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\(a,4:7+\frac{9}{5}-\frac{8}{14}=4:7+\frac{9}{5}-\frac{4}{7}=\frac{4}{7}+\frac{9}{5}-\frac{4}{7}=\)\(\frac{4}{7}-\frac{4}{7}+\frac{9}{5}=0+\frac{9}{5}=\frac{9}{5}\)
\(b,6:8:\frac{3}{4}-1=\frac{6}{8}:\frac{3}{4}-1=\frac{3}{4}:\frac{3}{4}-1=1-1=0\)
3/2+3/6+3/12+3/20+3/30
=3/2+1/2+1/4+3/20+1/10
=30/20+10/20+5/20+3/20+2/20
=30+10+5+3+2/20
=50/20=5/2
\(\frac{3}{2}\)+\(\frac{3}{6}\)+\(\frac{3}{12}\)+ \(\frac{3}{20}\)+\(\frac{3}{30}\)
= \(\frac{3}{2}\) + \(\frac{1}{2}\)+ \(\frac{1}{4}\)+ \(\frac{3}{20}\)+ \(\frac{1}{10}\)
= \(\frac{30}{20}\)+ \(\frac{10}{20}\)+ \(\frac{5}{20}\)+\(\frac{3}{20}\)+\(\frac{2}{20}\)
= \(\frac{50}{20}\)= \(\frac{5}{2}\)
2 x 5 + 5 x 7 + 9 x 3
= 5 x ( 2 + 7 ) + 9 x 3
= 5 x 9 + 9 x 3
= 9 x ( 5 + 3 )
= 9 x 8
= 72
2x5+5x9+9x3 15:5+27:5+8:5
=9x5+(2+3) =(15+8+27):5
=9x5+5 =50:5
=9x5+5x1 =10
=5x(9+1) 9+9x3+18:2x6
=5x10 =1x9+9x3+9x6
=50 =9x(1+6+3)
=9x10
=90
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\)= \(\frac{2-1}{2}.\frac{3-1}{3}.\frac{4-1}{4}\)= \(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}\)= \(\frac{1.2.3}{2.3.4}=\frac{1}{4}\)
\(\left(1+\frac{1}{2}\right):\left(1+\frac{1}{3}\right):\left(1+\frac{1}{4}\right)\)= \(\frac{2+1}{2}:\frac{3+1}{3}:\frac{4+1}{4}\)= \(\frac{3}{2}:\frac{4}{3}:\frac{5}{4}=\frac{3}{2}.\frac{3}{4}.\frac{4}{5}=\frac{3.3.4}{2.4.5}=\frac{3.3}{2.5}=\frac{9}{10}\)
\(\frac{6}{5}-\frac{4}{5}.\frac{4}{8}+1=\frac{6}{5}+1-\frac{4.4}{5.8}=\frac{6+5}{5}-\frac{4}{5.2}=\frac{11}{5}-\frac{2}{5}=\frac{9}{5}\)
x < \(\frac{3}{4}+\frac{4}{5}=\frac{15}{20}+\frac{16}{20}=\frac{31}{20}=\frac{20}{20}+\frac{11}{20}=1\frac{11}{20}\)=> x = 0 ; 1
\(\frac{1}{2}+\frac{2}{3}< x< 4-\frac{5}{4}\)<=> \(\frac{3}{6}+\frac{4}{6}< x< \frac{16}{4}-\frac{5}{4}\)<=> \(\frac{7}{6}< x< \frac{11}{4}\)=> \(\frac{14}{12}< \frac{12x}{12}< \frac{33}{12}\)
=> 14 < 12x < 33 => 12x = 24 => x = 24 : 12 = 2