Is 2/5 (1/9 +2/5 ) = 2/5 1/9 + 2/5 2/5 ?

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Solution

yes you are right

you can write any expression of form a(b+c) as ab+ac

a(b+c)=ab+ac

put a =2/5,b=1/9,c=2/5

2/5(1/9+2/5)=2/51/9 +2/5* 2/5

Proof

L.H.S =2/5(1/9+2/5)

L.H.S =2/5(23/45)

L.H.S =46/225

R.H.S= 2/51/9 + 2/52/5

R.H.S =2/45 +4/25 L.C.M of 45 and 25 =225

R.H.S =10/225+36/225

R.H.S =46/225

L.H.S=R.H.S

Hence proved

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