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1+2+3+4+5+6+7+8+9 = ( 1+9) + ( 2+8) + (3+7) + (4+6) +5
= 10 + 10 + 10 + 10 + 5
= 45
a.\(\dfrac{2}{3}\times\dfrac{4}{9}+\dfrac{2}{3}\times\dfrac{5}{9}=\dfrac{2}{3}\times\left(\dfrac{4}{9}+\dfrac{5}{9}\right)=\dfrac{2}{3}\times1=\dfrac{2}{3}\)
b.\(\dfrac{7}{5}\times\dfrac{3}{4}-\dfrac{1}{2}\times\dfrac{3}{4}=\dfrac{3}{4}\times\left(\dfrac{7}{5}-\dfrac{1}{2}\right)=\dfrac{3}{4}\times\dfrac{9}{10}=\dfrac{27}{40}\)
c.\(\left(\dfrac{5}{6}+\dfrac{5}{8}\right)\times\dfrac{2}{3}=\dfrac{35}{24}\times\dfrac{2}{3}=\dfrac{35}{36}\)
a) 2/3 x 4/9 + 2/3 x 5/9
=2/3 x ( 4/9 + 5/9)
= 2/3 x 1
= 2/3
b, 7/5 x 3/4 - 1/2 x 3/4
= ( 7/5 - 1/2 ) x 3/4
= 9/10 x 3/4
= 21/40
c, ( 5/6 + 5/8 ) x 2/3
= 35/24 x 2/3
= 35/36
`2/3 xx 2/8 +2/3 : 8 +2/3 xx 5/8`
`=2/3 xx 2/8 +2/3 xx 1/8 +2/3 xx 5/8`
`=2/3 xx (2/8+1/8+5/8)`
`=2/3 xx 8/8`
`=2/3 xx 1`
`=2/3`
= 17/2 x 3/5 + 3/5 x 1/2 + 3/5 x 1
= 3/5 x ( 17/2 + 1/2 + 1 )
= 3/5 x 10
= 30/5
= 1/6
\(\frac{17}{2}\cdot\frac{3}{5}+\frac{3}{5}\cdot\frac{1}{2}+\frac{3}{5}\)
\(=\left(\frac{17}{2}+\frac{1}{2}+1\right)\cdot\frac{3}{5}\)
\(=\left(\frac{17}{2}+\frac{1}{2}+\frac{2}{2}\right)\cdot\frac{3}{5}\)
\(=10\cdot\frac{3}{5}=6\)
2/
a)\(\dfrac{1}{5}+\dfrac{4}{5}+\dfrac{4}{11}+\dfrac{7}{11}\)
= \(\dfrac{5}{5}+\dfrac{11}{11}\)
= \(1+1\)
= \(2\)
b) \(\left(\dfrac{1}{8}+\dfrac{3}{8}\right)+\left(\dfrac{4}{12}+\dfrac{5}{12}\right)\)
= \(\dfrac{4}{8}+\dfrac{8}{12}\)
= \(\dfrac{12}{24}+\dfrac{16}{24}\)
= \(\dfrac{28}{24}\)
= \(\dfrac{7}{6}\)
`1/3xx 1/2 + 1/2 xx 1/5`
`=1/2 xx (1/3 +1/5)`
`= 1/2 xx ( 5/15 +3/15)`
`= 1/2 xx 8/15`
`= 8/30`
`=4/15`
__
`1/3 xx 1/2 - 1/5 xx 1/2`
`= 1/2 xx (1/3 -1/5)`
`= 1/2 xx ( 5/15 -3/15)`
`=1/2 xx 2/15`
`= 2/30`
`=1/15`
a)
`1/3xx1/2+1/2xx1/5`
`=1/2xx(1/3+1/5)`
`=1/2xx(5/15+3/15)`
`=1/2xx8/15`
`=4/15`
b)
`1/3xx1/2-1/5xx1/2`
`=1/2xx(1/3-1/5)`
`=1/2xx(5/15-3/15)`
`=1/2xx2/15`
`=1/15`
=1 + (1/2×5/2×3/2)+2/3
=1 + 15/8 + 2/3
=1 + 61/24
=85/24