$\mathbf{Natural}\mathbf{sonni}\mathbf{kasrga}{\mathbf{ko}}^{\mathbf{\text{'}}}\mathbf{paytirish}$

Natural sonni kasrga ko‘paytirish — bu natural sonni kasrning surati bilan ko‘paytirib, maxrajni saqlab qolishdir.

Qoida:

$\mathrm{a}·\frac{\mathrm{b}}{\mathrm{c}}=\frac{\mathrm{a}·\mathrm{b}}{\mathrm{c}}\iff \frac{\mathrm{b}}{\mathrm{c}}·\mathrm{a}=\frac{\mathrm{b}·\mathrm{a}}{\mathrm{c}}$

Masalan, $5·\frac{1}{4}$ ni hisoblaymiz.

Natural sonni kasrning suratiga ko`paytiramiz va natijani aralash kasr ko`rinishida yozamiz.

Demak, natija $1\frac{1}{4}$ ga teng ekan.

$\mathbf{Natural}\mathbf{sonni}\mathbf{aralash}\mathbf{songa}{\mathbf{ko}}^{\mathbf{\text{'}}}\mathbf{paytirish}$

Natural sonni aralash songa ko‘paytirish uchun avval aralash sonni noto‘g‘ri kasr shaklida yozamiz, so‘ngra ko‘paytirishni bajaramiz.

Qoida: 

• Aralash sonni noto‘g‘ri kasr shaklida yozing.

• Natural sonni kasrga ko‘paytiring.

Masalan, $2·1\frac{1}{3}$ ni hisoblaymiz.

Aralash kasrni noto`g`ri kasr ko`rinishida ifodalaymiz. Natural sonni kasrga ko`paytirib, noto`g`ri kasrga o`tkazamiz.

Demak, natija  $2\frac{2}{3}$ ga teng.

$\mathbf{Natural}\mathbf{sonni}\mathbf{kasrga}{\mathbf{bo}}^{\mathbf{\text{'}}}\mathbf{lish}$

Natural sonni kasrga bo‘lish — bu natural sonni kasrning teskarisiga ko‘paytirish orqali amalga oshiriladi.

Qoida: $\mathbf{a}\mathbf{:}\frac{\mathbf{b}}{\mathbf{c}}\mathbf{=}\mathbf{a}\mathbf{·}\frac{\mathbf{c}}{\mathbf{b}}$

Masalan, $4:\frac{1}{7}$ ni hisoblaylik.

Natural sonni kasrga teskari kasrga ko`paytiramiz.

Demak, natija $28$ ga teng ekan.

$\mathbf{Kasrni}\mathbf{natural}\mathbf{songa}{\mathbf{bo}}^{\mathbf{\text{'}}}\mathbf{lish}$

Kasrni natural songa bo‘lish — bu kasrni natural songa teskari songa ko‘paytirish orqali amalga oshiriladi.

Qoida:  $\frac{\mathbf{a}}{\mathbf{b}}\mathbf{:}\mathbf{c}\mathbf{=}\frac{\mathbf{a}}{\mathbf{b}}\mathbf{·}\frac{\mathbf{1}}{\mathbf{c}}$

Masalan,  $\frac{5}{4}:3$ ni hisoblaylik.

Kasrni natural songa teskari bo`lgan songa ko`paytiramiz.

Demak, natija  $\frac{5}{12}$ ga teng ekan.

${\mathbf{O}}^{\mathbf{\text{'}}}\mathbf{nli}\mathbf{kasrni}\mathbf{natural}\mathbf{songa}{\mathbf{ko}}^{\mathbf{\text{'}}}\mathbf{paytirish}$

O‘nli kasrni natural songa ko‘paytirish uchun quyidagi qadamlarni bajaramiz:

• O‘nli kasrni oddiy kasrga o‘tkazing.

• Oddiy kasrni natural songa ko‘paytiring.

• Natijani soddalashtiring va kerak bo‘lsa, o‘nli kasr shaklida yozing.

Masalan, $8·1,25$ ni hisoblaymiz.

O`nli kasrni kasr ko`rinishida ifodalab, natural songa ko`paytiramiz.

Demak, natija $9,84$ ga teng ekan.

Bolajonlar, bugungi darsimizga yakun yozish vaqti keldi. Bugun biz quyidagi muhim mavzularni o‘rganib chiqdik:

• Natural sonni kasrga ko‘paytirish : Suratni ko‘paytirib, maxrajni saqlab qolish.

• Natural sonni aralash songa ko‘paytirish : Aralash sonni noto‘g‘ri kasr shaklida yozib, keyin ko‘paytirish.

• Natural sonni kasrga bo‘lish : Teskari kasr bilan ko‘paytirish.

• Kasrni natural songa bo‘lish : Maxrajni natural songa ko‘paytirish.

• O‘nli kasrni natural songa ko‘paytirish : Oddiy ko‘paytirish va vergulni to‘g‘ri joylashtirish.

Endi sizlar kasrlar va o‘nli kasrlar bilan ishlashni osongina amalga oshira olasiz. Bu bilimlar sizga hayotda ham, o‘qishda ham katta yordam beradi.

Matematika – ilm-fanning qirolichasi.

Karl Fridrix Gauss