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\(\frac{9}{10}\)+\(\frac{7}{9}\)+\(\frac{5}{8}\)+\(\frac{3}{7}+\frac{3}{5}+\frac{2}{5}+\frac{4}{7}+\frac{3}{8}+\frac{2}{9}+\frac{1}{10}\)
\(=\left(\frac{9}{10}+\frac{1}{10}\right)+\left(\frac{7}{9}+\frac{2}{9}\right)+\left(\frac{5}{8}+\frac{3}{8}\right)\)\(+\left(\frac{3}{7}+\frac{4}{7}\right)+\left(\frac{3}{5}+\frac{2}{5}\right)\)
\(=1+1+1+1+1\)
\(=5\)
9/10 + 7/9 + 5/8 + 3/7 + 3/5 + 2/5 + 4/7 + 3/8 + 2/9 + 1/10
= ( 9/10 + 1/10 ) + ( 7/9 + 2/9 ) + ( 5/8 + 3/8 ) + ( 3/7 + 4/7 ) + ( 3/5 + 2/5 )
= 1 + 1 + 1 + 1 + 1
= 5
\(\frac{9}{10}+\frac{7}{9}+\frac{5}{8}+\frac{3}{7}+\frac{3}{5}+\frac{2}{5}+\frac{4}{7}+\frac{3}{8}+\frac{2}{9}+\frac{1}{10}\)
= \(\left(\frac{9}{10}+\frac{1}{10}\right)+\left(\frac{7}{9}+\frac{2}{9}\right)+\left(\frac{5}{8}+\frac{3}{8}\right)+\left(\frac{3}{7}+\frac{4}{7}\right)+\left(\frac{3}{5}+\frac{2}{5}\right)\)
= \(\frac{10}{10}+\frac{9}{9}+\frac{8}{8}+\frac{7}{7}+\frac{5}{5}\)
= \(1+1+1+1+1\)
= \(1\times5\)
= \(5\)
Gọi A là tổng của 9/10 + 7/9 + 5/8 + 3/7 + 3/5 + 2/5 + 4/7 + 3/8 + 2/9 + 1/10, ta có :
A = 9/10 + 7/9 + 5/8 + 3/7 + 3/5 + 2/5 + 4/7 + 3/8 + 2/9 + 1/10
A = (9/10 + 1/10) + (7/9 + 2/9) + (5/8 + 3/8) + (3/7 + 4/7) + (3/5 + 2/5)
A = 1 + 1 + 1 + 1 + 1
A = 5
\(a)\frac{4}{9}+\frac{3}{8}+\frac{5}{8}=\frac{4}{9}+(\frac{3}{8}+\frac{5}{8})=\frac{4}{9}+1=\frac{4+9}{9}=\frac{13}{9}\)
\(b)\frac{3}{7}+\frac{2}{3}+\frac{4}{7}=(\frac{3}{7}+\frac{4}{7})+\frac{2}{3}=1+\frac{2}{3}=\frac{3+2}{3}=\frac{5}{3}\)
\(\frac{9}{10}+\frac{7}{9}+\frac{5}{8}+\frac{3}{7}+\frac{3}{5}+\frac{2}{5}+\frac{4}{7}+\frac{3}{8}+\frac{2}{9}+\frac{1}{10}\)\(=\frac{9}{10}+\frac{1}{10}+\frac{7}{9}+\frac{2}{9}+\frac{5}{8}+\frac{3}{8}+\frac{3}{7}+\frac{4}{7}+\frac{3}{5}+\frac{2}{5}\)
\(=\left[\frac{9}{10}+\frac{1}{10}\right]+\left[\frac{7}{9}+\frac{2}{9}\right]+\left[\frac{5}{8}+\frac{3}{8}\right]+\left[\frac{3}{7}+\frac{4}{7}\right]+\left[\frac{3}{5}+\frac{2}{5}\right]\)
\(=1+1+1+1+1\)
\(=5\)
\(\frac{9}{10}+\frac{7}{9}+\frac{5}{8}+\frac{3}{7}+\frac{3}{5}+\frac{2}{5}+\frac{4}{7}+\frac{3}{8}+\frac{2}{9}+\frac{1}{10}\)
= \(\left(\frac{9}{10}+\frac{1}{10}\right)+\left(\frac{7}{9}+\frac{2}{9}\right)+\left(\frac{5}{8}+\frac{3}{8}\right)+\left(\frac{3}{7}+\frac{4}{7}\right)+\left(\frac{3}{5}+\frac{2}{5}\right)\)
= 1 + 1 + 1 + 1 + 1
= 5
\(=\dfrac{5}{9}\times\dfrac{7}{4}+\dfrac{13}{9}\times\dfrac{7}{4}\\ =\left(\dfrac{5}{9}+\dfrac{13}{9}\right)\times\dfrac{7}{4}\\ =2\times\dfrac{7}{4}\\ =\dfrac{7}{2}\)
1+2+3+4+5+6+7+8+9
= (9+1)+(8+2)+(7+3)+(6+4)+5
= 10 + 10 + 10 + 10 + 5
= 40 + 5
= 45
( 1/10 + 2/9 + 3/8 + 4/7 + 5/6 + 1/6 + 3/7 + 5/8 + 7/9 + 9/10 ) * 48
= [ ( 1/10 + 9/10 ) + ( 2/9 + 7/9 ) + ( 3/8 + 5/8 ) + ( 4/7 + 3/7 ) + ( 5/6 + 1/6 ) ] * 48
=( 1 + 1 + 1 + 1 + ) *48
=5 * 48
= 240
=(3/7+4/7)+(4/9+5/9)
=1+1=2
\(\dfrac{3}{7}+\dfrac{4}{9}+\dfrac{4}{7}+\dfrac{5}{9}=\left(\dfrac{3}{7}+\dfrac{4}{7}\right)+\left(\dfrac{4}{9}+\dfrac{5}{9}\right)=\dfrac{7}{7}+\dfrac{9}{9}=1+1=2\)