Ответы к параграфу 14. Деление дробей
Задание 446. Выполните деление:
Решение
1) $\frac37:\frac56=\frac37\ast\frac65=\frac{18}{35}$
2) $\frac3{14}:\frac2{21}=\frac3{14}\ast\frac{21}2=\frac32\ast\frac32=\frac94=2\frac14$
3) $\frac7{16}:\frac{42}{43}=\frac7{16}\ast\frac{43}{42}=\frac1{16}\ast\frac{43}6=\frac{43}{96}$
4) $\frac34:\frac{21}{40}=\frac34\ast\frac{40}{21}=\frac11\ast\frac{10}7=1\frac37$
5) $\frac9{25}:\frac{27}{50}=\frac9{25}\ast\frac{50}{27}=\frac11\ast\frac23=\frac23$
6) $\frac{45}{56}:\frac{63}{64}=\frac{45}{56}\ast\frac{64}{63}=\frac57\ast\frac87=\frac{40}{49}$
7) $\frac23:\frac16=\frac23\ast\frac61=2\ast2=4$
8) $\frac{65}{98}:\frac{26}{49}=\frac{65}{98}\ast\frac{49}{26}=\frac{65}2\ast\frac1{26}=\frac{65}{52}=1\frac{13}{52}$
Задание 447. Выполните деление:
Решение
1) $\frac{11}{15}:\frac38=\frac{11}{15}\ast\frac83=\frac{88}{45}=1\frac{43}{45}$
2) $\frac6{35}:\frac{18}{25}=\frac6{35}\ast\frac{25}{18}=\frac17\ast\frac53=\frac5{21}$
3) $\frac{12}{55}:\frac{48}{77}=\frac{12}{55}\ast\frac{77}{48}=\frac15\ast\frac74=\frac7{20}$
4) $\frac{21}{40}:\frac34=\frac{21}{40}\ast\frac43=\frac7{10}\ast\frac11=\frac7{10}$
5) $\frac{27}{50}:\frac9{25}=\frac{27}{50}\ast\frac{25}9=\frac32\ast\frac11=1\frac12$
6) $\frac{63}{64}:\frac{45}{56}=\frac{63}{64}\ast\frac{56}{45}=\frac78\ast\frac75=\frac{49}{40}=1\frac9{40}$
7) $\frac58:\frac5{32}=\frac58\ast\frac{32}5=\frac11\ast\frac41=4$
8) $\frac{14}{55}:\frac15=\frac{14}{55}\ast\frac51=\frac{14}{11}\ast\frac11=1\frac3{11}$
Задание 448. Найдите частное:
Решение от 7 гуру
1) $10:\frac56=10\ast\frac65=2\ast6=12$
2) $12:\frac{15}{16}=12\ast\frac{16}{15}=4\ast\frac{16}5=\frac{64}5=12\frac45$
3) $\frac34:2=\frac34\ast\frac12=\frac38$
4) $\frac{10}{11}:10=\frac{10}{11}\ast\frac1{10}=\frac1{11}$
5) $1:\frac78=1\ast\frac87=1\frac17$
6) $7\frac35:\frac{19}{25}=\frac{38}5\ast\frac{25}{19}=\frac21\ast\frac51=10$
7) $1\frac78:2\frac{11}{32}=\frac{15}8\ast\frac{32}{75}=\frac11\ast\frac45=\frac45$
8) $5\frac13:1\frac59=\frac{16}3\ast\frac9{14}=\frac81\ast\frac37=\frac{24}7=3\frac37$
Задание 449. Найдите частное:
Решение
1) $6:\frac79=6\ast\frac97=\frac{54}7=7\frac57$
2) $16:\frac4{11}=16\ast\frac{11}4=4\ast11=44$
3) $13:\frac{26}{29}=13\ast\frac{29}{26}=\frac{29}2=14\frac12$
4) $\frac79:5=\frac79\ast\frac15=\frac7{45}$
5) $\frac9{16}:6=\frac9{16}\ast\frac16=\frac3{16}\ast\frac12=\frac3{32}$
6) $1\frac59:1\frac8{27}=\frac{14}9\ast\frac{27}{35}=\frac21\ast\frac35=\frac65=1\frac15$
7) $2\frac{10}{13}:3\frac3{26}=\frac{36}{13}\ast\frac{26}{81}=\frac41\ast\frac29=\frac89$
8) $2\frac47:1\frac1{35}=\frac{18}7\ast\frac{35}{36}=\frac11\ast\frac52=2\frac12$
