Bài 8: Quy tắc dấu ngoặc

a: \(\left[\left(-59\right)+71\right]-\left[\left(-83\right)-\left(-95\right)\right]\)

\(=\left[71-59\right]-\left[-83+95\right]\)
=12-12

=0

b: \(\left(435-167-89\right)-\left(435-89\right)\)

\(=435-167-89-435+89\)

\(=\left(435-435\right)+\left(89-89\right)-167\)

=0+0-167

=-167

c: \(\left(-624\right)-\left[\left(376+245\right)-45\right]\)

\(=\left(-624\right)-\left[376+245-45\right]\)

\(=\left(-624\right)-376-200\)

=-1000-200

=-1200

a: \(-59+71-\left\{-83-\left(95\right)\right\}\)

\(=71-59+81+95\)

\(=12+81+95\)

\(=93+95=188\)

b: \(-257-\left\{\left(-257+156\right)-56\right\}\)

\(=-257-\left(-257+156-56\right)\)

\(=-257-\left(-257+100\right)\)

\(=-257+257-100=-100\)

c: Sửa đề:\(\left(435-167\right)-89-\left(435-89\right)\)

\(=435-167-89-435+89\)

=\(\left(435-435\right)+\left(-89+89\right)-167\)

=0+0-167

=-167

d: \(-329+\left(15-101\right)-\left(25-440\right)\)

\(=-329+15-101-25+440\)

\(=\left(440-329-101\right)+\left(15-25\right)\)

=10-10

=0

e: \(\left(116+124\right)+\left(215-116-124\right)\)

\(=116+124+215-116-124\)

\(=\left(116-116\right)+\left(124-124\right)+215\)

=0+0+215

=215

f: \(4524-\left(864-999\right)-\left(36-999\right)\)

\(=4524-864+999-36+999\)

\(=4524-\left(864+36\right)+999\cdot2\)

\(=4524-900+1998=5622\)

\(324+\left\{12-\left(112+324\right)\right\}\)

\(=324+12-\left(112+324\right)\)

\(=324+12-112-324\)

=12-112

=-100

=12-112

=-100

\(-323+\left(874+564-241\right)\)

\(=-323+\left(874+323\right)\)

=-323+874+323

=874

\(12\cdot\left(-47\right)+12\cdot\left(-19\right)+\left(-66\right)\cdot88\)

\(=12\left(-47-19\right)+\left(-66\right)\cdot88\)

\(=-66\cdot12+88\cdot\left(-66\right)\)

\(=-66\left(12+88\right)\)

\(=-66\cdot100=-6600\)

d) -37 . (-19) + 37 . (-119)

= -37.(-19 + 119)

= -37 . 100

= -3700

a: \(-317+402-583+98\)

\(=\left(-317-583\right)+\left(402+98\right)\)

\(=-900+500=-400\)

b: \(-200-\left(1861-655\right)+61-2655\)

\(=-200-1861+655+61-2655\)

\(=-200-\left(1861-61\right)+\left(655-2655\right)\)

\(=-200-1800-2000\)

=-4000

VT=\(-\left(-a+b+c\right)+\left(b+c-1\right)\)

\(=a-b-c+b+c-1\)

=a-1

\(VP=\left(b-c+6\right)-\left(7-a+b\right)+c\)

\(=b-c+6-7+a-b+c\)

=a-1

=>VT=VP

=>\(-\left(-a+b+c\right)+\left(b+c-1\right)=\left(b-c+6\right)-\left(7-a+b\right)+c\)

1: \(-5+\left(-37-45+51\right)-\left(-37+51\right)\)

\(=-5-37-45+51+37-51\)

\(=-5-45=-50\)

2: \(\left(53-45-49\right)-\left(53+45-49\right)\)

\(=53-45-49-53-45+49\)

=-45-45

=-90

3: \(-15+\left(89+15-72\right)-\left(89-72\right)\)

\(=-15+89+15-72-89+72\)

=-15+15

=0

4: \(-\left(81-32-47\right)+81-\left(32+2\right)\)

\(=-81+32+47+81-32-2\)

=47-2

=45

5: \(50-\left(47+50-18\right)+\left(47-18\right)\)

\(=50-47-50+18+47-18\)

=50-50

=0

6: \(-\left(15-47+58\right)+\left(15-47\right)+3\)

\(=-15+47-58+15-47+3\)

=-58+3

=-55

7: \(13-15+49-13+15-48\)

\(=\left(13-13\right)+\left(15-15\right)+\left(49-48\right)\)

=0+0+1

=1

8: \(-28+32-45-32+28+45-8\)

\(=\left(-28+28\right)+\left(32-32\right)+\left(45-45\right)-8\)

=0+0+0-8

=-8

9: \(42-56+33-\left(33-56+42\right)\)

\(=42-56+33-33+56-42\)

\(=\left(42-42\right)+\left(56-56\right)+\left(33-33\right)\)

=0+0+0

=0

10: \(54-\left(45-30+54\right)-30+5\)

\(=54-45+30-54-30+5\)

=-45+5

=-40