ÇÀôz-±m-hP-qôü IPÅ-;ü 19 · 20 ÇÀôz-±m-GZÛÅ-qü IPÅ-ˆÛ-¯-zºÛ-¯Û-fzÅü 20 ÇÀôz-±m-GZÛÅ-qü IPÅ-ˆÛ-¯-zºÛ-¯Û-fzÅü Chapter 2: Basic Operations on

D) G¾-bï-GmÅ-fP-VßP-zºÛ-IPÅ-;-ŸÛG-GmÅ-fP-Vï-zºÛ-IPÅ-;ºÛ-G»Å-xôGÅ-ÅÞ-ƒÛÅ-mü P-±ôÅ-GmÅ-fP-VßP-z-hï-GmÅ-fP-Vï-zºÛ-fôG-Çkô¤-hGôÅü

G) G¾-bï-GmÅ-fP-VßP-zºÛ-IPÅ-;-ŸÛG-GmÅ-fP-Vï-zºÛ-IPÅ-;ºÛ-G»ôm-xôGÅ-ÅÞ-ƒÛÅ-mü P-±ôÅ-GmÅ-fP-VßP-z-hï-GmÅ-fP-Vï-z-mÅ-ºfïm-hGôÅü

P) dGÅ-V hP-L, D zTÅ-mÛ-GmÅ-fP-Vï-z-ŸÛG-GÛ-G»ôm-xôGÅ-ÅÞ-hÝÅ-m¤-»P-¤Û-ºƒÛ-z-hP-ü hï-hG-zB¼-¹ôÅ-ˆP-¤Û-‚ïh-hôü ü

T) dGÅ-I mÛ-V hP-X GZÛÅ-Dô-mºÛ-G»ôm-xôGÅ-ÅÞ-ºƒÛ-z-»ÛmüV) dGÅ-X mÛ-L hP-C GZÛÅ-Dô-mºÛ-G»ôm-xôGÅ-ÅÞ-ºƒÛ-z-»Ûmü

ÇÀôz-±m-hP-qôü IPÅ-;ü 1919191919

19

ÇÀôz-±m-GZÛÅ-qü IPÅ-ˆÛ-¯-zºÛ-¯Û-fzÅü 2020202020

20

ÇÀôz-±m-GZÛÅ-qü IPÅ-ˆÛ-¯-zºÛ-¯Û-fzÅü Chapter 2: Basic Operations on Numbers

º²Ûm-IÔ-ÇSôm-¤ºÛ-Ç+zÅü ÇÀôz-yâG-±ôÅ-Çkô¤-fzÅ-hP-ü ºfïm-fzÅü Nå¼-fzÅü zGôh-fzÅ-zTÅ-ˆÛ-¯-zºÛ-¯Û-fzÅ-zŸÛºÛ-ÇKô-mÅ-IPÅ-GmÅ-5 Tm-HÛ-IPÅ-;-z¼-HÛ-¯Û-fzÅ-Ç+ô¼-HÛ-¢ôP-zl¼-ºhP-PïÅ-‚Å-»ôhü ºhÛ¼ü ¯-zºÛ-¯Û-fzÅ-ˆÛ-ÇKô-mÅ-h;º-½‰ôG-Åï¾-Ç+zÅ-mô¼-Bôm-º‚ãP-ÆÛh-q-ŸÛG-mÛü ¢ôP-zl¼-¤-‚Å-q-¤-»Ûm-q¼ü Gô-hôm-¤-dôGÅ-qºÛ-Aïm-HÛÅ-»Ûm-ÁÅ-Vï-zÅü ºhÛ-¿e-zÞºÛ-GmÅ-ÇePÅ-¾-GhôP-¾ïm-‚ïh-ÇePÅ-ˆÛ-¢ôP-zl¼-mÛ-hGôÅ-PïÅ-»Ûmü

Çkô¤-¯ÛÅü Addition

ÇÀôz-yâG-±ô-Çkô¤- Û̄Å-hP-ºƒï¾-zºÛ-f-Ç‰h-DG-¾-¥ôP-MãÅ-GP-º±¤Å-»ôhü hqï¼-mü IPÅ-;-GZÛÅ-Å¤ü hï-¾Å-¤P-z-Çkô¤-Ç+zÅü hï-hG-¾-Çkô¤-‚ïh-IPÅ-Çkô¤-‚ïh-IPÅ-Çkô¤-‚ïh-IPÅ-Çkô¤-‚ïh-IPÅ-Çkô¤-‚ïh-IPÅ-(Addends) ï̧¼-ŸÛP.ü hïºÛ- Û̄Å-ºƒÅ-¾-zÇkô¤Å-zÇkô¤Å-zÇkô¤Å-zÇkô¤Å-zÇkô¤Å-fôz-fôz-fôz-fôz-fôz-(Sum) ï̧¼ü Ç+zÅ-ºhÛ¼ü hGï-Lm-HÛÅ-Gô-hôm-zB¼-ºIï¾-‚-Mã-¤-»Ûm-q¼ü ¯-zºÛ- Û̄-fzÅ-¾ïGÅ-q¼-FÛh-hGôÅü zÇeàh-¤ºÛ-Çkô¤- Û̄Å- Û̂-h;º-½‰ôG-Fôhü Çkô¤- Û̄Å- Û̂-¯-zºÛ-fzÅ-±ß¾-im-q¼-‚-Mã-hï-mÛü ÇÀôz-yâG-±ôÅ-h;º-½‰ôG-¤HôGÅ-qô-hP-»P-hG-qºÛ-ÇKô-mÅ-Åï¾-z¼-‚ïh-qºÛ-V-Aïm-G¾-Vïm-ŸÛG-»Ûmü ÇÀôz-yâG-n¤Å-¾-IPÅ-GmÅ-AP-q-ŸÛG-¾ü IPÅ-GmÅ-GZÛÅ-Tm-ŸÛG-DôG- Û̄Å-zMz-Çeï-Çkô¤-qºÛ-½‰ôG-º²ÛP-Vï-zºÛ-Çkô¤- Û̄Å-MG-fÞz-q¼-‚-hGôÅü hqï¼-mü 27 + 16 + 39 Çkô¤-Ç+zÅü GTÛG-GmÅ-fôG-9 ÇeïP-13(6 + 7)

DôG-¯ÛÅ-ˆÛÅ-Çoôm-hGôÅü ½‰ôG-º²ÛP-Vï-zºÛ-Çkô¤-¯ÛÅ-MG-ÇePÅ-¾-‚P-Vßz-q¼-‚-z-¾ü ÇÀôz-yâG-±ô¼-ºhÛ-Ç+ô¼-HÛ-¢ôP-zl¼-ÁÝGÅ-Vï¼-‚-MãºÛ-hGôÅ-¤Dô-»ôhü

G¾-bï-ÇÀôz-yâG-TÛG-¾-IPÅ-GmÅ-G»¼-¾ïm-(zB¼-OÛG-)fh-DôG-¯ÛÅ-MG-Mã¼-h;º-P¾-ºyh-±ïü DôP-¾-G»¼-¾ïm-‚ïh-Å-ŸÛG-¾ôGÅ-ÅÞ-vh-hï-‚ïh-hÝ-zTßG-VôG GP-¿e¼ü ¤fº-hôm-ÇÀôz-yâG-±ô¼-G»¼-¾ïm-¾ôGÅ-ÅÞ-¤-‚Å-qºÛ-ÇKô-mÅ-zÇkô¤Å-fôz-º±ô¾-fÞz-q¼-‚ïh-qºÛ-Ç+Ý¾-¤-GbôP-hGôÅü


20


21

hï-®¤-¤-¸hü ÇÀôz-yâG-±ô¼-IPÅ-GmÅ-zB¼-OÛG-hGôÅ-qºÛ-Çkô¤- Û̄Å-MG-ÇePÅ-fh-ºôÅ-º±¤Å-ˆÛ-¾¤-Çeôm-hGôÅ-PïÅ-»Ûmü hïºÛ-Vïh-hÝü GTÛG-GmÅ-hï-GTÛG-GmÅ-hP-zTß-GmÅ-ÅÞ-zXï-Nå¼-‚-z-hP.üzTß-GmÅ-hï-zTß-GmÅ-hP-zM-GmÅ-ÅÞ-zXï-Nå¼-‚-zü zM-GmÅ-hï-zM-GmÅ-hP-ÇeôP-GmÅ-ÅôGÅ-ÅÞ-zXï-Nå¼-‚-±ß¾-ÁïÅ-q¼-‚-hGôÅü hqï¼-mü GTÛG-Tm-17 mÛ-zTß-Tm-1 hP-GTÛG-Tm-7 »Ûm-¾ü zTß-Tm-28

mÛ-zM-Tm-2 hP-zTß-Tm-8 »Ûmü zM-Tm-35 mÛ-ÇeôP-Tm-3 hP-zM-Tm-5 »Ûm-q-ÅôGÅ-Åôü ü

ºfïm- Û̄Åü Subtraction

ºfïm-¯ÛÅ-Ç+zÅü zïh-uôh-‚ïh-zŸÛm-qºÛ-f-Ç‰h-mÛ-ºfïm-‚ºÛ-IPÅ-ºfïm-‚ºÛ-IPÅ-ºfïm-‚ºÛ-IPÅ-ºfïm-‚ºÛ-IPÅ-ºfïm-‚ºÛ-IPÅ-(Minuend)hP.ü ºfïm-ºfïm-ºfïm-ºfïm-ºfïm-‚ïh-IPÅü‚ïh-IPÅü‚ïh-IPÅü‚ïh-IPÅü‚ïh-IPÅü(Subtrahend) Èï-zG-Èï-zG-Èï-zG-Èï-zG-Èï-zG-G¤-ºfïm-fôz-ºfïm-fôz-ºfïm-fôz-ºfïm-fôz-ºfïm-fôz-(Difference)zTÅ-»Ûmü f-Ç‰h-ºhÛ-hG-GÛ-Gô-hôm-ÁïÅ-qºÛ-xÛ¼-P-±ôÅ-ºhÛ-¿e¼-zÁh-VôG ºfïm-‚ºÛ-IPÅ-ºfïm-‚ºÛ-IPÅ-ºfïm-‚ºÛ-IPÅ-ºfïm-‚ºÛ-IPÅ-ºfïm-‚ºÛ-IPÅ-¾Å-ºfïm-‚ïh-IPÅ-ºfïm-‚ïh-IPÅ-ºfïm-‚ïh-IPÅ-ºfïm-‚ïh-IPÅ-ºfïm-‚ïh-IPÅ-ºfïm-mü Èï-zG-Èï-zG-Èï-zG-Èï-zG-Èï-zG-º‚ãP-ü

42 28 = 14

¯ÛÅ-ºƒÅ-ºhÛ-¾-ŸÛz-zÁï¼-‚ïh-q¼ü P-±ôÅ-ºhÛ-¿e¼-‚-hGôÅü28 + 14 = 42

±ÛG-GŸm-HÛÅ-zÁh-mü ºfïm-‚ïh-IPÅ-hP-Èï-zG-GZÛÅ-ˆÛ-zÇkô¤Å-fôz-mÛ-ºfïm-‚ºÛ-IPÅ-hP-¤±ßPÅü ŸïÅ-zÁh-VôG

Ç+zÅ-ºhÛ¼ü ¤HôGÅ-qô-hP-»P-hG-q-»ôP-Vïhü ÇÀôz-yâG-±ô¼-PG-¯ÛÅ-hP-ºƒÛ-¯ÛÅ-GZÛÅ-;ºÛ-¢ôP-zl¼-ºhP-PïÅ-vôh-hGôÅü

IPÅ-GmÅ-zB¼-OÛG-‚ïh-Ç+zÅü zTß-GmÅ-IPÅ-ÁÛG-Iô¾-(IPÅ-GmÅ-zB¼-OÛG-‚Å-)bï-zTß-GmÅ-hP-GTÛG-GmÅ-z¸ô-ÇePÅ-hP.ü zM-GmÅ-ÁÛG-Iô¾-bï-zM-GmÅ-hP-zTß-GmÅ-ÅÞ-Nå¼-ÇePÅ-ÅôGÅ-

ºfïm-‚ºÛ-IPÅü

ºfïm-‚ïh-IPÅü ºfïm-fôzü

ºfïm-‚ºÛ-IPÅü

ºfïm-fôzüºfïm-‚ïh-IPÅü


21


22

¾-Gô-z-ºôÅ-º±¤Å-ÁÛG-zBïh-hGôÅü hqï¼-mü zTß-GmÅ-8 + GTÛG-GmÅ-5 mÛ-zTß-GmÅ-7 + GTÛG-GmÅ-15 ¿e¼-¤±ôm-VôG-¾ü zM-GmÅ-5 + zTß-GmÅ-2 mÛ-zM-GmÅ-4 + zTß-GmÅ-12 ÅôGÅ-ÅÞ-¤±ôm-VôGü

Nå¼-¯ÛÅü Multiplication

Nå¼-¯ÛÅ-Ç+zÅü zïh-uôh-‚ïh-zŸÛm-qºÛ-f-Ç‰h-mÛ-zNå¼-‚ºÛ-IPÅ-zNå¼-‚ºÛ-IPÅ-zNå¼-‚ºÛ-IPÅ-zNå¼-‚ºÛ-IPÅ-zNå¼-‚ºÛ-IPÅ-(Multiplicand)hP.ü Nå¼-Nå¼-Nå¼-Nå¼-Nå¼-‚ïh-IPÅü‚ïh-IPÅü‚ïh-IPÅü‚ïh-IPÅü‚ïh-IPÅü(Multiplier) zNå¼-fôz-zNå¼-fôz-zNå¼-fôz-zNå¼-fôz-zNå¼-fôz-(Product)zTÅ-»Ûmü hï-hG-GÛ-ºƒï¾-z-mÛ-GÁ¤-hÝ-zÇem-»ôhü

13 x 9 = 117

13 x 9 = 117

Nå¼-¯ÛÅ-Ç+zÅü P-±ôÅ-Nå¼-IPÅ-n¤Å-ˆÛ-Gô-¼Û¤-WÛ-¿e¼-zOÛGÅ-ˆP-¼ÞP.ü zNå¼-fôz-mÛ-GTÛG-¤±ßPÅ-º‚ãP.ü

‚ ïh-Ç K ô ü‚ ïh-Ç K ô ü‚ ïh-Ç K ô ü‚ ïh-Ç K ô ü‚ ïh-Ç K ô ü ÇÀôz-yâG-±ô¼-GÁ¤-HÛ-ÍP-;Û¼-¿e-ŸÛz-‚ïh-q¼-Ç+Ý¾ü ÇeôP-V-hP-qô-¿S-qô¼-zÇ+PÅ-qºÛ-ÍP-;Û-mÛü ÍP-;Û-XïÅ-¤-hï-ÇSôm-¤ºÛ-¿kz-GZÛÅ-»Ûm-q-¤fôP-fÞzü

ÇÀôz-yâG-±ô¼-¼ôGÅ-ºhïGÅ-‚Å-bï-z¼-ÇeôP-¿ËG-¤-n¤Å-¼ïÅ-¤ôÅ-ˆÛÅ-Ç+ôP-hÝ-VßG ÍP-;Û-¤fº-¤-hï-65536 ¼ïh-h¤ü hqï-ºIôÅ-ºhÛºÛ-ÍP-;Û-XïÅ-¤-GP-¼ïh-h¤ü

»P-mü 1 3

x 9

1 1 7 zNå¼-fôzüNå¼-‚ïh-IPÅüzNå¼-‚ºÛ-IPÅü

»P-ü

zNå¼-‚ºÛ-IPÅü

Nå¼-‚ïh-IPÅü zNå¼-fôzü

zGôh-IPÅü

zGôh-IPÅü ¿kz-IPÅü

1 2 4 8 16

(13 hP-9 GZÛÅ- Û̂ü)


22


23

zGôh- Û̄Åü Division

zGôh-¯ÛÅ-Ç+zÅü zïh-uôh-‚ïh-zŸÛm-qºÛ-f-Ç‰h-mÛ-zGô-‚ºÛ-IPÅ-zGô-‚ºÛ-IPÅ-zGô-‚ºÛ-IPÅ-zGô-‚ºÛ-IPÅ-zGô-‚ºÛ-IPÅ-(Dividend)hP.ü zGôh-‚ïh-zGôh-‚ïh-zGôh-‚ïh-zGôh-‚ïh-zGôh-‚ïh-IPÅüIPÅüIPÅüIPÅüIPÅü(Divisor) zGôÅ-fôz-zGôÅ-fôz-zGôÅ-fôz-zGôÅ-fôz-zGôÅ-fôz-(Quotient)zTÅ-»Ûmü hï-hG-GÛ-ºƒï¾-z-mÛ-GÁ¤-hÝ-zÇem-»ôhü

117 ÷ 9 = 13

117 ÷ 13 = 9

ÇÀôz-yâG-±ô¼-¼ôGÅ-ºhïGÅ-‚Å-bïü Nå¼-¯ÛÅ-ˆÛ-Iâz-V-¼ï-¼ïºÛ-mP.ü zGôh-¯ÛÅ-ˆÛ-Iâz-V-GZÛÅ-¼ï-»ôh-q-¤fôP-z¼-‚-Mãü

G¾-bï-zGô-‚ºÛ-IPÅ-hï-zGôh-‚ïh-IPÅ- Û̂-¿kz-IPÅ-¤Ûm-mü P-±ô¼-zGôh- Û̄Å- Û̂-¤WâG-bà-¿ËG-IPÅ-ÁÛG-ºfôz-q-hï-¾-zGôÅ-¿ËG-zGôÅ-¿ËG-zGôÅ-¿ËG-zGôÅ-¿ËG-zGôÅ-¿ËG-(Remainder)¸ï¼ü hqï¼-mü

Ÿ Ûz-zÁï¼üŸ Ûz-zÁï¼üŸ Ûz-zÁï¼üŸ Ûz-zÁï¼üŸ Ûz-zÁï¼ü ¯ÛÅ-ºƒÅ-¾-zÁï¼-¯ÛÅ-MG-Ç+zÅü ºhÛ-¿e¼-‚-hGôÅü

85 = 12 x 7 + 1

»P-ü

zGô-‚ºÛ-IPÅü

zGôh-‚ïh-IPÅü zGôÅ-fôzü

zGô-‚ºÛ-IPÅü

zGôh-‚ïh-IPÅü zGôÅ-fôzü

1 27 8 5 - 7 0 1 5 - 1 4 1

zGôÅ-fôzüzGôh-‚ïh-IPÅü zGô-‚ºÛ-IPÅü

zGôÅ-¿ËG

zGô-‚ºÛ-IPÅü zGôh-‚ïh-IPÅüzGôÅ-fôzü zGôÅ-¿ËG


23


24

»Û-GïºÛ-¯ÛÅ-GŸÛ-z¸ô-zü Framing Word Problems

ÇÀôz-yâG-±ô¼-¯-zºÛ-¯Û-fzÅ-DG-hP-ºƒï¾-zºÛ-»Û-GïºÛ-¯ÛÅ-GŸÛ-ºIô¾-ÇePÅ-ˆÛ-¢ôP-zl¼-ºhP-PïÅ-vôh-hGôÅü ¾ï-±m-ºhÛºÛ-mP.ü ÍP-;ÛÛ-¯ÛÅ-GŸÛ-DG-¤±ßPÅ-zÇkÝ¼-‚-hGôÅ-qºÛ-Gô-¿kôG-qºÛ-GmÅ-ÇePÅ-¤P-qô-vh-hïü ÇÀôz-yâG-±ôÅ-¼P-ÇeôzÅ-ˆÛÅ-»Û-GïºÛ-¯ÛÅ-GŸÛ-z¸ô-fÞz-q-»ôP-zºÛ-ºzh-¯ô¾-‚Å-»ôhü vh-¸Ûm-qºÛ-¯ÛÅ-GŸÛ-GP-»P-¼ÞP-z-ŸÛG-¾ü »Û-GïºÛ-¯ÛÅ-GŸÛ-¤P-qô-ŸÛG-z¸ô-fÞzü Ç+zÅ-ºhÛ¼-±h-z;G-TÛG-»ôh-q-mÛü Û̄Å-GŸÛ-Åô-Åô¼-»Û-Gïº¤-q¼-¼ÛÅ-GP-¼ÞP-fôG-zl-Çeôm-(Clue)ÁÛG-»ôh-hGôÅü ¢ôP-zl¼-ºhÛ-¼ÛGÅ-mÛ-ÇÀôz-¤-±ôºÛ-ZÛm-¼ïºÛ-º±ô-zºÛ-h;º-½‰ôG-Åï¾-z-¾-wm-mÝÅ-Vïm-qô-»ôhü »Û-GïºÛ-¯ÛÅ-GŸÛ-z¸ô-Ç+zÅü¤ÛP-±ÛG-±h-¿km-zïh-uôh-GbôP-Mã-hï-®¤-G¾-Vïm-qô-z¯Û-¤Û-¼ÞP.ü GP-¿e¼ü fzÅ-¾¤-¾ïGÅ-ÁôÅ-ÁÛG-mÛ-ÇÀôz-¤-n¤Å-¾-Gb¤-JÀïP-‚ïh-qºÛ-Fôhü DôP-±ô¼-Ç+h-»ÛG-GÛ-GmÅ-±h-»¼-MÅ-GbôP-fzÅ-‚-hGôÅü zMãh-¼Û¤-ºhÛºÛ-Fôhü »Û-GïºÛ-¯ÛÅ-GŸÛ-z¸ô-Mã-hï-Ç+h-»ÛG-»P-hG-»Ûm-¤Ûm-¾Å-G¾-Vï¼-z¯Û-zºÛ-Gô-z-ºyôh-q¼-‚-hGôÅü Ç+zÅ-ºhÛ¼ü ÇÀôz-yâG-n¤Å-¾-¼P-ÇeôzÅ- Û̂Å-ÍP-;ÛºÛ- Û̄Å-GŸÛ-hP-»Û-GïºÛ- Û̄Å-GŸÛ-z ô̧-¼Þ-ºWâG-hGôÅü

hqï-ºIôÅ-z¸ô-zü Generating Patterns

ÇÀôz-yâG-±ôÅ-º²Ûm-IÔ-zŸÛ-qºÛ-Ç+zÅ-hqï-ºIôÅ-hqï-ºIôÅ-hqï-ºIôÅ-hqï-ºIôÅ-hqï-ºIôÅ-(Pattern)Ç+ô¼-ÇÀôz-¢ôP-‚Å-»ôhü hïºÛ-h¤ÛGÅ-»Þ¾-mÛ-ÇÀôz-yâG-±ô¼-hqï-ºIôÅ-¢PÅ-q-zMãh-hqï-ºIôÅ-¼ÛGÅ-zOï-zºÛ-mÝÅ-¯¾-zBïh-zÆÛPÅ-‚-zºÛ-Vïh-»ÛmüºhÛÅ-DôP-±ô¼-vh-¸Ûm-qºÛ-hqï-ºIôÅ-ÁÛG-Gô¤-q-hÝ-¤ºÛ-z¼-hÝ-M-zBïh-‚ïh-mÝÅü ºhÛ-Vïh-hÝü ‚ïh-ÇKô-M-Vï-z-Çtï¾-zºÛ-IôÅ-ºV¼-zbôm-»ôhü hGï-Lm-HÛÅ-ÇÀôz-yâG-±ôºÛ-Çoï-ºFÛh-hïü DôP-±ô-±ô-DG-hÝ-¤¼-zGôÅ-bï-‚ïh-ÇKô-Çtï¾-hGôÅü G¾-bï-ÇÀôz-yâG-¼ï-¸ÞP-GÛÅ-Dï¼-AP-fôG-‚ïh-ºhôh-»ôh-mü hï-¿e¼-‚-zºÛ-z;º-ºFô¾-vh-VôG ¾ï-±m-2-4-1 mP.ü ÇÀôz-yâG-±ôÅ-uÛ¼-zbP-GÛ-fzÅ-¾¤-ŸÛG-hqï-ºIôÅ-ÅÞ-uh-q¼-¿e-ŸÛz-‚Å-bïü 9 fôG-¤WâG-IÛ¾-zºÛ-Nå¼-¯ÛÅ-¼ïºÞ-¤ÛG-ºƒÛ-¼Þ-ºWâG-hGôÅü ¾ï-±m-2-4-4 mP.ü ÇÀôz-yâG-±ô¼-1,

3(1+2), 6(1+2+3) .. . ¿e-zÞ-ÅôGÅ- Þ̧¼-GÅÞ¤-IPÅ- Û̂-Eh-VôÅ-DG-TÛG-zïh-uh-hï-hqï-ºIôÅ-¤P-®¤-¼ÛGÅ-zOï-ÇePÅ-Pô-vôh-‚Å-»ôhü

¼ÛGÅ-zOïÅ-qºÛ-¯ÛÅ-GŸÛ-DG-ºƒÛ-Ç+zÅü z¼-ÇeôP-Ç+ôP-zºÛ-‚ïh-ÇKôºÛ-¼ÛGÅ-zïh-uôh-GbôP-ºôÅü


24


25

2-1 2-1 2-1 2-1 2-1 Çkô¤-¯ÛÅ-hP-ºfïm-¯ÛÅü Addition and Subtraction

º²Ûm-IÔ-GôP-¤ºÛ-Ç+zÅü P-±ôÅ-Çkô¤-¯ÛÅ-hP-ºfïm-¯ÛÅ-Ç+ô¼-¢PÅ-»ôhü P-±ôºÛ-ZÛm-¼ïºÛ-º±ô-zºÛ-Fôh-ˆÛ-h;º-½‰ôG-Åï¾-fzÅ-Vïhü ¯Û-fzÅ-ºhÛ-hG-Ç+ô¼-h-hÝP-¢ôP-zl¼-‚-Mã-»Ûmü

¯ÛÅ-hqïü 1. 25796, 18647, 418 n¤Å-Çkô¤Å-ÁÛGü¾mü¾mü¾mü¾mü¾mü

¯ÛÅ-hqïü 2. 1703, 45, 632, 81303 zTÅ- Û̂-zÇkô¤Å-fôz-±ô¾ü¾mü¾mü¾mü¾mü¾mü

¯ÛÅ-hqïü 3. 50791 mÅ-22536 ºfïm-q¼-‚ü¾mü¾mü¾mü¾mü¾mü

¯ÛÅ-hqïü4.‚ÛÅ-qºÛ-ZÛm-¤ô¼ü ÇÀôz-yâG-15633 ¼Û-¤ô-ºIm-zÇkÝ¼-ŸÛG-¾-º²â¾-ŸÝGÅ-‚Å-»ôhü hïºÛ-Fôh-zÞ-¤ô-8749 »ôh-qÅü zÞ-G-±ôh-»ôh-h¤ü

2 5 7 9 6 1 8 6 4 7

+ 4 1 8 4 4 8 6 1

1 7 0 3 4 5 6 3 2+ 8 1 3 0 3 8 3 6 8 3

5 0 7 9 1 2 2 5 3 6 2 8 2 5 5


26

¾mü¾mü¾mü¾mü¾müºIm-zÇkÝ¼-¾-ŸÝGÅ-qºÛ-ÇÀôz-yâG-IPÅü = 15633

zÞ-¤ô-º²â¾-ŸÝGÅ-‚Å-qºÛ-IPÅü = 8749

zÞ-º²â¾-ŸÝGÅ-‚Å-qºÛ-IPÅü = 15633 8749

¯ÛÅ-hqïü5.IôP-Çkï-ŸÛG-GÛ-¤Û-100000 ¾-iÛ-z¯h-‚Å-q-mü hï-hG-¾Å-¤Û-36552 ºIâ¾-ºDô¼-zMãh-mÅ-ºIâ¾-zŸÝh-‚ïh-q-hP.ü ¤Û-54448 ®¤-HÛÅ-¤ï-ºDô¼-uôh-TÛP.ü ¿ËG-¤-n¤Å-ˆÛÅ-ÇoÝ¤-ºDô¼-zMãh-¾Å-;¼-zBôh-ˆÛ-»ôh-ºhÝG-mü ÇoÝ¤-ºDô¼-zMãh-¾Å-;¼-Bôh-¤Dm-¤Û-G-±ôh-ºhÝG-G¤ü¾mü¾mü¾mü¾mü¾mü

IôP-Çkï-hï¼-»ôh-qºÛ-¤Û-IPÅü = 100000

ºIâ¾-ºDô¼-mP-zBôh-qºÛ-¤Û-IPÅü = 36552

¤ï-ºDô¼-zMãh-zBôh-qºÛ-¤Û-IPÅü = 54448

ºIâ¾-ºDô¼-hP-¤ï-ºDô¼-GZÛÅ- Û̂-mP-Bôh-¤Dm-¤Û-IPÅ-mÛü = 36552 + 54448

ÇoÝ¤-ºDô¼-zMãh-¾Å-;¼-zBôh-qºÛ-¤Û-IPÅü = 100000 91000

hï¼-zdïmü ÇoÝ¤-ºDô¼-zMãh-¾Å-;¼-zBôh-qºÛ-¤Û-IPÅ-mÛ-9000 ¼ïhü

1 5 6 3 3 8 7 4 9 6 8 8 4

1 0 0 0 0 0 9 1 0 0 0

9 0 0 0

3 6 5 5 2+ 5 4 4 4 8

9 1 0 0 0


27

¢ôP-±mü 2.11ü Çkô¤Åü

;) 23095 hP-600, 250D) 60218 hP-3521, 6400

2ü GÁ¤-GÅ¾-n¤Å-ˆÛ-zÇkô¤Å-fôz-±ô¾ü;) 67504 hP-16370, 8976 D) 54398 hP-4068, 7560

3ü IPÅ-;-GZÛÅ-q-hï-hP-qô-mÅ-ºfïmü;) 50216, 31552 D) 100000, 99999

4ü IPÅ-;-GZÛÅ-ˆÛ-Èï-zG-±ô¾ü;) 40201 hP-7436 D) 38165 hP-85707 G) 31720 hP-758

5ü ¾ô-ŸÛG-¾ü Û̄Å-¼ÛG-hGï-Lm-77193 »ôh-q-hP.ü ±m-¼ÛG-hGï-Lm-14070 »ôh-mü ÇÀôz-±m-hï-GZÛÅ-ˆÛ-hGï-Lm-Eôm-zÇkô¤Å-G-±ôh-»ôh-h¤ü

6ü ºôÅ-zÇkÝ-ŸÛG-GÛ-mP.ü ºôÅ-¤Û-GÅÞ¤-»ôh-q-¾-ºôÅ-IPÅ-38097, 8954, 15784 zTÅ-fôz-»ôh-mü ºôÅ-¤Û-»ôPÅ-¾-ºôÅ-ÁôG-ºwïm-¤Dm-G-±ôh-‚ãP-ºhÝG-G¤ü

7ü ;Û¼-;ï‡-¯ïh-ºIm-ŸÛG-GÛ-Ç+zÅü ZÛm-hP-qôºÛ-¼ÛP-¾G-ºEï¼-3608 z®ôPÅ-»ôhü ZÛm-GZÛÅ-q¼-¾G-ºEï¼-4896 z®ôPÅ-»ôh-q-hP.ü ZÛm-GÅÞ¤-q¼-¾G-ºEï¼-3702 z®ôPÅ-»ôhü ºô-mü ZÛm-GÅÞ¤-¼ÛP-¾G-ºEï¼-G-±ôh-z®ôPÅ-»ôh-h¤ü

8ü hqï-¤²ôh-TÛG-GÛ-mP-h‚Ûm-»ÛG-hïz-9575 hP.ü ÈÛm-hÛ-hïz-5930 Ç+h-»ÛG-GŸm-HÛ-hqï-hïz-2045

zTÅ-»ôhü hqï-¤²ôh-hïºÛ-mP-hqï-hïz-G-±ôh-»ôh-h¤ü9ü ¤Pº-Çkï-ŸÛG-GÛ-mP-IôP-Çkï-86465 »ôhü IôP-Çkï-hï-hG-¾Å-57781 mP-GŸÛ-¼Û¤-ºôG-¤ºÛ-ÇÀôz-IÔ-»ôh-

qÅü GŸÛ-¼Û¤-ºôG-¤ºÛ-ÇÀôz-IÔ-¤ïh-qºÛ-IôP-Çkï-G-±ôh-»ôh-h¤ü10ü 19317 ¾Å-2197 ¤P-zºÛ-IPÅ-;-hï-GP-»Ûm-m¤ü11ü 63709 ¾Å-1073 ZÝP-zºÛ-IPÅ-;-hï-GP-»Ûm-m¤ü


28

12ü 80000 ºfôz-q-¾ü 62345 fôG-IPÅ-;-GP-Çoôm-hGôÅ-Å¤ü13ü hzP-xãG-GÛÅ-Ç~G-Ç~G-TÛG-¾-ÇKô¼-40578 vh-hï-Zô-hGôÅ-zÅ¤Å-»ôhü DôP-GÛ-hPÞ¾-hïz-fôG-ÇKô¼-

38057 »ôh-mü DôP-¾-h-hÝP-hPÞ¾-G-±ôh-hGôÅ-Å¤ü14ü 36490 »Û-6 hP-9 »Û-IPÅ-GmÅ-GZÛÅ-wm-±ßm-zXï-qô-zMz-mü IPÅ-;-fôG-¤-hP-XïÅ-¤-GZÛÅ- Û̂-

hz¼-HÛ-Èï-zG-G-±ôh-¼ïh-h¤ü15ü IPÅ-GmÅ-5 Tm-HÛ-IPÅ-;-Vï-ÁôÅ-hP.ü IPÅ-GmÅ-6 Tm-HÛ-IPÅ-;-VßP-ÁôÅ-hz¼-HÛ-Èï-zG-±ô¾ü

;) 5 11 5 1 5

5 4 8+ 2 1 5 6

4 0 3 4 1

4 8 3 95 7 6

4 8 2+ 9 7 2

5 8 7 9

7 4 3

2 6 9 5 3 2 1

D) G)1 5 1 0

1 2 4

+ 4 7 6 8 9 2 2 3

P) T)4 8 4 2

9 8 4 0 6 1

16ü IP-JÀôG-TÛG-GÛ-GôP-±h-ÇKô¼-5296 hP.ü ;¤-qÞ-‡¼-ŸÛG-GÛ-GôP-±h-mÛ-IP-JÀôG-¾Å-ÇKô¼-25050 »ÛÅ-Vï-z-»ôhü ºô-mü;) ;¤-qÞ-‡¼-HÛ-GôP-±h-±ô¾üD) IP-JÀôG-hP-;¤-qÞ-‡¼-HÛ-Eôm-zÇkô¤Å-GôP-±h-±ô¾ü

17ü IôP-l¾-ŸÛG-mP-¤Û-30000 ¾Å-;¼-zBôh- Û̂-»ôhü hï-hG-¾Å-¤Û-9807 z ô̧-IÔºÛ-mP-¾Å-;-‚ïh- Û̂-»ôh-q-hP.ü ¤Û-11531 ±ôP-DP-mP-¾Å-;-‚ïh-q-hP.ü hï-ºyôÅ-n¤Å-GŸÝP-GÛ-ÆÛ-ŸÝ-z-»Ûm-qÅü GŸÝP-GÛ-ÆÛ-ŸÝ-z-IPÅ-G-±ôh-»ôh-h¤ü

18ü 405 hP-3207 GZÛÅ- Û̂-zÇkô¤Å-fôz-hï-10370 ¾Å-ºfïm-q-mü P-±ô¼-Èï-zG-GP-ºfôz-z¤ü19ü GÁ¤-HÛ-Ç+¼-dGÅ-( )»ôh-qºÛ-IPÅ-GmÅ-n¤Å-ÅÞ-ÍP-;Û-GP-ºôÅ-¼ï-ƒÛÅü


29

2-2 2-2 2-2 2-2 2-2 Nå¼-¯ÛÅ-hP-zGôh-¯ÛÅü Multiplication and Division

º²Ûm-IÔ-zŸÛ-qºÛ-Ç+zÅü P-±ôÅ-IPÅ-;-GZÛÅ-Nå¼-ÇePÅ-Ç+ô¼-¢PÅ-»ôhü Ç+zÅ-hï¼-zNå¼-fôz-IPÅ-GmÅ-5 ¾Å-zL¾-HÛ-¤ïhü h-¿e-P-±ôÅ-zNå¼-fôz-IPÅ-GmÅ-5 z¼-º‚ãP-zºÛ-Nå¼-¯ÛÅ-ˆÛ-¢ôP-zl¼-¤Þ-¤fÞh-‚Å-bïü Nå¼- Û̄Å-MG-ÇePÅ-‚P-Vßz-q¼-‚-Mã-»Ûmü

IPÅ-;-GP-¼ÞP-ŸÛG-Çeï-hqï¼-mü 209 ¾-425 »ÛÅ-zNå¼-hGôÅ-mü P-±ôÅ-GÁ¤-GÅ¾-¿e¼-zNå¼-VôG

¯ÛÅ-hqïü6.fô-hïz-TÛG-¾-ÁôG-PôÅ-256 »ôhü ÁôG-PôÅ-¼ï-¼ï¼-»ÛG-yïP-35 »ôh-mü fô-hïz-hïºÛ-ÇeïP-Eôm-zÇkô¤Å-»ÛG-yïP-G-±ôh-»ôh-h¤ü¾mü¾mü¾mü¾mü¾mü

h;º-½‰ôG-ºhÛºÛ-mP.ü P-±ôÅ-256 ¾-35 »ÛÅ-zNå¼-hGôÅ-q-GÅ¾-qô-¼ïhü

hï¼-zdïmü fô-hïz-hïºÛ-mP-Eôm-zÇkô¤Å-»ÛG-yïP-8960 »ôhüº²Ûm-IÔ-GôP-¤ºÛ-Ç+zÅü P-±ôÅ-IPÅ-GmÅ-4 Tm-HÛ-IPÅ-;-ŸÛG-¾-IPÅ-GmÅ-1 G¤-2 Tm-

HÛ-IPÅ-;-ŸÛG-GÛÅ-zGôh-ÇePÅ-Ç+ô¼-¢PÅ-»ôhü h-¿eü P-±ôÅ-ÇS¼-¾¤-¿e¼ü IPÅ-GmÅ-5 Tm-¾-IPÅ-

2 0 9

× 4 2 5

1 0 4 5

4 1 8 0

+ 8 3 6 0 08 8 8 2 5

209 × 5

209 × 20

209 × 400

2 5 6

× 3 5

1 2 8 0

+ 7 6 8 0 8 9 6 0


30

GmÅ-2 »P-m-3 Tm-HÛÅ-zGôh-ÇePÅ-Ç+ô¼-¢P-Mã-»Ûmü

¯ÛÅ-hqïü7.27685 hï-47 HÛÅ-zGôÅü¾mü¾mü¾mü¾mü¾mü P-±ôÅ-GÁ¤-GÅ¾-Gô¤-¼Û¤-¿e¼-zGô-hGôÅü

hï¼-zdïmü zGôÅ-fôzü = 589 zGôÅ-¿ËG = 2

¯ÛÅ-hqïü8.32980 hï-325 »ÛÅ-zGôÅü¾mü¾mü¾mü¾mü¾mü P-±ôÅ-GÁ¤-GÅ¾-Gô¤-¼Û¤-¿e¼-zGô-hGôÅü


547 27685 –2 3 5 4 1

5847 27685 –235 4 1 8 – 3 7 6 4 2

58947 276 8 5 –235 4 1 8 – 3 7 6 4 2 5 – 4 2 3

2

Gô¤-q-1 Gô¤-q-2

Gô¤-q-3

Gô¤-q-1 Gô¤-q-2 Gô¤-q-3 13 2 5 3 2 9 8 0 – 3 2 5 4

1 03 2 5 3 2 9 8 0 – 3 2 5 4 8

1 0 13 2 5 3 2 9 8 0 – 3 2 5 4 8 0 – 3 2 5

1 5 5


31

¯ÛÅ-hqïü9. 70104 hï-205 »ÛÅ-zGôÅü¾mü¾mü¾mü¾mü¾mü P-±ôÅ-GÁ¤-GÅ¾-¿e¼-zGô-hGôÅü


¯ÛÅ-hqïü10. hôÅ-ÇK¤-ŸÛG-GÛ-mP.ü ºƒÛ-hïz-125 zTßG-»ôhü ºƒÛ-hïz-hï-ºi-35875 ºWâG-q¼-hôÅ-ÇK¤-G-±ôh-hGôÅ-Å¤ü¾mü¾mü¾mü¾mü¾mü

Eôm-zÇkô¤Å-»ôh-qºÛ-hïz-IPÅü = 35875

hôÅ-ÇK¤-1 GÛ-mP-»ôh-qºÛ-hïz-IPÅü = 125

hGôÅ-¤DôºÛ-hôÅ-ÇK¤-IPÅü = 35875 ÷ 125

hï¼-zdïmü ºƒÛ-hïz-hï-ºi-35875 ºWâG-q¼-hôÅ-ÇK¤-287 hGôÅü

3 4 12 0 5 7 0 1 0 4 – 6 1 5 8 6 0 – 8 2 0 4 0 4 – 2 0 5 1 9 9

2 8 71 2 5 3 5 8 7 5 – 2 5 0 1 0 8 7 – 1 0 0 0 8 7 5 – 8 7 5 0


32

¢ôP-±mü 2.21ü GÁ¤-GÅ¾-DG-GÛ-zNå¼-fôz-±ô¾ü

;) 2578 × 27 D) 4016 × 19 G) 318 × 33

P) 874 × 69 T) 590 × 143 V) 148 × 367

W) 107 × 210 Z) 3005 × 32 b) 1029 × 91

2ü GÁ¤-GÅ¾-DG-GÛ-zGôÅ-fôz-hP-zGôÅ-¿ËG-±ô¾ü;) 21594 ÷ 21 D) 71683 ÷ 36 G) 92508 ÷ 165

P) 49040 ÷ 29 T) 93456 ÷ 58 V) 74816 ÷ 64

W) 41359 ÷ 358 Z) 78509 ÷ 267 b) 38095 ÷ 416

3ü PG-¯ÛÅ-zMz-Çeï-GÁ¤-GÅ¾-DG-GÛ-zNå¼-fôz-±ô¾ü;) 3146 × 0 D) 7169 × 10 G) 458 × 100

P) 72 × 1000 T) 2 × 50 × 67 V) 643 × 4 × 25

W) 1095 × 0 × 3 Z) 703 × 1 × 100 b) 10 × 825 × 10

4ü ZÛm-ŸÛG-ÇtôÅ-Eï¼-D-q¼-±ôP-DP-ŸÛG-GÛÅ-D-q¼-35 z®ôPÅ-q-¼ïhü ÇtôÅ-Eï¼-D-q¼-1 GÛ-GôP-±h-ÇKô¼-1225 »Ûm-mü ±ôP-zhG-hï¼-hPÞ¾-ºzô¼-G-±ôh-fôz-»ôh-h¤ü

5ü ÁôG-ÇK¤-ŸÛG-GÛ-mP-ºWÛz-¼Û¾-365 »ôh-mü ÁôG-ÇK¤-hï-ºi-202 mP-ºWÛz-¼Û¾-G-±ôh-»ôh-h¤ü6ü hôÅ-ÇK¤-ŸÛG-GÛ-mP-;Ý-ÁÝ-58 ¼ï-zTßG-»ôhü ;Ý-ÁÝ-55216 ºWâG-q¼-hôÅ-ÇK¤-G-±ôh-I-OÛG-‚-hGôÅ-

Å¤ü7ü Åô-wG-z ô̧-IÔ-ŸÛG-GÛÅ-Eôm-zÇkô¤Å-Åô-wG-40729 z ô̧Å-»ôhü Åô-wG-hï-hG-V-Ç‰ô¤Å-Çe¼-q-169 ‚Å-

mÅ-z¯ÛGÅ-»ôh-mü Çe¼-q-¼ï¼-Åô-wG-G-±ôh-»ôh-h¤ü8ü P-±ôÅ-ÁïÅ-GÅ¾-¿e¼ü Ç+¼-¤-GTÛG-¾-Ç+¼-V-60 »ôh-¾ü Vß-±ôh-GTÛG-¾-Ç+¼-¤-60 »ôhü ºô-mü

Vß-±ôh-24 ¾-Ç+¼-V-G-±ôh-»ôh-h¤ü9ü GÁ¤-HÛ-Ç+¼-dGÅ-( )»ôh-qºÛ-IPÅ-GmÅ-n¤Å-ÅÞ-ÍP-;Û-GP-ºôÅ-¼ï-ƒÛÅü


33

;) 3 8

× 0 9

3 4 5

0 0 0

+ 7 7 0 0 0 0 4 5

D)6 4

× 3

5 9 2

+ 2 0 0 2 5 1

G) P) 1 83 6 5 7 0 6 – 3 2 1 – 1 8 0 3 0 – 2 8 8 2 1 6

0

9 15 0 4 9 5 0 – 4 5 0 5 – 5 0 4 5 – 4 5

2-3 2-3 2-3 2-3 2-3 »Û-GïºÛ-¯ÛÅ-GŸÛ-z¸ô-zü Framing Word Problems

P-±ôÅ-¯-zºÛ- Û̄-fzÅ-zŸÛ-hP-ºƒï¾-zºÛ-ÍP-;ÛºÛ- Û̄Å-GŸÛ-zOÛGÅ-qºÛ-ÇKô-mÅü »Û-GïºÛ- Û̄Å-GŸÛº¤-h;º-½‰ôG-Åï¾-ÇePÅ-Ç+ô¼-¢PÅ-»ôhü zMãh-¼Û¤-ºhÛ-Fôhü iÛ-z-ŸÛG-»ôP-ÆÛh-q-mÛü G¾-bï-P-±ô¼-ÍP-;ÛºÛ- Û̄Å-GŸÛ-ŸÛG-vh-mü P-±ôÅ-ÍP-;ÛºÛ- Û̄Å-GŸÛ-hï-hP-¤±ßPÅ-qºÛ-»Û-GïºÛ- Û̄Å-GŸÛ-ŸÛG-z ô̧-fÞz-z¤ü ºhÛ¼-P-±ôÅ-vh-¸Ûm-qºÛ-ÍP-;ÛºÛ-¯ÛÅ-GŸÛ-ŸÛG-¾-»Û-GïºÛ-¯ÛÅ-GŸÛ-z¸ô-ÇePÅ-Ç+ô¼-¢P-Mã-»Ûmü


34

h-¿e-P-±ôÅ-GÁ¤-GÅ¾-GmÅ-ÇePÅ-¾-zÅ¤-„Àô-GbôP-Mãü3 + 4 = ?

GôP-GÛ-¯ÛÅ-GŸÛ-hï-hGï-Lm-HÛÅ-mG-qP-fôG-ƒÛÅ-bï-ÇÀôz-yâG-±ô¼ü ¯ÛÅ-GŸÛ-hï-hP-¤±ßPÅ-qºÛ-»Û-GïºÛ-¯ÛÅ-GŸÛ-ŸÛG-z¸ô-¼Þ-ºWâG-hGôÅü ºhÛ¼-ÇÀôz-yâG-±ôÅ-¾m-ºhïzÅ-‚ïh-±ß¾-ºGº-ŸÛG-GÁ¤-GÅ¾-¿e¼-º‚ãP-Pô.ü ü1ü zÇem-º²Ûm-¼z-hGº-»ÛÅ-Ÿ-«åG-3 ZôÅ-q-hP.ü zÇem-º²Ûm-¼z-¤²ïÅ- Û̂Å-Ÿ-«åG-4 ZôÅ-»ôhü DôP-

GZÛÅ-;¼-Eôm-zÇkô¤Å-Ÿ-«åG-G-±ôh-»ôh-h¤ü2ü ZÛ-Oôm-HÛÅ-¼ïÅ-G¸º-¹-z-ZÛm-iÛ-z-3 ¾-¾m-ƒÛÅ-q-hP.ü ¼ïÅ-G¸º-¤ÛG-h¤¼-ZÛm-iÛ-z-4 ¾-¾m-ƒÛÅ-

»ôh-mü ZÛm-GZÛÅ-¼ÛP-iÛ-z-G-±ôh-¾-¾m-ƒÛÅ-»ôh-h¤ü3ü EÛ¤-±P-ŸÛG-GÛ-mP-mP-¤Û-3 »ôh-q-hP.ü EÛ¤-±P-GŸm-ŸÛG-mP-mP-¤Û-4 »ôhü EÛ¤-±P-hï-GZÛÅ-

;¼-Eôm-zÇkô¤Å-mP-¤Û-G-±ôh-»ôh-h¤üP-±ôÅ-ºhÛ-¿e-zÞºÛ-»Û-GïºÛ-¯ÛÅ-GŸÛ-¤P-qô-z¸ô-fÞzü GP-¿e¼ü ÇÀôz-yâG-±ôÅ-GôP-GÛ-iÛ-z-¼ï-¼ïºÛ-¾m-

3 + 4 = ? »Ûm-±ï-ºIÛGÅ-»ôhü hï¼-zdïmü ÍP-;ÛºÛ- Û̄Å-GŸÛ-PïÅ-Tm-ŸÛG-¾ü P-±ôÅ-»Û-GïºÛ- Û̄Å-GŸÛ-¤Û-ºi-z-È-TP-¤P-qô-z ô̧-fÞzü ºôm-ˆP.ü G¾-bï- Û̄Å-GŸÛ-z ô̧-Ç+zÅ-V-Aïm-hP-zl-Çeôm-(Clue)h¤ÛGÅ-zÅ¾-vh-»ôh-±ïü P-±ôÅ-¯ÛÅ-GŸÛºÛ-mP-vh-¸Ûm-qºÛ-V-Aïm-n¤Å-ƒÛÅ-bï-±ôh-º²Ûm-‚-hGôÅü

hqï¼-mü±ÛG-Gmhü ‘‘zÇem-º²Ûm-¼z-hGºü zÇem-º²Ûm-¼z-¤²ïÅü Ÿ-«åG’’P-±ôÅ-h;º-½‰ôG-z¸ô-Ç+zÅ-±ôh-º²Ûm-‚Å-bï-GôP-GÛ-iÛ-z-1 qô-Dô-m-¿e¼-z¸ô-hGôÅühï-P-±ôÅ-¯ÛÅ-hqï-ºGº-zMãh-mÅ-ºIï¾-zXôh-‚ïh-hôü ü

¯ÛÅ-hqïü11. GÁ¤-HÛ-¯ÛÅ-GŸÛ-¾-»Û-GïºÛ-¯ÛÅ-GŸÛ-ŸÛG-z¸ôÅü4 + 5 = ?

(±ÛG-Gmhü zÅôh-m¤Å-zhï-BÛhü ±ï-¼ÛP-n¤-M¾ü TôG-¾ï-‡Ûü)¾mü¾mü¾mü¾mü¾mü


35

h;º-½‰ôG-ºhÛ-GÁ¤-GÅ¾-¿e¼-z¸ô-VôGzÅôh-m¤Å-zhï-BÛh-¾-TôG-¾ï-‡Û-4 »ôhü ±ï-¼ÛP-n¤-M¾-¾-TôG-¾ï-‡Û-5 »ôhü ºô-mü DôP-GZÛÅ-¾-

TôG-¾ï-‡Û-G-±ôh-»ôh-h¤ü

¯ÛÅ-hqïü12. GÁ¤-HÛ-¯ÛÅ-GŸÛ-¾-»Û-GïºÛ-¯ÛÅ-GŸÛ-ŸÛG-z¸ôÅü8 – 3 = ?

(±ÛG-Gmhü ºôG-GÛ-¼Û-¤ô¼-¿eôÅü)

¾mü¾mü¾mü¾mü¾müP-±ôÅ-h;º-½‰ôG-ºhÛ-GÁ¤-GÅ¾-¿e¼-z¸ô-VôGÇkôP-qôºÛ-»¾-G-ŸÛG-GÛ-ÇeïP-‚ïºÞ-8 zzÅ-»ôhü hï-hG-¾Å-‚ïºÞ-3 ºwÞ¼-xÛm-mü »¾-GºÛ-ÇeïP-»ôh-

qºÛ-‚ïºÞ-IPÅ-ºzô¼-G-±ôh-»Ûm-m¤ü

¯ÛÅ-hqïü13. GÁ¤-HÛ-¯ÛÅ-GŸÛ-¾-»Û-GïºÛ-¯ÛÅ-GŸÛ-ŸÛG-z¸ôÅü452 × 15 = ?

(±ÛG-Gmhü Í-§ü Í¤-ÇkôP.ü)¾mü¾mü¾mü¾mü¾mü


36

P-±ôÅ-h;º-½‰ôG-ºhÛ-GÁ¤-GÅ¾-¿e¼-z¸ô-VôGBïh-±¾-ŸÛG-GÛ-mP-Í¤-ÇkôP-15 »ôhü G¾-bï-Í¤-ÇkôP-¼ïºÛ-fôG-ÁÛP-bôG-Í-§-452 ¼ï-»ôh-mü Bïh-

±¾-hïºÛ-mP-GÛ-Í¤-ÇkôP-fôG-Eôm-zÇkô¤Å-Í-§-G-±ôh-»ôh-h¤ü

¯ÛÅ-hqïü14. GÁ¤-HÛ-¯ÛÅ-GŸÛ-hP-¤fÞm-qºÛ-»Û-GïºÛ-¯ÛÅ-GŸÛ-ŸÛG-z¸ôÅü28 ÷ 7 = ?

(±ÛG-Gmhü „ËÛ-ÅÛ-;ô-‡Ûü ÇÀôz-yâG)¾mü¾mü¾mü¾mü¾mü

P-±ôÅ-h;º-½‰ôG-ºhÛ-GÁ¤-GÅ¾-¿e¼-z¸ô-VôG„ËÛ-ÅÛ-;ô-‡Û-28 V-Ç‰ô¤Å-ÇÀôz-yâG-7 ¾-zGôÅ-mü ÇÀôz-yâG-¼ï-¼ï¼-„ËÛ-ÅÛ-;ô-‡Û-G-±ôh-ºfôz-z¤ü

¯ÛÅ-hqïü15. GÁ¤-HÛ-¯ÛÅ-GŸÛ-hP-¤fÞm-qºÛ-»Û-GïºÛ-¯ÛÅ-GŸÛ-ŸÛG-z¸ôÅü12 × 4 = ?

±ÛG-Gmhü

¾mü¾mü¾mü¾mü¾mü;ï-¾-VG-q-ŸÛG-¾-;ï-¾-12 »ôh-mü ;ï-¾-VG-q-4 ¾-;ï-¾-G-±ôh-»ôh-h¤ü


37

¢ôP-±mü 2.3

GÁ¤-GÅ¾-±ÛG-Gmh-DG-¾-GŸÛGÅ-bï-hï-¤±ßPÅ-ˆÛ-»Û-GïºÛ-¯ÛÅ-GŸÛ-¼ï-z¸ôÅü1) 879 + 448 = ?

(±ÛG-Gmhü ÇÀôz-yâG ÇÀôz-IÔü)2) 122 + 207 + 115 = ?

(±ÛG-Gmhü Í-§ü ;Ý-ÁÝü ;ï-¾ü Bïh-±¾ü)3) 100 – 57 = ?

(±ÛG-Gmhü ±ôP-zhG ½ÀâP-ºDô¼ü)4) 150 + 200 + 125 = ?

(±ÛG-Gmhü ÈÛm-ÇKô¼ü ¤Û-±P-Z¤-fG Bôz-GÅô-±ôGÅ-qü)5) 4 × 4 = ?

±ÛG-Gmhü

6) 12 ÷ 2 = ? 7) 25 × 12 = ?

(±ÛG-Gmhü ¿KP-wÞG IôGÅ-qôü) (±ÛG-Gmhü ¤ï-bôG yïP-zü)


38

8) 50 × 7 = ? 9) 18 × 24 = ?

(±ÛG-Gmhü ¿KP-wÞG ÁôG-ÇK¤ü) (±ÛG-Gmhü zÞ-¤ôü Çe¼-qü)

10) 1920 ÷ 8 = ? 11) 80 × 90 = ?

(±ÛG-Gmhü Iô-ŸÛz-GÅô-Nïü hôÅ-DP.ü ½ÀPÅ-ºDô¼ü) (±ÛG-Gmhü zNå¼-fôzü IPÅ-;ü)

12) 3648 ÷ 24 = ? 13) 35 × 12 = ?

(±ÛG-Gmhü ºWÛz-¼Û¾ü ÁôG-ÇK¤ü) (±ÛG-Gmhü º²Ûm-IÔ-¿S-qü ÇÀôz-»ômü)

14) 750 × 8 = ? 15) 45 × 30 = ?

(±ÛG-Gmhü GôP-±hü Vß-±ôh-ºDô¼-¾ôü) (±ÛG-Gmhü GôP-±hü hqï-hïzü)

16) 60 × 60 = ? 17) 2920 ÷ 365 = ?

(±ÛG-Gmhü Ç+¼-¤ü Ç+¼-Vü) (±ÛG-Gmhü ZÛmü ¾ôü)

18) 14 × 120 = ?

(±ÛG-Gmhü GôP-±hü ¼Å-Vü ¤Û-‡¼ü)


39

2-4 2-4 2-4 2-4 2-4 hqï-ºIôÅü Pattern

2-4-1 2-4-1 2-4-1 2-4-1 2-4-1 9 ¤fº-Tm-HÛ-¿kz-IPÅ-¾Å-‚ãP-zºÛ-hqï-ºIôÅü Patterns in Multiples of Numbers Ending in 9

º²Ûm-IÔ-zŸÛ-qºÛ-Ç+zÅü P-±ôÅ-hqï-ºIôÅ-DG-TÛG-¢PÅ-»ôhü ºhÛ¼ü P-±ôÅ-Pô-¤±¼-Tm-HÛ-hqï-ºIôÅ-DG-TÛG-¾-ÇÀôz-¢ôP-‚ºôü ü

fôG-¤¼-P-±ôÅ-9 ¤fº-Tm-HÛ-¿kz-IPÅ-ºfôz-qºÛ-‚ïh-ÇKô-DG-TÛG-mÅ-ºGô-º²âGÅ-q¼-‚ü‚ïh-ÇK ôü1‚ïh-ÇK ôü1‚ïh-ÇK ôü1‚ïh-ÇK ôü1‚ïh-ÇK ôü1 Gô¤-qü1Gô¤-qü1Gô¤-qü1Gô¤-qü1Gô¤-qü1 1 ƒÛÅü

Gô¤-qü2Gô¤-qü2Gô¤-qü2Gô¤-qü2Gô¤-qü2 hï¼-2 zÇkô¤Å-bïü zÇkô¤Å-fôz-1 GÛ-ºôG-bà-ƒÛÅüG ô¤-qü3Gô¤-qü3Gô¤-qü3Gô¤-qü3Gô¤-qü3 zÇkô¤Å-fôz-19 ¤-ÇÀïzÅ-z¼-hÝ-Gô¤-q-2 q-zB¼-¹ôÅ-‚ôÅüG ô¤-qü4Gô¤-qü4Gô¤-qü4Gô¤-qü4Gô¤-qü4 GÁ¤-HÛ-IPÅ-;-¿e¼-ÇÀïzÅ-»ôh-¤ïh-ŸÛz-zÁï¼-‚ôÅüG ô¤-qü5Gô¤-qü5Gô¤-qü5Gô¤-qü5Gô¤-qü5 19 »Û-G»Å-xôGÅ-ÅÞ-0 ƒÛÅü

G ô¤-qü6Gô¤-qü6Gô¤-qü6Gô¤-qü6Gô¤-qü6 0 GôP-hÝ-¼Û¤-q-zŸÛm-1,2,3, ..., 9 zTÅ-ƒÛÅüG ô¤-qü7Gô¤-qü7Gô¤-qü7Gô¤-qü7Gô¤-qü7 ¤fº-¤¼-GÁ¤-HÛ-IPÅ-;-¿e¼-ÇÀïzÅ-»ôh-¤ïh-ŸÛz-zÁï¼-‚ôÅü

13579

1 11 31 51 71 9


40

Gô¤-qü8Gô¤-qü8Gô¤-qü8Gô¤-qü8Gô¤-qü8 GôP-GÛ-IPÅ-;-n¤Å-19 »Û-¿kz-IPÅ-»Ûm-¤Ûm-ŸÛz-zÁï¼-‚ôÅü‚ïh-ÇKô-XïÅ-¤-ºhÛ-»P-GôP-GÛ-‚ïh-ÇKô-1 qô-hP-¤±ßPÅü

‚ïh-ÇK ôü2‚ïh-ÇK ôü2‚ïh-ÇK ôü2‚ïh-ÇK ôü2‚ïh-ÇK ôü2 Gô¤-qü1Gô¤-qü1Gô¤-qü1Gô¤-qü1Gô¤-qü1 2 ƒÛÅüGô¤-qü2Gô¤-qü2Gô¤-qü2Gô¤-qü2Gô¤-qü2 hï¼-3 zÇkô¤Å-bïü zÇkô¤Å-fôz-2 Û̂-ºôG-bà-ƒÛÅüG ô¤-qü3Gô¤-qü3Gô¤-qü3Gô¤-qü3Gô¤-qü3 zÇkô¤Å-fôz-29 ¤-ÇÀïzÅ-z¼-hÝ-Gô¤-q-2 q-zB¼-¹ôÅ-‚ôÅüG ô¤-qü4Gô¤-qü4Gô¤-qü4Gô¤-qü4Gô¤-qü4 29 »Û-G»Å-xôGÅ-ÅÞ-0 ƒÛÅüG ô¤-qü5Gô¤-qü5Gô¤-qü5Gô¤-qü5Gô¤-qü5 ‚ïh-ÇKô-1 qôºÛ-Gô¤-q-6 q-hP-7 q-¿e¼-‚ôÅüG ô¤-qü6Gô¤-qü6Gô¤-qü6Gô¤-qü6Gô¤-qü6 fôz-¸Ûm-qºÛ-IPÅ-;-n¤Å-29 »Û-¿kz-IPÅ-»Ûm-¤Ûm-ŸÛz-zÁï¼-‚ôÅü

GôP-GÛ-‚ïh-ÇKô-1 hP-2 GZÛÅ-¾-¿e-ŸÛz-mm-bm-‚Å-bïü ºôG-GÛ-iÛ-z-DG-¾-¾m-fôzÅü;) Gô¤-q-1 qôºÛ-IPÅ-;-ºGô-¤-hï-hP.ü Gô¤-q-2 qºÛ-Çkô¤-‚ïh-IPÅ-hz¼-ºƒï¾-z-WÛ-¿e¼-»ôh-h¤üD) G¾-bï-39 »Û-¿kz-IPÅ-ºƒÛ-hGôÅ-mü P-±ôÅ-ºGô-º²âGÅ-ÅºÛ-IPÅ-;-hï-GP-»Ûm-hGôÅ-q-hP.ü ¤fº-

¤WâG-GÛ-IPÅ-hï-GP-»Ûm-m¤ü‚ïh-ÇK ôü3‚ïh-ÇK ôü3‚ïh-ÇK ôü3‚ïh-ÇK ôü3‚ïh-ÇK ôü3 GôP-GÛ-‚ïh-ÇKô-hP-¤±ßPÅ-q¼ü 49, 59, 69 ÅôGÅ- Û̂-¿kz-IPÅ-fôG-¤-zTß-ƒÛÅü hï-XïÅ-Eôh-ˆÛ-ºƒÛ-ÇePÅ-ˆÛ-fzÅ-¾¤-bG-bG-»Ûm-¤Ûm-ŸÛz-zÁï¼-‚ôÅü

1 93 85 77 69 5

1 1 41 3 31 5 21 7 11 9 0


41

2-4-2 2-4-2 2-4-2 2-4-2 2-4-2 ¼ÛGÅ-zOï-zü Generalisation

D-Ç+ôPÅü

G¾-bï-P-±ôÅ-IPÅ-GmÅ-¤fº-¤- »Ûm-qºÛ-IPÅ-GmÅ-GZÛÅ-Tm-HÛ-¿kz-IPÅ-fôG-¤-

zTß-ºƒÛ-hGôÅ-mü fôG-¤¼-P-±ôÅ-IPÅ-GmÅ- (G»Å-qº¤-G»ôm-¤-)mÅ-hï-¾ü IPÅ-;-

¼P-ZÛh-¾Å- Vï-zºÛ-IPÅ-Çkô¤-hGôÅü ºhÛ-¿e¼-P-±ôÅ-º±ô¾-hGôÅ-qºÛ-IPÅ-GmÅ-GZÛÅ-Tm-

HÛ-IPÅ-;-hï-¤-ÇÀïzÅ-z¼-hÝ-zB¼-¹ôÅ-‚-hGôÅü hï-mÅ-P-±ôÅ-IPÅ-;-¤fº-¤-hïºÛ-G»Å-¤fº-¼Þ-

ºƒÛ-z-hP.ü 0 Û̂- (GôP-P¤-ºôG-)mÅ-1,2, 3, ..., 9 z¼-¼Û¤-q-zŸÛm-ºƒÛ-hGôÅü

‚ïh-ÇK ôü4‚ïh-ÇK ôü4‚ïh-ÇK ôü4‚ïh-ÇK ôü4‚ïh-ÇK ôü4 fzÅ-¾¤-ºhÛ-zïh-uh-hï-9 »Û-¿kz-IPÅ-ƒÛÅüGÁ¤-GÅ¾-iÛ-z¼-¾m-fôzÅü

;) fzÅ-¾¤-ºhÛ-zïh-uh-hïü P-±ôÅ-9 ¤fº-Tm-¤-»Ûm-qºÛ-IPÅ- Û̂-¿kz-IPÅ-ºƒÛ-fÞz-z¤üD) fzÅ-¾¤-ºhÛ-zïh-uh-hïü P-±ôÅ-IPÅ-GmÅ-3 Tm-HÛ-9 ¤fº-Tm-HÛ-IPÅ-;-DG-GÛ-

¿kz-IPÅ-ºƒÛ-fÞz-z¤ü


42

2 1

3 2 + 1 = 3

4 3 + 2 + 1 = 6

5 4 + 3 + 2 + 1 = 10

6 5 + 4 + 3 + 2 + 1 = 15

. ..

.

.

.

.

.

.

.

.

. .

.. .

. . . .

fÛG-ºhÛºÛ-ÇeïP-±ïG-GÅÞ¤-»ôh-q-hP.ü AB, AC, BC zTÅ-fÛG-hÝ¤-»P-GÅÞ¤-bG-bG-ºhÝG h-¿e-P-±ôÅ-GÁ¤-GÅ¾-hqï-ºIôÅ-DG-¾-¿e-ŸÛz-‚-Mãü

hqï-¼ÛÅü fÛG-ÇeïP-GÛ-±ïG-IPÅü fÛG-hÝ¤-IPÅü

2-4-3 2-4-3 2-4-3 2-4-3 2-4-3 fÛG-hÝ¤-zIP-zºÛ-hqï-ºIôÅü Patterns in Counting Line Segments

GÁ¤-HÛ-hqï-¼ÛÅ-¾-¿eôÅ-hP.ü

A CB. ..

‚ïh-ÇK ôü5‚ïh-ÇK ôü5‚ïh-ÇK ôü5‚ïh-ÇK ôü5‚ïh-ÇK ôü5 iP-fÛG-GTÛG-GÛ-ÇeïP-»ôh-qºÛ-±ïG-IPÅ-7, 8, 9 zTÅ- Û̂-fÛG-hÝ¤-WÛ-»ôh-hPôÅ-ÅÞ-¤-zIPÅ-qºÛ-ÇKô-mÅ-º±ô¾-z¼-‚ü


43

2-4-4 2-4-4 2-4-4 2-4-4 2-4-4 IPÅ-;-¸Þ¼-GÅÞ¤-¤ºÛ-hqï-ºIôÅü Patterns in Triangular Numbers

GÁ¤-GÅ¾-¼ïºÞ-¤ÛG-¾-¿e-ŸÛz-HÛÅ-hP.ü

1

1 + 2 = 3

1 + 2 + 3 = 6

1 + 2 + 3 + 4 = 10

1 + 2 + 3 + 4 + 5 = 15


44

ºhÛ¼-P-±ô¼-fôz-qºÛ-IPÅ-1, 3, 6, 10, 15, ... n¤Å-¾ü ̧ Þ¼-GÅÞ¤-IPÅ-Þ̧¼-GÅÞ¤-IPÅ-Þ̧¼-GÅÞ¤-IPÅ-Þ̧¼-GÅÞ¤-IPÅ-Þ̧¼-GÅÞ¤-IPÅ-(Triangular Numbers) ï̧¼üÞ̧¼-GÅÞ¤-IPÅ-hP-iP-fÛG-fôG-±ïG-ºi-¤Ûm-HÛÅ-Iâz-qºÛ-fÛG-hÝ¤-GZÛÅ- Û̂-hz¼-Eïh- Û̂Å-ºƒï¾-z-ŸÛG-¤fôP-GÛm-ºhÝG-G¤ü

‚ïh-ÇK ôü6‚ïh-ÇK ôü6‚ïh-ÇK ôü6‚ïh-ÇK ôü6‚ïh-ÇK ôü6 GÁ¤-HÛ-hqï-ºIôÅ-ÇÀôz-¢ôP-‚Å-bïü hqï-ºIôÅ-hïºÛ-¤Þ-¤fÞh-hï-Gô¤-q-GÅÞ¤-¾-M-Bïhü

¸Þ¼-GÅÞ¤-IPÅü¸Þ¼-GÅÞ¤-IPÅü¸Þ¼-GÅÞ¤-IPÅü¸Þ¼-GÅÞ¤-IPÅü¸Þ¼-GÅÞ¤-IPÅü hq ï -ºI ôÅühq ï -ºI ôÅühq ï -ºI ôÅühq ï -ºI ôÅühq ï -ºI ôÅü

hP-qôü 1 =

221×

GZÛÅ-qü 3 =

232 ×

GÅÞ¤-qü 6 =

243 ×zŸÛ-qü 1 0 =

254 ×

¿S-qü 1 5 =

265 ×

‚ïh-ÇK ôü7‚ïh-ÇK ôü7‚ïh-ÇK ôü7‚ïh-ÇK ôü7‚ïh-ÇK ôü7 GÁ¤-HÛ- Þ̧¼-GÅÞ¤-IPÅ-DG-GÛ-hqï-ºIôÅ-ÇÀôz-¢ôP-‚Å-bïü hqï-ºIôÅ-hïºÛ-¤Þ-¤fÞh-hï-Gô¤-q-zŸÛ-M-zBïh-q¼-‚ü


45

h-¿e-GÁ¤-HÛ-z¼-ÇeôP-Ç+ôP-z¼-‚ºôü ü

;) Þ̧¼-GÅÞ¤-IPÅ-10 q-hP-11 qºÛ-zÇkô¤Å-fôz-mÛü × =

D) Þ̧¼-GÅÞ¤-IPÅ- q-hP- qºÛ-zÇkô¤Å-fôz-mÛ-= 25 × 25 = 625 ¼ïhü

‚ïh-ÇK ôü8‚ïh-ÇK ôü8‚ïh-ÇK ôü8‚ïh-ÇK ôü8‚ïh-ÇK ôü8 GÁ¤-HÛ-¸Þ¼-GÅÞ¤-IPÅ-ˆÛ-hqï-ºIôÅ-ÇÀôz-¢ôP-‚Å-bïü hqï-ºIôÅ-hïºÛ-¤Þ-¤fÞh-hï-Gô¤-q-GÅÞ¤-M-zBïh-q¼-‚ü

1 + 3 = 4 = 2 × 2

3 + 6 = 9 = 3 × 3

6 + 1 0 = 1 6 = 4 × 4

1 0 + 1 5 = 2 5 = 5 × 5

1 5 + 2 1 = 3 6 = 6 × 6

8 x 1 + 1 = 9 = 3 × 3

8 x 3 + 1 = 2 5 = 5 × 5

8 x 6 + 1 = 4 9 = 7 × 7

8 x 1 0 + 1 = 8 1 = 9 × 9

8 x 1 5 + 1 = 1 2 1 = 1 1 × 1 1


46

h-¿e-GÁ¤-HÛ-z¼-ÇeôP-Ç+ôPÅü

;) Þ̧¼-GÅÞ¤-IPÅ-12 qºÛ-¿kz-8 ¾-1 zÇkô¤Å-mü = × =

D) Þ̧¼-GÅÞ¤-IPÅ- qºÛ-¿kz-8 ¾-1 zÇkô¤Å-mü = 27 × 27 = ¼ïhü

¢ôP-±mü 2.4

1ü G¾-bï-D-GP-h‚ÛzÅ-hP-qô-hï-±h-GŸÛ-ŸÛG-»Ûm-mü GÁ¤-HÛ-hqï-¼ÛÅ-DG-GÛÅ-¤±ôm-qºÛ-±h-GŸÛºÛ-IPÅ-ˆÛ-hqï-ºIôÅ-±ô¾ü


47

2ü GÁ¤-GÅ¾-DG-GÛ-hqï-ºIôÅ-º±ô¾-mÅü hqï-ºIôÅ-HÛ-¤Þ-¤fÞh-mÅ-Gô¤-q-GÅÞ¤-ƒÛÅü

;) 0, 2, 6, 12, , ,

D) 1, 4, 6, 19, , ,

G) 3, 10, 17, 24, , ,

P) 1, 3, 9, 27, , ,

T) 1, 9, 25, 49, , ,

V) 2, 5, 8, 11, , ,

W) 1, 12, 23, 34, , ,

3ü GÁ¤-GÅ¾-Iâ-m¼-h‚ÛzÅ-n¤Å-zIPÅ-mÅü hqï-ºIôÅ-GP-»Ûm-dôGÅ-q¼-HÛÅü

, , ,

Iâ-m¼-h‚ÛzÅ-¼ï-¼ï-‚Å-mÅ-¤-zIPÅ-ˆP-ÁïÅ-fÞz-qºÛ-FÛ¤Å-Æô¾-ŸÛG-±ô¾ü4ü GÁ¤-HÛ-1 mÅ-ºGô-z®ßGÅ-bïü Èï-zG-4 »Ûm-qºÛ-IPÅ-GZÛÅ- Û̂-zNå¼-fôz-fôG-¤-zŸÛ-¼Û¤-zŸÛm-ƒÛÅü

1, 2, 3, 4, 5, 6, ...

zNå¼-fôz-ˆÛ-hqï-ºIôÅ-PôÅ-z¸ÞP-Çeï-zNå¼-fôz-XïÅ-¤-GÅÞ¤-ƒÛÅü5ü GÁ¤-HÛ-hqï-ºIôÅ-ÁïÅ-q¼-zHÛÅ-bï-ºôG-GÛ-z¼-ÇeôP-Ç+ôPÅü

1 × 8 + 1 = 9

1 2 × 8 + 2 = 9 8

1 2 3 × 8 + 3 = 9 8 7

1 2 3 4 × 8 + 4 = . . . . . .

1 2 3 4 5 × 8 + 5 = . . . . . .


48

6ü GÁ¤-HÛ-hqï-ºIôÅ-¾-¿e-ŸÛz-‚Å-XïÅü ºôG-GÛ-z¼-ÇeôP-Ç+ôPÅü 9 × 9 + 7 = 8 8

9 8 × 9 + 6 = 8 8 8

9 8 7 × 9 + 5 = . . . . . .

9 8 7 6 × 9 + 4 = . . . . . .

7ü GÁ¤-HÛ-hqï-ºIôÅ-¾-¿e-ŸÛz-‚Å-XïÅü hqï-ºIôÅ-ˆÛ-¤Þ-¤fÞh-hï-Gô¤-q-GÅÞ¤-ƒÛÅü6 × 2 – 5 = 7

7 × 3 – 12 = 9

8 × 4 – 21 = 11

9 × 5 – 32 = 13

. . . . . .× . . . . . . – . . . . . . = . . . . . .

. . . . . .× . . . . . . – . . . . . . = . . . . . .

. . . . . .× . . . . . . – . . . . . . = . . . . . .

Documents

ÇÀôz-±m-hP-qôü IPÅ-;ü 19 · 20 ÇÀôz-±m-GZÛÅ-qü IPÅ-ˆÛ-¯-zºÛ-¯Û-fzÅü 20 ÇÀôz-±m-GZÛÅ-qü IPÅ-ˆÛ-¯-zºÛ-¯Û-fzÅü Chapter 2: Basic Operations on