PHẦN 2: TỰ LUẬN (7,0 điểm)
Câu 1. (2 điểm) Tính:
a) \(\frac{3}{7} + \frac{4}{7} \cdot \frac{-3}{4}\)
b) \(\frac{-5}{17} \cdot \frac{4}{13} + \frac{9}{13} \cdot \frac{-5}{17}\)
c) \(\frac{-20}{41} + \frac{4}{37} - \frac{20}{41} + \frac{33}{37} + 0,5\)
d)
3. \(\left(-\frac{3}{2}\right)^2 + \frac{1}{9} \cdot \sqrt{56}\)
a) \(\dfrac{3}{7}+\dfrac{4}{7}.\dfrac{-3}{4}\)
\(=\dfrac{3}{7}-\dfrac{3}{7}\)
\(=0\)
b) \(\dfrac{-5}{17}.\dfrac{4}{13}+\dfrac{9}{13}.\dfrac{-5}{17}\)
\(=\dfrac{-5}{17}.\left(\dfrac{4}{13}+\dfrac{9}{13}\right)\)
\(=\dfrac{-5}{17}.1\)
\(=\dfrac{-5}{17}\)
c) \(\dfrac{-20}{41}+\dfrac{4}{37}-\dfrac{20}{41}+\dfrac{33}{37}+0,5\)
\(=\left(\dfrac{-20}{41}-\dfrac{20}{41}\right)+\left(\dfrac{4}{37}+\dfrac{33}{37}\right)+0,5\)
\(=-\dfrac{40}{41}+1+0,5\)
\(=-\dfrac{40}{41}+\dfrac{3}{2}\)
\(=\dfrac{43}{82}\)
d) \(3.\left(-\dfrac{3}{2}\right)^2+\dfrac{1}{9}.\sqrt{56}\)
\(=3.\dfrac{9}{4}+\dfrac{1}{9}.2\sqrt{14}\)
\(=\dfrac{27}{4}+\dfrac{2\sqrt{14}}{9}\)
a) 3/7 + 4/7 . (-3/4)
= 3/7 + (4/7 . -3/4)
= 3/7 + (-3/7)
= 0
b) -5/17 . 4/13 + 9/13 . -5/17
= -5/17 . (4/13 + 9/13)
= -5/17 . 13/13
= -5/17 . 1
= -5/17
c) -20/41 + 4/37 - 20/41 + 33/37 + 0,5
= (-20/41 + -20/41) + (4/37 + 33/37) + 1/2
= -40/41 + 37/37 + 1/2
= -40/41 + 1 + 1/2
= -40/41 + 3/2
= (-80 + 123) / 82
= 43/82
d) 3 . (-3/2)^2 + 1/9 . √56
= 3 . 9/4 + 1/9 . √(4*14)
= 27/4 + 1/9 . 2√14
= 27/4 + 2√14 / 9
= (243 + 8√14) / 36
a) 3/7 + 4/7 . (-3/4)
= 3/7 + (4/7 -3/4)
= 3/7 + (-3/7)
= 0
b) -5/17 . 4/13 + 9/13 . -5/17
= -5/17 . (4/13 + 9/13)
= -5/17 . 13/13
= -5/17 . 1
= -5/17
c) -20/41 + 4/37 - 20/41 + 33/37 + 0,5
= (-20/41 + -20/41) + (4/37 + 33/37) + 1/2
= -40/41 + 37/37 + 1/2
= -40/41 + 1 + 1/2
= -40/41 + 3/2
= (-80 + 123) / 82
= 43/82
d) 3 . (-3/2)² + 1/9 . √56
= 3 . 9/4 + 1/9 . √(4x14)
= 27/4 + 1/9 . 2√14
= 27/4 + 2√14 /9
= (243 + 8√14) /36
