$\frac{3}{4}+\frac{5}{6}-\frac{2}{3}$ ifodasini soddalashtiring.
- A. $\frac{7}{12}$
- B. $\frac{5}{6}$
- C. $\frac{11}{12}$
- D. $\frac{13}{12}$
Oddiy kasrlar va ular ustida amallar bo‘yicha savol
Javob va yechimni ko‘rish
Javob: $\frac{11}{12}$
Kasrlarni qo‘shish va ayirish uchun avvalo ularning umumiy (bir xil) maxrajini topamiz. $4$, $6$ va $3$ sonlarining eng kichik umumiy bo‘luvchisi $12$ ga teng, shuning uchun barcha kasrlarni $12$ ga teng bo‘lishi kerak:
$$\frac{3}{4}=\frac{3\cdot3}{4\cdot3}=\frac{9}{12},\qquad
\frac{5}{6}=\frac{5\cdot2}{6\cdot2}=\frac{10}{12},\qquad
\frac{2}{3}=\frac{2\cdot4}{3\cdot4}=\frac{8}{12}.$$
Endi bu kasrlarni birga hisoblaymiz:
$$\frac{9}{12}+\frac{10}{12}-\frac{8}{12}= \frac{9+10-8}{12}= \frac{11}{12}.$$
Demak, ifoda soddalashtirilganda $\displaystyle \frac{11}{12}$ ga teng bo‘ladi, ya’ni to‘g‘ri javob C.
Mavzuni mustahkamlang
Bu savol Oddiy kasrlar va ular ustida amallar mavzusiga tegishli. Ta’riflar, formulalar va misollarni mavzu sahifasida ko‘ring.
Mavzuni o‘rganishShu mavzudagi boshqa savollar
$\frac{7}{9}\times\frac{3}{14}$ ni hisoblang va soddalashtiring.$\frac{x}{5}-\frac{2}{3}=\frac{1}{15}$ tenglamasida $x$ ni toping.$\frac{2}{5}\div\left(\frac{4}{15}\right)+\frac{1}{2}$ ifodasini hisoblang.Agar $\frac{3}{x}=\frac{9}{12}$ bo‘lsa, $x$ ni toping va $x-\frac{1}{4}$ ning qiymatini hisoblang.Kasrni qisqartiring: $\frac{10}{24}$