ISSN:
2181-3906
2023
International scientific journal
«MODERN SCIENCE АND RESEARCH»
VOLUME 2 / ISSUE 5 / UIF:8.2 / MODERNSCIENCE.UZ
880
MENTAL ARIFMETIKADA 5 GACHA BO’LGAN SONLARNI QO’SHISH VA
AYIRISH. ,,KICHIK DO’ST’’ FORMULASI ( PARA ) HAQIDA TUSHUNCHA
Shаrоfutdinоvа Rа’nоxоn
Muhtоrоv Tоshpо’lаtjоn
https://doi.org/10.5281/zenodo.7954871
Annotatsiya.
Mazkur maqolada mental arifmetikada 5 gacha bo’lgan sonlarni qo’shish va
ayirish. ,,Kichik do’st’’ formulasi ( para ) haqida tushuncha masalalari yoritib berilgan.
Kalit so’zlar:
abakus, mental arifmetika, hisob-kitob, ayirish amali.
ADDING AND SUBTRACTING NUMBERS UP TO 5 IN MENTAL ARITHMETIC.
UNDERSTANDING OF THE "LITTLE FRIEND" FORMULA (PARA)
Abstract.
Add and subtract numbers up to 5 in mental arithmetic in this article. Concept
issues about the "little friend" formula (para) are explained.
Key words:
abacus, mental arithmetic, calculation, subtraction.
СЛОЖЕНИЕ И ВЫЧИТАНИЕ ЧИСЕЛ ДО 5 В УМЕ. ПОНИМАНИЕ ФОРМУЛЫ
«МАЛЕНЬКИЙ ДРУГ» (ПАРА)
Аннотация.
Эта статья посвящена сложению и вычитанию чисел до 5 в
ментальной арифметике. Объяснены вопросы понятия о формуле «маленький друг»
(параграф).
Ключевые слова:
счеты, ментальная арифметика, счет, вычитание.
Bizga abakusning tepa toshlari osmon toshlari, pastki toshlar yer toshlari va o’rtadagi chiziq
esa bulut deb ataladi. Abakusdagi birinchi qator toshlari birlar xonasi hisoblanadi.Ya’ni bu qator
1 dan 9 gacha bo’lgan sonlarni o’z ichiga olishi, keyingi o’nlar xonasi esa,10 dan 99 gacha bo’lgan
sonlarni o’z ichiga oladi, mana shu sonlar ustida qo’shish va ayirish amallarinibilamiz. Bu hisob-
kitob amallari oddiy usulda bajarildi.
Keling endi bizga hali tanish bo’lmagan 5 gacha sonlarni ya’ni ,,Kichik do’st” formulasi
bilan tanishib chiqamiz. Chunki birlar xonasida hisob-kitobni amalga oshirishimizda ushbu
formuladan foydalanib amallarni bajarishimiz mumkin.
ISSN:
2181-3906
2023
International scientific journal
«MODERN SCIENCE АND RESEARCH»
VOLUME 2 / ISSUE 5 / UIF:8.2 / MODERNSCIENCE.UZ
881
Ushbu rasmdagi uyda barcha sonlar birga yashar ekan. Har bir sonning o’z sherigi bo’lib,
faqat 5 soning sherigi o’zi ekan. Ya’ni 1 soninig sherigi 4soni, 2sonining sherigi 3soni, 3sonining
sherigi 2soni, 4sonining sherigi esa 1 ekan. Aytganimizdek 5 soning sherigi 5 soni ekan. Bu
formulani doimo yodda saqlash lozim. Chunki bu formula abakusda matematik hisoblashlarda
bizga yordam beradi va mana shu formula kichik do’st deb ataladi. Keling mana shu formula
yordamida misollarni ishlash yo’llari haqida tanishib chiqamiz. Biz abakusda 4 soniga 4 sonini
qo’shmoqchi bo’lsak avvalo yer toshlaridan 4 sonini hosil qilamiz.
Endi biz yana 4 sonini qo’shishimiz kerak. Lekin yer toshlarida 4 soni yo’qligi sababli, osmon
toshlaridagi 5 sonini qo’shamiz. Shunda abakusimizda 9 soni hosil
bo’ldi.
Endi esa 4 soning sherigi bo’lgan 1 sonini hosil bo’lgan sondan ayirib qo’yamiz. Shunda bizda 8
soni hosil bo’ladi. Va bu son misolning javobi bo’ladi.
ISSN:
2181-3906
2023
International scientific journal
«MODERN SCIENCE АND RESEARCH»
VOLUME 2 / ISSUE 5 / UIF:8.2 / MODERNSCIENCE.UZ
882
Haqiqatdan ham 4+4=8
Bu faqat qo’shish uchun qo’llangan formula.
Biz bu formuladan nafaqat qo’shish uchun balki ayirish amalida ham foydalanamiz, chunki bu
formula bir xonali sonlarni qo’shish va ayirish uchun ishlatiladi. ,,Kichik do’st” formulasini
quyidagi jadval asosida yod olish oson.
Yuqoridagi jadval asosida keling yana bir nechta misollar ko’rib chiqamiz.
1)
Bu misolimizda 3 ga 2 ni qo’shishda 5 ni qo’shib, so’ng 2 ni sherigi 3 ni ayirib qo’yamiz.
Undan so’ng yana 3 ta tosh qo’shamiz va natija 8 bo’ladi.
Ushbu misolimiz faqat birlar xonasi uchun va qo’shish
amalidan foydalanib bajardik. 3+2+3=8
Endi ,,Kichik do’st” formulasi bilan ayirish amallarini ko’rib chiqamiz.
2)
5-4+5-3=3
Ushbu misolda abakusda 5 ni hosil qilib olib, undan yana 5 ni ayiramiz va 4 ni
sherigi 1 ni qo’shamiz. 1 hosil bo’ladi. Hosil bo’lgan songa 5 ni qo’shamiz va yana 3 ni
ayiramiz. 3 ni ayirish uchun oldin 5 ni ayirib 3 ni sherigi bo’lgan 2 ni qo’shib qo’yamiz. Javob
3 bo’ladi.
ISSN:
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2023
International scientific journal
«MODERN SCIENCE АND RESEARCH»
VOLUME 2 / ISSUE 5 / UIF:8.2 / MODERNSCIENCE.UZ
883
Yana bir misolni ko’rib chiqaylik.
5+4-9+3+3=6 Bu misolda qo’shish amali ham, ayirish amali ham aralash holda berilgan.
Abakusda 5 sonini hosil qilib, unga 4ni qo’shamiz. Natijadan 9 ni ayirib, unga 3 ni
qo’shamiz.So’ng oxirgi 3ni qo’shish uchun 5 soni qo’shib , 3 ni do’sti 2 ni ayirimiz. Natija 6
1-qadam.
Abakusda 5 sonini
hosil qilish.
2-qadam.
5+4 sonini qo’shib
9 soni hosil
qilinadi.
3
-qadam.Hosil
bo’lgan yig’indidan
9 ni ayiramiz.
ISSN:
2181-3906
2023
International scientific journal
«MODERN SCIENCE АND RESEARCH»
VOLUME 2 / ISSUE 5 / UIF:8.2 / MODERNSCIENCE.UZ
884
Ikki xonali sonlar ustida ,,Kichik do’st” usulida abakusda misollar ishlash.
1-misol. 23+14=37
Bu misolda o’nlar xonasidan 20ni hosil qilib olamiz, birlar xonasidan esa 3ni. So’ng bu songa
o’nlar xonasidan 10soni, birlar xonasidan 4soni qo’shiladi. 4 sonini qo’sha olmaymiz shuning
uchun 5 ni qo’shib 4ni do’sti 1ni ayiramiz. Natija =37
2-misol. 12+13=25
4-qadam.
3 soni qo’shiladi.
5-qadam.3 soniga 3
ni qo’shish uchun 5
soni qo’shiladi.
Chunki bizga tosh
yetmaydi.
6-qadam.Hosil
bo’lgan sondan 3
soning do’sti 2 soni
ayiriladi va
natijada 6 soni
hosil bo’ladi.
ISSN:
2181-3906
2023
International scientific journal
«MODERN SCIENCE АND RESEARCH»
VOLUME 2 / ISSUE 5 / UIF:8.2 / MODERNSCIENCE.UZ
885
Bu misolda esa o’nlar xonasidan 10sonini hosil qilamiz, birlar xonasidan 2 sonini hosil qilamiz.
So’ng bu sonimizga o’nlar xonasidan yana 10 soni hamda birlar xonasidan 3ni qo’shishimiz kerak.
O’n qo’sha olamiz, lekin 3 qo’sha olmimiz. Shuning uchun 5ni qo’shib 3ni do’sti 2ni ayirib olamiz.
Natijada 25 soni hosil bo’ladi. Haqiqatdan ham 12+13=25.
Uch xonali sonlar ustida ,,Kichik do’st” usulida abakusda misollar ishlash.
1-misol. 323+512=835
Ushbu misolimiz ham ikki xonali misol kabi ishlanadi. Yuzlar qatoridan 300, o’nlar
xonasidan 20 va birlar xonasidan 3ni hosil qilamiz, keying qadam esa unga yuzlar xonasidan 500ni
qo’shish, o’nlar xonasidan 10 va birlar xonasidan 2ni qo’shish bo’ladi. Lekin birlar xonasidan 2ni
qo’sha olmaymiz, 5ni qo’shib 2ni do’sti 3 sonini qo’shamiz.
2-misol. 425-213=212
ISSN:
2181-3906
2023
International scientific journal
«MODERN SCIENCE АND RESEARCH»
VOLUME 2 / ISSUE 5 / UIF:8.2 / MODERNSCIENCE.UZ
886
Navbatdagi misolimizda abakusda 423 sonini hosil qilib olamiz, so’ng undan yuzlar xonasidan
200 sonini, o’nlar xonasidan 10 sonini hamda birlar xonasidan 3 ayiramiz. 3sonini ayira olmaymiz,
shunda biz 5 sonini ayirib 3 sonini do’sti 2 sonini ayirib qo’yamiz. Shunda natija = 212.
Haqiqatdan ham 425-213=212
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