mana shuni daftarga yozafigan qilib ishlabber
Сверь числа и знаки с фото.
[обрезано]жение и вычитание обыкновенных дробей
1 Найдите сумму дробей. a) \( \frac{1}{4}+\frac{2}{5}= \) [рукописные пометки неразборчиво] ? b) \( \frac{3}{7}+\frac{1}{10}= \) [рукописные пометки неразборчиво] ? c) \( \frac{5}{6}+\frac{3}{4}= \) [рукописные пометки неразборчиво] ? d) \( \frac{5}{8}+\frac{2}{3}= \) [рукописные пометки неразборчиво] ?
2 Найдите разность дробей. a) \( \frac{4}{5}-\frac{1}{2}= \) [рукописные пометки неразборчиво] ? b) \( \frac{7}{8}-\frac{3}{5}= \) [рукописные пометки неразборчиво] ? c) \( \frac{7}{9}-\frac{3}{4}= \) [рукописные пометки неразборчиво] ? d) \( 4-\frac{1}{3}= \) [рукописные пометки неразборчиво] ?
Qisqa javob
1) Qo‘shish: a) \( \frac{13}{20} \); b) \( \frac{37}{70} \); c) \( 1\frac{7}{12} \); d) \( 1\frac{7}{24} \).
2) Ayirish: a) \( \frac{3}{10} \); b) \( \frac{11}{40} \); c) \( \frac{1}{36} \); d) \( 3\frac{2}{3} \).
Qoida (shu asosda o‘zing ham yechasan)
- Maxrajlarning eng kichik umumiy karralisini topamiz — bu umumiy maxraj bo‘ladi.
- Har bir kasrning surat va maxrajini shunday ko‘paytiramizki, maxraj umumiy maxrajga aylansin.
- Suratlarni qo‘shamiz yoki ayiramiz, maxraj o‘zgarmaydi.
- Natijani qisqartiramiz; noto‘g‘ri kasr bo‘lsa, butun qismni ajratamiz.
Daftarga yozish uchun
1. Kasrlarning yig‘indisi
\[ \frac{1}{4}+\frac{2}{5}=\frac{5}{20}+\frac{8}{20}=\frac{13}{20} \]
\[ \frac{3}{7}+\frac{1}{10}=\frac{30}{70}+\frac{7}{70}=\frac{37}{70} \]
\[ \frac{5}{6}+\frac{3}{4}=\frac{10}{12}+\frac{9}{12}=\frac{19}{12}=1\frac{7}{12} \]
\[ \frac{5}{8}+\frac{2}{3}=\frac{15}{24}+\frac{16}{24}=\frac{31}{24}=1\frac{7}{24} \]
2. Kasrlarning ayirmasi
\[ \frac{4}{5}-\frac{1}{2}=\frac{8}{10}-\frac{5}{10}=\frac{3}{10} \]
\[ \frac{7}{8}-\frac{3}{5}=\frac{35}{40}-\frac{24}{40}=\frac{11}{40} \]
\[ \frac{7}{9}-\frac{3}{4}=\frac{28}{36}-\frac{27}{36}=\frac{1}{36} \]
\[ 4-\frac{1}{3}=\frac{12}{3}-\frac{1}{3}=\frac{11}{3}=3\frac{2}{3} \]
Tekshirish: \( 3\frac{2}{3}+\frac{1}{3}=4 \) — to‘g‘ri; \( 1\frac{7}{12}-\frac{3}{4}=\frac{19}{12}-\frac{9}{12}=\frac{10}{12}=\frac{5}{6} \) — ham to‘g‘ri.
Обсуждение
2 сообщенияMana, daftarga ko‘chirish uchun to‘g‘ri yechimlar. Rasmdagi qalam bilan yozilgan javoblarning bir qismi xato; pastdagi natijalardan foydalaning.
1. Qo‘shish
a) \(2\frac14+2\frac38=2\frac28+2\frac38=4\frac58\)
b) \(4\frac23+2\frac49=4\frac69+2\frac49=6\frac{10}{9}=7\frac19\)
c) \(1\frac12+2\frac23=1\frac36+2\frac46=3\frac76=4\frac16\)
d) \(3\frac56+2=5\frac56\)
e) \(4+2\frac29=6\frac29\)
f) \(3\frac13+3\frac45=3\frac5{15}+3\frac{12}{15}=6\frac{17}{15}=7\frac2{15}\)
g) \(1\frac13+2\frac78=1\frac8{24}+2\frac{21}{24}=3\frac{29}{24}=4\frac5{24}\)
h) \(2\frac23+4\frac47=2\frac{14}{21}+4\frac{12}{21}=6\frac{26}{21}=7\frac5{21}\)
2. Ayirish
a) \(2\frac78-1\frac12=2\frac78-1\frac48=1\frac38\)
b) \(6\frac5{12}-2\frac14=6\frac5{12}-2\frac3{12}=4\frac2{12}=4\frac16\)
c) \(5\frac25-3\frac12=5\frac4{10}-3\frac5{10}=4\frac{14}{10}-3\frac5{10}=1\frac9{10}\)
d) \(7-3\frac56=6\frac66-3\frac56=3\frac16\)
e) \(4\frac67-2\frac23=4\frac{18}{21}-2\frac{14}{21}=2\frac4{21}\)
f) \(8\frac29-3\frac45=8\frac{10}{45}-3\frac{36}{45}=7\frac{55}{45}-3\frac{36}{45}=4\frac{19}{45}\)
g) \(5\frac7{10}-4=1\frac7{10}\)
h) \(6\frac34-1\frac9{10}=6\frac{15}{20}-1\frac{18}{20}=5\frac{35}{20}-1\frac{18}{20}=4\frac{17}{20}\)
3. Butun songa ko‘paytirish
a) \(\frac92\cdot24=9\cdot12=108\)
b) \(\frac{20}{9}\cdot45=20\cdot5=100\)
c) \(\frac75\cdot85=7\cdot17=119\)
d) \(\frac87\cdot98=8\cdot14=112\)
e) \(\frac83\cdot96=8\cdot32=256\)
f) \(\frac{11}{6}\cdot246=11\cdot41=451\)
4. Kasrni kasrga ko‘paytirish — 1-jadval
a) \(\frac25\cdot\frac45=\frac8{25}\)
b) \(\frac17\cdot\frac34=\frac3{28}\)
c) \(\frac23\cdot\frac34=\frac6{12}=\frac12\)
d) \(\frac27\cdot\frac12=\frac2{14}=\frac17\)
e) \(\frac9{10}\cdot\frac23=\frac{18}{30}=\frac35\)
f) \(\frac7{12}\cdot\frac45=\frac{28}{60}=\frac7{15}\)
5. Kasrni kasrga ko‘paytirish — 2-jadval
a) \(\frac23\cdot\frac98=\frac{18}{24}=\frac34\)
b) \(\frac87\cdot\frac34=\frac{24}{28}=\frac67\)
c) \(\frac23\cdot\frac73=\frac{14}{9}=1\frac59\)
d) \(\frac45\cdot\frac85=\frac{32}{25}=1\frac7{25}\)
e) \(\frac56\cdot\frac85=\frac{40}{30}=\frac43=1\frac13\)
f) \(\frac{11}{12}\cdot\frac94=\frac{99}{48}=\frac{33}{16}=2\frac1{16}\)
6. To‘g‘ri to‘rtburchak masalasi
Rasmda gapning oxiri ko‘rinmayapti. Ko‘paytirish mavzusiga ko‘ra, odatda yuza so‘raladi:
\[ S=\frac85\cdot\frac34=\frac{24}{20}=\frac65=1\frac15\ \text{m}^2 \]
Agar topshiriqda perimetr so‘ralgan bo‘lsa:
\[ P=2\left(\frac85+\frac34\right) =2\left(\frac{32}{20}+\frac{15}{20}\right) =2\cdot\frac{47}{20} =\frac{47}{10}=4\frac7{10}\ \text{m} \]
Tekshirish: qo‘shishni ayirish bilan, ayirishni qo‘shish bilan tekshirish mumkin. Masalan, \(1a)\) da \(4\frac58-2\frac38=2\frac14\) — to‘g‘ri.
