Câu trong ảnh làm như nào các bạn ơi... Bài 4. Thực hiện phép tính (tính nhanh nêu có thể),$m)~(-12.\frac27+\frac89:3\frac12-\frac27.\frac5{18}).3\frac12$ $n)~(13\frac35+4\frac34)-8\frac35$ $p)~11\frac14-(2\frac57+5\frac14)$,$q)~(8\frac5{11}+3\frac58)-3\frac5{11}$ $u)~\frac{-1}4.13\frac9{11}-0,25.6\frac2{11}$ $v)~\frac49:(-\frac17)+6\frac59:(-\frac17)$,Bài 5. Thực hiện phép tính(tính hợp lý),$a)~\frac23-4.(\frac12+\frac34)$ $b)~(-\frac13+\frac56).11-7$,$c)~(-\frac59).\frac3{11}+(-\frac{13}{18}).\frac3{11}$ $d)~(\frac{-2}3).\frac3{11}+(\frac{-16}9).\frac3{11}$,$e)~(\frac{-1}4).(-\frac2{13})-\frac7{24}.(-\frac2{13})$ $f)~(\frac{-1}{27}).\frac37+(\frac59).(-\frac37)g)(-\frac15+\frac37):\frac2{11}+(-\frac45+\frac47):\frac2{11}$

Question

Huycindy · Accepted Answer

Bài $4:$ 
$m)$ $\left(-12 \cdot \dfrac{2}{7} + \dfrac{8}{9} : 3\dfrac{1}{2} - \dfrac{2}{7} \cdot \dfrac{5}{18}\right) \cdot 3\dfrac{1}{2}$
$= -12 \cdot \dfrac{2}{7} \cdot 3\dfrac{1}{2} + \dfrac{8}{9} : 3\dfrac{1}{2} \cdot 3\dfrac{1}{2} - \dfrac{2}{7} \cdot \dfrac{5}{18} \cdot 3\dfrac{1}{2}$
$= -12 \cdot \dfrac{2}{7} \cdot \dfrac{7}{2} + \dfrac{8}{9} - \dfrac{2}{7} \cdot \dfrac{5}{18} \cdot \dfrac{7}{2}$
$= -12 \cdot 1 + \dfrac{8}{9} - \dfrac{5}{18}$
$= -12 + \dfrac{16}{18} - \dfrac{5}{18}$
$= -12 + \dfrac{11}{18}$
$= -\dfrac{205}{18}$
$n)$ $\left(13\dfrac{3}{5} + 4\dfrac{3}{4}\right) - 8\dfrac{3}{5}$
$= 13\dfrac{3}{5} + 4\dfrac{3}{4} - 8\dfrac{3}{5}$
$= \left(13\dfrac{3}{5} - 8\dfrac{3}{5}\right) + 4\dfrac{3}{4}$
$= 5 + 4\dfrac{3}{4}$
$= \dfrac{39}{4}$
$p)$ $11\dfrac{1}{4} - \left(2\dfrac{5}{7} + 5\dfrac{1}{4}\right)$
$= 11\dfrac{1}{4} - 2\dfrac{5}{7} - 5\dfrac{1}{4}$
$= \left(11\dfrac{1}{4} - 5\dfrac{1}{4}\right) - 2\dfrac{5}{7}$
$= 6 - 2\dfrac{5}{7}$
$= \dfrac{23}{7}$
$q)$ $\left(8\dfrac{5}{11} + 3\dfrac{5}{8}\right) - 3\dfrac{5}{11}$
$= 8\dfrac{5}{11} + 3\dfrac{5}{8} - 3\dfrac{5}{11}$
$= \left(8\dfrac{5}{11} - 3\dfrac{5}{11}\right) + 3\dfrac{5}{8}$
$= 5 + 3\dfrac{5}{8}$
$= \dfrac{69}{8}$
$u)$ $-\dfrac{1}{4} \cdot 13\dfrac{9}{11} - 0,25 \cdot 6\dfrac{2}{11}$
$= -\dfrac{1}{4} \cdot 13\dfrac{9}{11} - \dfrac{1}{4} \cdot 6\dfrac{2}{11}$
$= -\dfrac{1}{4} \cdot \left(13\dfrac{9}{11} + 6\dfrac{2}{11}\right)$
$= -\dfrac{1}{4} \cdot \left(\dfrac{152}{11} + \dfrac{68}{11}\right)$
$= -\dfrac{1}{4} \cdot \dfrac{220}{11}$
$= -\dfrac{1}{4} \cdot 20$
$= -5$
$v)$ $\dfrac{4}{9} : \left(-\dfrac{1}{7}\right) + 6\dfrac{5}{9} : \left(-\dfrac{1}{7}\right)$
$= \left(\dfrac{4}{9} + 6\dfrac{5}{9}\right) : \left(-\dfrac{1}{7}\right)$
$= \left(\dfrac{4}{9} + \dfrac{59}{9}\right) \cdot \left(-7\right)$
$= \dfrac{63}{9} \cdot \left(-7\right)$
$= 7 \cdot \left(-7\right)$
$= -49$
Bài $5:$
$a)$ $\dfrac{2}{3} - 4 \cdot \left(\dfrac{1}{2} + \dfrac{3}{4}\right)$
$= \dfrac{2}{3} - 4 \cdot \left(\dfrac{2}{4} + \dfrac{3}{4}\right)$
$= \dfrac{2}{3} - 4 \cdot \dfrac{5}{4}$
$= \dfrac{2}{3} - 5$
$= -\dfrac{13}{3}$
$b)$ $\left(-\dfrac{1}{3} + \dfrac{5}{6}\right) \cdot 11 - 7$
$= \left(-\dfrac{2}{6} + \dfrac{5}{6}\right) \cdot 11 - 7$
$= \dfrac{3}{6} \cdot 11 - 7$
$= \dfrac{1}{2} \cdot 11 - 7$
$= \dfrac{11}{2} - \dfrac{14}{2}$
$= -\dfrac{3}{2}$
$c)$ $\left(-\dfrac{5}{9}\right) \cdot \dfrac{3}{11} + \left(-\dfrac{13}{18}\right) \cdot \dfrac{3}{11}$
$= \dfrac{3}{11} \cdot \left(-\dfrac{5}{9} - \dfrac{13}{18}\right)$
$= \dfrac{3}{11} \cdot \left(-\dfrac{10}{18} - \dfrac{13}{18}\right)$
$= \dfrac{3}{11} \cdot \left(-\dfrac{23}{18}\right)$
$= -\dfrac{23}{66}$
$d)$ $\left(-\dfrac{2}{3}\right) \cdot \dfrac{3}{11} + \left(-\dfrac{16}{9}\right) \cdot \dfrac{3}{11}$
$= \dfrac{3}{11} \cdot \left(-\dfrac{2}{3} - \dfrac{16}{9}\right)$
$= \dfrac{3}{11} \cdot \left(-\dfrac{6}{9} - \dfrac{16}{9}\right)$
$= \dfrac{3}{11} \cdot \left(-\dfrac{22}{9}\right)$
$= -\dfrac{2}{3}$
$e)$ $\left(\dfrac{-1}{4}\right) \cdot \left(-\dfrac{2}{13}\right) - \dfrac{7}{24} \cdot \left(-\dfrac{2}{13}\right)$
$= \left(-\dfrac{2}{13}\right) \cdot \left(\dfrac{-1}{4} - \dfrac{7}{24}\right)$
$= \left(-\dfrac{2}{13}\right) \cdot \left(-\dfrac{6}{24} - \dfrac{7}{24}\right)$
$= \left(-\dfrac{2}{13}\right) \cdot \left(-\dfrac{13}{24}\right)$
$= \dfrac{1}{12}$
$f)$ $\left(-\dfrac{1}{27}\right) \cdot \dfrac{3}{7} + \left(\dfrac{5}{9}\right) \cdot \left(-\dfrac{3}{7}\right)$
$= \left(-\dfrac{1}{27}\right) \cdot \dfrac{3}{7} - \dfrac{5}{9} \cdot \dfrac{3}{7}$
$= \dfrac{3}{7} \cdot \left(-\dfrac{1}{27} - \dfrac{15}{27}\right)$
$= \dfrac{3}{7} \cdot \left(-\dfrac{16}{27}\right)$
$= -\dfrac{16}{63}$
$g)$ $\left(-\dfrac{1}{5} + \dfrac{3}{7}\right) : \dfrac{2}{11} + \left(-\dfrac{4}{5} + \dfrac{4}{7}\right) : \dfrac{2}{11}$
$= \left(-\dfrac{1}{5} + \dfrac{3}{7} - \dfrac{4}{5} + \dfrac{4}{7}\right) : \dfrac{2}{11}$
$= \left[ \left(-\dfrac{1}{5} - \dfrac{4}{5}\right) + \left(\dfrac{3}{7} + \dfrac{4}{7}\right) \right] : \dfrac{2}{11}$
$= \left(-1 + 1\right) : \dfrac{2}{11}$
$= 0 : \dfrac{2}{11}$
$= 0$

Timi · Answer

Để giải các bài toán này, chúng ta sẽ thực hiện từng phép tính một cách chi tiết.

**Bài 4:**

**(m)** $-12 \cdot \frac{2}{7} + \frac{8}{9} : 3\frac{1}{2} - \frac{2}{7} \cdot \frac{5}{18}$

1. Tính từng phần:
   - $-12 \cdot \frac{2}{7} = -\frac{24}{7}$
   - $3\frac{1}{2} = \frac{7}{2} \Rightarrow \frac{8}{9} : \frac{7}{2} = \frac{8}{9} \cdot \frac{2}{7} = \frac{16}{63}$
   - $\frac{2}{7} \cdot \frac{5}{18} = \frac{10}{126} = \frac{5}{63}$

2. Ghép các phần lại:
   $$
   -\frac{24}{7} + \frac{16}{63} - \frac{5}{63} = -\frac{24}{7} + \frac{11}{63}
   $$
   Đưa về cùng mẫu:
   $$
   -\frac{24}{7} = -\frac{24 \cdot 9}{63} = -\frac{216}{63}
   $$
   Vậy:
   $$
   -\frac{216}{63} + \frac{11}{63} = -\frac{205}{63}
   $$

3. Nhân với $3\frac{1}{2} = \frac{7}{2}$:
   $$
   -\frac{205}{63} \cdot \frac{7}{2} = -\frac{1435}{126}
   $$

**Kết quả m:** $-\frac{1435}{126}$

---

**(n)** $(13\frac{3}{5} + 4\frac{3}{4}) - 8\frac{3}{5}$

1. Chuyển đổi sang số tự nhiên:
   - $13\frac{3}{5} = \frac{68}{5}$
   - $4\frac{3}{4} = \frac{19}{4}$
   - $8\frac{3}{5} = \frac{43}{5}$

2. Tính tổng:
   $$
   \frac{68}{5} + \frac{19}{4} = \frac{68 \cdot 4 + 19 \cdot 5}{20} = \frac{272 + 95}{20} = \frac{367}{20}
   $$

3. Trừ đi:
   $$
   \frac{367}{20} - \frac{43}{5} = \frac{367}{20} - \frac{172}{20} = \frac{195}{20} = \frac{39}{4}
   $$

**Kết quả n:** $\frac{39}{4}$

---

**(p)** $11\frac{1}{4} - (2\frac{5}{7} + 5\frac{1}{4})$

1. Chuyển đổi sang số tự nhiên:
   - $11\frac{1}{4} = \frac{45}{4}$
   - $2\frac{5}{7} = \frac{19}{7}$
   - $5\frac{1}{4} = \frac{21}{4}$

2. Tính tổng:
   $$
   \frac{19}{7} + \frac{21}{4} = \frac{19 \cdot 4 + 21 \cdot 7}{28} = \frac{76 + 147}{28} = \frac{223}{28}
   $$

3. Trừ đi:
   $$
   \frac{45}{4} = \frac{315}{28} \Rightarrow \frac{315}{28} - \frac{223}{28} = \frac{92}{28} = \frac{23}{7}
   $$

**Kết quả p:** $\frac{23}{7}$

---

**(q)** $(8\frac{5}{11} + 3\frac{5}{8}) - 3\frac{5}{11}$

1. Chuyển đổi sang số tự nhiên:
   - $8\frac{5}{11} = \frac{93}{11}$
   - $3\frac{5}{8} = \frac{29}{8}$
   - $3\frac{5}{11} = \frac{38}{11}$

2. Tính tổng:
   $$
   \frac{93}{11} + \frac{29}{8} = \frac{93 \cdot 8 + 29 \cdot 11}{88} = \frac{744 + 319}{88} = \frac{1063}{88}
   $$

3. Trừ đi:
   $$
   \frac{1063}{88} - \frac{38 \cdot 8}{88} = \frac{1063 - 304}{88} = \frac{759}{88}
   $$

**Kết quả q:** $\frac{759}{88}$

---

**(u)** $\frac{-1}{4} \cdot 13\frac{9}{11} - 0,25 \cdot 6\frac{2}{11}$

1. Chuyển đổi:
   - $13\frac{9}{11} = \frac{152}{11}$
   - $6\frac{2}{11} = \frac{68}{11}$

2. Tính:
   $$
   \frac{-1}{4} \cdot \frac{152}{11} - 0,25 \cdot \frac{68}{11} = \frac{-152}{44} - \frac{17}{11} = \frac{-152}{44} - \frac{68}{44} = \frac{-220}{44} = -5
   $$

**Kết quả u:** $-5$

---

**(v)** $\frac{4}{9} : (-\frac{1}{7}) + 6\frac{5}{9} : (-\frac{1}{7})$

1. Tính từng phần:
   $$
   \frac{4}{9} \cdot (-7) + 6\frac{5}{9} \cdot (-7) = -\frac{28}{9} - \frac{47}{9} = -\frac{75}{9} = -\frac{25}{3}
   $$

**Kết quả v:** $-\frac{25}{3}$

---

**Bài 5:**

**(a)** $\frac{2}{3} - 4 \cdot (\frac{1}{2} + \frac{3}{4})$

1. Tính trong dấu ngoặc:
   $$
   \frac{1}{2} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4}
   $$

2. Tính:
   $$
   4 \cdot \frac{5}{4} = 5 \Rightarrow \frac{2}{3} - 5 = \frac{2}{3} - \frac{15}{3} = -\frac{13}{3}
   $$

**Kết quả a:** $-\frac{13}{3}$

---

**(b)** $(- \frac{1}{3} + \frac{5}{6}) \cdot 11 - 7$

1. Tính trong dấu ngoặc:
   $$
   -\frac{1}{3} + \frac{5}{6} = \frac{-2 + 5}{6} = \frac{3}{6} = \frac{1}{2}
   $$

2. Tính:
   $$
   \frac{1}{2} \cdot 11 - 7 = \frac{11}{2} - \frac{14}{2} = -\frac{3}{2}
   $$

**Kết quả b:** $-\frac{3}{2}$

---

**(c)** $(- \frac{5}{9}) \cdot \frac{3}{11} + (-\frac{13}{18}) \cdot \frac{3}{11}$

1. Tính từng phần:
   $$
   (- \frac{5}{9}) \cdot \frac{3}{11} + (-\frac{13}{18}) \cdot \frac{3}{11} = -\frac{15}{99} - \frac{39}{198}
   $$
   (Đưa về cùng mẫu)
   $$
   -\frac{15 \cdot 2}{198} - \frac{39}{198} = -\frac{30 + 39}{198} = -\frac{69}{198} = -\frac{23}{66}
   $$

**Kết quả c:** $-\frac{23}{66}$

---

**(d)** $(\frac{-2}{3}) \cdot \frac{3}{11} + (\frac{-16}{9}) \cdot \frac{3}{11}$

1. Tính từng phần:
   $$
   (\frac{-2}{3}) \cdot \frac{3}{11} + (\frac{-16}{9}) \cdot \frac{3}{11} = -\frac{6}{33} - \frac{48}{99}
   $$
   (Đưa về cùng mẫu)
   $$
   -\frac{6 \cdot 3}{99} - \frac{48}{99} = -\frac{18 + 48}{99} = -\frac{66}{99} = -\frac{2}{3}
   $$

**Kết quả d:** $-\frac{2}{3}$

---

**(e)** $(\frac{-1}{4}) \cdot (-\frac{2}{13}) - \frac{7}{24} \cdot (-\frac{2}{13})$

1. Tính từng phần:
   $$
   \frac{1 \cdot 2}{4 \cdot 13} + \frac{7 \cdot 2}{24 \cdot 13} = \frac{2}{52} + \frac{14}{312}
   $$
   (Đưa về cùng mẫu)
   $$
   \frac{2 \cdot 6}{312} + \frac{14}{312} = \frac{12 + 14}{312} = \frac{26}{312} = \frac{13}{156}
   $$

**Kết quả e:** $\frac{13}{156}$

---

**(f)** $(\frac{-1}{27}) \cdot \frac{3}{7} + (\frac{5}{9}) \cdot (-\frac{3}{7})$

1. Tính từng phần:
   $$
   \frac{-3}{189} + \frac{-15}{63} = -\frac{3}{189} - \frac{45}{189} = -\frac{48}{189} = -\frac{16}{63}
   $$

**Kết quả f:** $-\frac{16}{63}$

---

**(g)** $(- \frac{1}{5} + \frac{3}{7}) : \frac{2}{11} + (-\frac{4}{5} + \frac{4}{7}) : \frac{2}{11}$

1. Tính từng phần trong dấu ngoặc:
   - $-\frac{1}{5} + \frac{3}{7} = \frac{-7 + 15}{35} = \frac{8}{35}$
   - $-\frac{4}{5} + \frac{4}{7} = \frac{-28 + 20}{35} = \frac{-8}{35}$

2. Tính chia:
   $$
   \frac{8}{35} : \frac{2}{11} + \frac{-8}{35} : \frac{2}{11} = \frac{8 \cdot 11}{70} + \frac{-8 \cdot 11}{70} = \frac{88}{70} - \frac{88}{70} = 0
   $$

**Kết quả g:** $0$

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Tất cả các kết quả trên đã được tính toán chi tiết. Nếu có phần nào không rõ, hãy cho tôi biết để tôi giải thích thêm!