This document presents a method for multiplying multi-digit numbers by breaking them down into place values. It demonstrates multiplying two sample numbers, 12 x 7 and 9 x 5, step-by-step. It then shows how to use the distributive property to calculate the multiplication more efficiently by distributing the multiplication across place values. For example, 12 x 7 is calculated as (10 + 2) x (5 + 2) which is equivalent to 10 x 5 + 10 x 2 + 2 x 5 + 2 x 2.

2. PREVIOUS
KNOWLEDGE
 F´mWv A[nkwJyÄ ?
kwJymtcJbn ]qPy¯np heXphi¯p hcp¶ kwJyIÄ
 𝟓 + 𝟏𝟎 F{XbmWv ?
𝟏𝟓
 𝟓 × 𝟏𝟎 F{XbmWv ?
𝟓𝟎
 NXpc¯nXv F{X hi§Ä?
𝟒
 NXpc¯nsâ ]c¸fhv ImWmpff kq{XhmIyw?
nfw × hoXn

3. Presentation of the topic

4.  NXpc¯nsâofsb{X?
12 sk. ao
 NXpc¯nsâhoXnsb{X?
7 sk. ao
 NXpc¯nsâ]c¸fsb{X?
𝟏𝟐 × 𝟕 = 𝟖𝟒
 ]c¸fhnsâbqWnsä´v ?
NXpc{isk. ao.
 F¦n NXpc¯nsâ ]c¸fsb{X?
𝟖𝟒 NXpc{i sk. ao.
7 sk.ao
12 sk. ao

5. NXpc¯nsâofw F{XIpdªp?
3sk. ao
 NXpc¯nsâhoXnsbmWv ?
7 sk. ao
]c¸fhv F{X?
𝟗 × 𝟕 = 𝟔𝟑 N. sk. ao.
]c¸fhv F{XIpdªp ?
𝟖𝟒 − 𝟔𝟑 = 21N. sk. ao.
Cu NXpc¯nsâ ]c¸fhns ½ps¡§s KpW^e§Ä ]ncns¨gpXm³ FgpXmw?
𝟏𝟐 − 𝟑 × 𝟕 = 𝟏𝟐 × 𝟕 − 𝟑 × 𝟕
3 sk.ao

6. NXpc¯nsâhoXn F{XIpdªp?
2 sk. ao
hoXn Ipdªpt¸mÄ ]c¸fsb{X?
𝟏𝟐 × 𝟓 = 𝟔𝟎 N. sk. ao
]c¸fhv F{XIpdªp ?
𝟖𝟒 − 𝟔𝟎 = 𝟐𝟒 sk. ao
CXnsâ ]c¸fhnsâ KpW^e§Ä F§s ]ncns¨gpXmwFgpXmw?
𝟕 − 𝟐 × 𝟏𝟐 = 𝟏𝟐 × 𝟕 − 𝟏𝟐 × 𝟐
12 sk. ao
2 sk. ao

7.  ofwIpdªt¸mÄ ]c¸fhv IpdªXv ?
𝟐𝟏 sk. ao
 hoXn Ipdªt¸mÄ]c¸fhvIpdªXv ?
𝟐𝟒 sk. ao
 BsI IpdªXv?
𝟒𝟓 N. sk. ao
 sNdnb NXpc¯nsâ]c¸fhv?
6sk. ao
 Cu sNdnb NXpc¯nsâ]c¸fhv ?
𝟒𝟓 N. sk. ao
2 sk. ao
12 sk. ao
3 sk.ao

8.  Ipdª NXpc¯nsâ]c¸fhv?
𝟗 × 𝟓
 𝟗 × 𝟓 s KpW^e§fmbn ]ncns¨gpXpI?
𝟏𝟐 × 𝟕 − 𝟏𝟐 × 𝟐 − 𝟑 × 𝟕 + 𝟑 × 𝟐
 CXns aps¡§s amänXpIIfpsS KpWam¡mw ?
𝟏𝟐 − 𝟑 × 𝟕 − 𝟐
= 𝟏𝟐 × 𝟕 − 𝟏𝟐 × 𝟐 − 𝟑 × 𝟕 + 𝟑 × 𝟐
2 sk. ao
12 sk. ao
3 sk.ao

9.  𝟏𝟐 × 𝟕 s 𝟏𝟓 × 𝟗 B¡m³ F´mv sNbvXXv ?
− 𝟏𝟐 × 𝟗 s 𝟏𝟐 − 𝟑 × 𝟕 − 𝟐 F¶v ]ncns¨gpXn
−𝟏𝟐 s sImWvSv 𝟕 sbpw 𝟐 sbpwKpWn¨.
−3 s sImWvSv 𝟕 sbpw 𝟐 sbpwKpWn¨.
− AsXÃmwIpSn, Iqd¨.

10. CHART
A[nkwJyIfpsS XpIsb XpI sImWvSp KpWn¡m³,
BZys¯ XpIbnse Hmtcm kwJysbbpw cWvSmas¯
XpIbnse Hmtcm kwJysImWvSpw KpWn¨v
Ipdbv¡Ww.

11. APPLICATION
 𝟑𝟗𝟖 × 𝟏𝟗𝟕 s F¶nhbpsS hyXymkKpWwIsWvS¯pI
?
𝟑𝟗𝟖 × 𝟏𝟗 = 𝟒𝟎𝟎 − 𝟐 × 𝟐𝟎𝟎 − 𝟑
= 𝟒𝟎𝟎 × 𝟐𝟎𝟎 − 𝟒𝟎𝟎 × 𝟑 −
𝟐 × 𝟐𝟎𝟎 + 𝟏 × 𝟏
= 𝟖𝟎𝟎𝟎 − 𝟏𝟐𝟎𝟎 − 𝟒𝟎𝟎 + 𝟔
= 𝟕𝟖𝟒𝟎𝟎 + 𝟔
= 𝟕𝟖𝟒𝟎𝟔

12. revie
w
• A[nkwJyIfpsS XpIIfpsS hyXymk¯nsâ KpW^ew
F´mWv ?
A[nkwJyIfpsS XpIsb XpI sImWvSp KpWn¨v,
hyXymkw ImWp¶Xnv, BZys¯ XpIbnse Hmtcm
kwJysbbpw cWvSmas¯ XpIbnse Hmtcm kwJysImWvSpw
KpWn¨v KpWhyXymkw ImWpI.

13. Follow up activities
XpIIfpsSKpWhyXymkwIsWvS¯n FgpXpI.
1. 397× 𝟏𝟗𝟗
2. 𝟑𝟎𝟐 × 𝟐𝟎𝟓.