Question

    TÍNH NHANH

1x3x5+2x6x10+4x12x20+7x21x35 /

1x5x7+2x10x14+4x20x28+7x35x49

Answer 1

1X3X5+2X6X10+4X12X20+7X21X35 /1X5X7+2X10X14+4X20X28+7X35X49

=3+6+12+21 /7+14+28+49

=42 /98=3/7

Answer 2

Bài này chỉ có thể tính bình thường đc thôi ak, nếu muốn lời giải chuẩn thì tham khảo nhé!

\(\frac{1x3x5+2x6x10+4x12x20+7x21x35}{1x5x7+2x10x14+4x20x28+7x35x49}\)

Nhận xét:

a)Phần tử số:

2x6x10= (1 x 2) x (3x2) x (5x2) = (2x2x2) x (1x3x5)

4x12x20= (1x4) x (3x4) x (5x4) = (4x4x4) x (1x3x5)

7x21x35= (1x7) x (3x7) x (5x7) = (7x7x7) x (1x3x5)

b)Phần mẫu số:

2x10x14= (1x2) x (5x2) x (7x2) = (2x2x2) x (1x5x7)

4x20x28= (1x4) x (5x4) x (7x4) = (4x4x4) x (1x5x7)

7x35x49= (1x7) x (5x7) x (7x7) = (7x7x7) x (1x5x7)

Vậy:

        \(\frac{1x3x5+2x6x10+4x12x20+7x21x35}{1x5x7+2x10x14+4x20x28+7x35x49}\)

\(=\frac{\left(1x3x5\right)+\left(2x2x2\right)x\left(1x3x5\right)+\left(4x4x4\right)x\left(1x3x5\right)+\left(7x7x7\right)x\left(1x3x5\right)}{\left(1x5x7\right)+\left(2x2x2\right)x\left(1x5x7\right)+\left(4x4x4\right)x\left(1x5x7\right)+\left(7x7x7\right)x\left(1x5x7\right)}\)

\(=\frac{\left(1x3x5\right)x\left(1+2x2x2+4x4x4+7x7x7\right)}{\left(1x5x7\right)x\left(1+2x2x2+4x4x4+7x7x7\right)}\)

\(=\frac{1x3x5}{1x5x7}\)\(=\frac{3}{7}\)