:
Iyo ukuba umubare w’imibarwa 3 n’undi w’imibarwa 2:
1. Wandika imibare mu mbonerahamwe y’ibara
2. Ukubisha ikinyabumwe kugeza urangije imibarwa yose
3. Ukubisha ikinyacumi k’igikuba ukandika ikinyabumwe k’igikubo munsi y’inyacumi k’igikubo wabonye.
4. Uteranya ibikubo byose uhereye ku binyabumwe ujya ku binyagihumbi.
Itegereze neza imbonerahamwe ushake igikubo wabajijwe
1.15 Amahurizo yo gukuba umubare w’imibarwa 3 n’undi w’imibarwa 2 igikubo kitarenze 2 000
Urugero:
Mu cyumba k’inama harimo imirongo 19 y’intebe kandi kuri buri murongo hariho intebe 105. Shaka umubare w’intebe ziri mu cyumba k’inama.
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo gukuba imibare:
1. Ugaragaza ibyo baguhaye mu ihurizo
2. Ugaragaza ibyo bakubaza mu ihurizo
3. Wandika imibare wahawe mu ihurizo mu buryo
buhagaze maze ukayikuba hanyuma ukandika igikubo.
Nsuzuma ngusuzume
1) Data yatemye ibitoki abipakira imodoka 17 ziruzura. Shaka umubare w’ibitoki yatemye niba buri modoka
yaratwaye ibitoki 117.
2) Ibitaro by’Akarere kacu bifite ibyumba by’abarwayi 19. Muri buri cyumba harimo abarwayi 105. Shaka umubare w’abarwayi bari muri ibyo bitaro.
3) Mu gasanduku k’itora hajyamo amajwi 148. Shaka umubare w’amajwi ajya mu dusanduku tw’itora 13.
4) Mubumbyi abumba amatafari 165 buri munsi. Shaka umubare w’amatafari abumba mu minsi 12.
Reka nisuzume
1) Abanyeshuri bateye ibiti ku mirongo. Buri murongo bawuteyeho ibiti 162 batera imirongo 12. Bateye ibiti
bingahe muri rusange?
2) Butera yaguriye abana 135 bo mu Kagari amakayi. Buri mwana yamuguriye amakayi 14. Ubwo Butera yaguze amakayi angahe yose hamwe?
3) Umucuruzi acuruza isabune 124 buri munsi. Shaka umubare w’isabune acuruza mu minsi 16.
4) Mu kigo k’ishuri hari ibyumba by’amashuri 18 kandi muri buri shuri harimo intebe 15. Icyo kigo k’ishuri kirimo intebe zingahe?
1.16 Ikuba ry’imibare na 100 na 1 000 igikubo cyayo kitarenze 2 000
Igikorwa
Musubize ibibazo bikurikira mwifashishije urugero mwahawe.
Urugero:
a) 19 × 100 = 1 900 c) 1 × 1 000 = 1 000
b) 13 × 100 = 1 300 d) 2 × 1 000 = 2 000
a) 12 × 100 = c) 1 × 1 000 = e) 19 × 100 =
b) 17 × 100 = d) 10 × 100 = f) 2 × 1 000 =
Nsobanukiwe ko:
– Iyo ukuba umubare na 100 wandika uwo mubare ukandika amazeru abiri (00) inyuma y’uwo mubare.
– Iyo ukuba umubare na 1 000 wandika uwo mubare ukandika amazeru atatu (000) inyuma y’uwo mubare.
Uzurisha 100 cyangwa 1 000
1.17 Igabanya ridasagura ry’umubare w’imibarwa 4 n’umubare w’umubarwa 1 imibare
itarenze 2 000
Igikorwa cya 1
Mwuzuze iyi mbonerahamwe
Igikorwa cya 2
Musubize ibibazo bikurikira mukurikije ingero mwahawe
Urugero:
a) 1 236 : 4 =
b) 1 575 : 5 =
c) 1 648 : 8 =
d) 1 989 : 9 =
e) 1 768 : 2 =
f) 1 326 : 6 =
Nsuzuma ngusuzume
1) Mwifashishe amakarita yanditseho imibare n’andi ariho
ibimenyetso byo : na = .
– Mufate ikarita imwe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cyo :
– Mukurikizeho ikarita yo muri B iteganye n’iyo wafashe muri A
– Mukurikizeho ikarita yanditseho ikimenyetso cya =
– Muhitemo igisubizo mu makarita yo muri C
2) Mukore amakarita ariho imibare mwihitiyemo iri hagati ya 1 000 na 2 000 n’andi ariho ibimenyetso – na : .Mukore nk’ibyakozwe hejuru.
Nsobanukiwe ko:
Iyo ugabanya imibare ukora ibi bikurikira:
1. Wandika imibare mu mahembe
2. Uhera ku binyagihumbi ugabanya, ugakurikizaho
ibinyajana, ibinyacumi, ugaherukira ku binyabumwe.
3. Iyo ibinyagihumbi ari bike ugereranyije n’ikigabanya ufatira hamwe ibinyagihumbi n’ibinyajana.
4. Iyo ibyasigaye ku binyagihumbi n’ibinyajana hiyongereyeho n’ibinyacumi ari bike ugereranyije n’ikigabanya ushyiramo 0 ugakuramo hanyuma ukamanura ibinyabumwe.
Itegereze neza imbonerahamwe maze ukore ibyo wabajijwe
Shaka ikigabanyo k’imibare ikurikira
a) A 1 na B 2
b) A 2 na B 1
c) A 3 na B 5
d) A 4 na B 4
e) A 5 na B 3
f) A 4 na B 8
1.18 Amahurizo yo kugabanya
Urugero:
Abanyeshuri 96 bashyizwe mu matsinda 8 ku buryo bungana. Buri tsinda ririmo abanyeshuri bangahe?
Nsuzuma ngusuzume
1) Abanyeshuri 378 bashyizwe mu mashuri 9 ku buryo bungana. Buri shuri ryagiyemo abanyeshuri bangahe?
2) Akarere gafite ibitabo 894 gashaka gusaranganya ku buryo bungana amashuri 6. Buri shuri rizahabwa ibitabo bingahe?
3) Umurenge wacu ufite inzitiramibu 1 985 ushaka kugabanya ku buryo bungana utugari 5 tuwugize. Buri kagari kazabona inzitiramibu zingahe?
4) Umuhinzi yasaruye imifuka y’ibirayi 1 359 ayipakira amafuso 9 ku buryo bungana. Buri fuso yatwaye imifuka ingahe y’ibirayi?
Nsobanukiwe ko:
Iyo ugiye gukora ihurizo ririmo kugabanya imibare,
1. Ugaragaza ibyo baguhaye mu ihurizo
2. Ugaragaza ibyo bakubaza.
3. Wandika imibare wahawe mu ihurizo mu mahembe maze ukayigabanya hanyuma ukandika ikigabanyo.
Reka nisuzume
1) Keza afite amagi 1 768 ashaka gushyira mu makarito 8 ku buryo bungana. Buri karito izajyamo amagi angahe?
2) Abaterankunga bafite imipira yo gukina 1 484 bashaka gusaranganya ku buryo bungana uturere 7. Buri karere kazahabwa imipira ingahe?
3) Mubumbyi yabumbye amatafari 1 888 mu minsi 8. Shaka umubare w’amatafari abumba ku munsi umwe niba abumba amatafari angana buri munsi.
4) Gabanya ku buryo bungana ibitabo 1 845 ibigo by’amashuri
5. Buri kigo kizahabwa ibitabo bingahe?
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