Tìm các tích sau: a) 1 1/2*1 1/3*1 1/4*1 1/5*1 1/6*1 1/7; b) (1-1/2)(1-1/3)(1-1/4)...(1-1/50

Giải SBT Toán 6 Cánh diều Bài 4: Phép nhân, phép chia phân số  

Bài 46 trang 41 SBT Toán 6 Tập 2:

Tìm các tích sau:

a) $1\frac{1}{2}\cdot 1\frac{1}{3}\cdot 1\frac{1}{4}\cdot 1\frac{1}{5}\cdot 1\frac{1}{6}\cdot 1\frac{1}{7}$;

b) $\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\dots \left(1-\frac{1}{50}\right)$.

Lời giải

a) $1\frac{1}{2}\cdot 1\frac{1}{3}\cdot 1\frac{1}{4}\cdot 1\frac{1}{5}\cdot 1\frac{1}{6}\cdot 1\frac{1}{7}$

$=\frac{3}{2}\cdot \frac{4}{3}\cdot \frac{5}{4}\cdot \frac{6}{5}\cdot \frac{7}{6}\cdot \frac{8}{7}=\frac{8}{2}=4$.

b) $\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\dots \left(1-\frac{1}{50}\right)$

$=\left(\frac{2}{2}-\frac{1}{2}\right)\left(\frac{3}{3}-\frac{1}{3}\right)\left(\frac{4}{4}-\frac{1}{4}\right)\dots \left(\frac{50}{50}-\frac{1}{50}\right)$

$=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}\mathrm{...}\frac{49}{50}=\frac{1}{50}$.