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Giải mục 2 trang 21, 22 SGK Toán 8 tập 2 - Kết nối tri thức

Làm tính chia

🍎Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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LT 2

Video hướng dẫn giải

Làm tính chia: \(\frac{{3{{x}}}}{{2{y^2}}}:\left( {\frac{{ - 5{{{x}}^2}}}{{12{y^3}}}} \right)\)

Phương pháp giải:

Thực hiện theo quy tắc chia hai phân thức

Lời giải chi tiết:

\(\begin{array}{l}\frac{{3{{x}}}}{{2{y^2}}}:\left( {\frac{{ - 5{{{x}}^2}}}{{12{y^3}}}} \right)\\ = \frac{{3{{x}}}}{{2{y^2}}}.\frac{{12{y^3}}}{{ - 5{{{x}}^2}}}\\ = \frac{{3{{x}}.12{y^3}}}{{2{y^2}.\left( { - 5{{{x}}^2}} \right)}} = \frac{{36{{x}}{y^3}}}{{ - 10{{{x}}^2}{y^2}}} = \frac{{ - 18y}}{{5x}}\end{array}\)

TTN

Video hướng dẫn giải

Kết luận sau là đúng hay sai? \(\left( {\frac{1}{x}:\frac{1}{x}} \right):\frac{1}{x} = \frac{1}{x}:\left( {\frac{1}{x}:\frac{1}{x}} \right)\)

Phương pháp giải:

Thực hiện tính hai vế rồi đưa ra kết luận

Lời giải chi tiết:

Ta có: \(\begin{array}{l}\left( {\frac{1}{x}:\frac{1}{x}} \right):\frac{1}{x} = 1:\frac{1}{x} = 1.\frac{x}{1} = x\\\frac{1}{x}:\left( {\frac{1}{x}:\frac{1}{x}} \right) = \frac{1}{x}:1 = \frac{1}{x}\end{array}\) Vậy kết luận \(\left( {\frac{1}{x}:\frac{1}{x}} \right):\frac{1}{x} = \frac{1}{x}:\left( {\frac{1}{x}:\frac{1}{x}} \right)\) là kết luận sai

VD

Video hướng dẫn giải

ꦅBác Châu vay ngân hàng 1,2 tỉ đồng để mua nhà theo hình thức trả góp. Số tiền bác Châu phải trả mỗi tháng bao gồm số tiền gốc phải trả hằng tháng (bằng số tiền gốc chia đều cho số tháng vay) và số tiền lãi phải trả hằng tháng (bằng số tiền gốc nhân với lãi suất tháng).

🌸a) Gọi r là lãi suất năm của khoản vay trả góp này. Tính số tiền x (triệu đồng) mà bác Châu phải trả mỗi thàng theo số tháng vay y (tháng) và lãi suất năm r. Từ đó suy ra công thức tính lãi suất năm r theo x và y

♓b) Tính giá trị của r tại x = 30, y = 48 rồi cho biết, nếu trả góp mỗi tháng 30 triệu đồng trong vòng 4 năm thì lãi suất năm (tính theo %) của khoản vay là bao nhiêu?

Phương pháp giải:

a) Viết biểu thức dựa vào yêu cầu đề bài b) Thay giá trị vào biểu thức để tìm ẩn

Lời giải chi tiết:

a) Số tiền x (triệu đồng) mà bác Châu phải trả mỗi tháng là:  \(\begin{array}{l}x = \frac{{1200}}{y} + \left( {1200.\frac{r}{{12}}} \right)\\ \Rightarrow x = \frac{{1200}}{y} + 100{\rm{r}}\\ \Rightarrow r = \frac{{xy - 1200}}{{100y}}\end{array}\) b) Thay x = 30, y = 48, ta có: r = 0.05 Lãi suất năm của khoản vay khi mỗi tháng trả góp 30 triệu đồng trong vòng 4 năm là: \(r = \frac{{30.48 - 1200}}{{100.48}} = 0,05 = 5(\% )\)

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