Murakkab kasr kasrni ifodalaydi, bunda pay, maxraj yoki ikkala raqam va maxraj kasrni o'z ichiga oladi. Masalan:
\(\displaystyle \frac{^1/_2}{3}\) (Numerator - kasr)
\(\displaystyle \frac{2}{^1/_3}\) (Maxraj - kasr)
\(\displaystyle \frac{^1/_2}{^1/_3}\) (Numerator va maxraj ikkala kasr)
Murakkab kasrlar bilan ishlash oddiy kasrlar bilan bir xil tarzda amalga oshirilishi kerak. Birinchidan, murakkab kasrni eng kichik hadiga aylantiring. Murakkab kasrlarni oddiy kasrlarga aylantirish qoidalari quyida keltirilgan.
1) Kasrni bo'linish shaklida yozing
\(\displaystyle \frac{^1/_2}{3}\) quyidagicha ifodalanishi mumkin: \(\displaystyle \frac{1}{2} \div 3\)
\(\displaystyle\frac{2}{^1/_3}\) quyidagicha ifodalanishi mumkin: \(\displaystyle 2 \div \frac{1}{3}\)
\(\displaystyle \frac{^1/_2}{^1/_3}\) quyidagicha ifodalanishi mumkin: \(\displaystyle \frac{1}{2} \div \frac{1}{3} \)
2) Bo'lish belgisini ko'paytirishga o'zgartiring va maxrajni o'zgartiring. ya'ni bo'linish belgisining o'ng tomonida kelgan kasrni teskari qilish.
\(\displaystyle \frac{1}{2} \div 3\) \(\displaystyle = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}\)
\(\displaystyle 2 \div \frac{1}{3} = 2\times3 = 6\)
\(\displaystyle \frac{1}{2} \div \frac{1}{3} =\frac{1}{2} \times 3 = \frac{3}{2}\)
Murakkab kasrlar bilan bir nechta arifmetik amallarni bajaramiz.
Qo'shimcha:
\(\displaystyle \frac{^1/_2}{3} + \frac{2}{^1/_3} = \frac{1}{6} + \frac{6}{1}\)
Endi murakkab kasr oddiy kasrga keltiriladi. Ikkala kasrning maxrajini teng qilib, ikkita oddiy kasr qo'shing.
\(\displaystyle \frac{1}{6} + \frac{6\times6}{1\times6} = \frac{1}{6} + \frac{36}{6} = \frac{37}{6}\)
Ko'paytirish:
\(\displaystyle \frac{^1/_2}{3} \times \frac{2}{^1/_3} = \frac{1}{6} \times \frac{6}{1} = 1\)
Bo'lim:
\(\displaystyle \frac{^1/_2}{3} \div \frac{2}{^1/_3} = \frac{1}{6} \div \frac{6}{1} = \frac{1}{36}\)
Esda tutish kerak bo'lgan nuqta - Har qanday operatsiyani bajarishdan oldin murakkab kasrni oddiy kasrga kamaytiring.
Murakkab kasrlarni real hayotga qo'llash
Murakkab kasrlar mavhum ko'rinishi mumkin, ammo ular haqiqiy hayotda juda foydali. Misol uchun, pishirishda retsept \( \frac{3}{4} \) chashka shakarning yarmi talab qilinishi mumkin, bu esa aralash kasrga olib keladi. Bularni qanday soddalashtirishni tushunish sizga \( \frac{3}{8} \) chashka shakar kerakligini tezda aniqlashga yordam beradi.
Yana bir amaliy qo'llash o'lchovlar va konstruktsiyalarda bo'lib, unda o'lchamlar kasrlarda berilishi mumkin va hisob-kitoblar ushbu kasr o'lchovlarini keyingi bo'linish yoki ko'paytirishni talab qiladi. Murakkab kasrlarni soddalashtirishda ravon bo'lish vaqtni tejash va bunday vazifalarni bajarishda xatolarni kamaytirish imkonini beradi.
