Question

what is to be added to 5/9 of 4/9 to get 1/3व्हाट शुड बी आई गेट टूगेदर नाइन ऑफ 4923 ​

Answer 1

Let

• The number = x

=> x + $\frac{5}{9} \: \times \: \frac{4}{9} \: = \: \frac{1}{3}$

=> x + $\frac{ 5 \: × \: 4 }{ 9 }$ = $\frac{1}{3}$

=> x + $\frac{ 20 }{ 9 }$ = $\frac{1 }{ 3 }$

=> x = $\frac{ 1 }{ 3 } \: - \: \frac{ 20 }{ 9 }$

=> x = $\frac{ 1 \: × \: 9 }{ 3 \: × \: 9 } \: - \: \frac{ 20 \: × \: 3 }{ 9 \: × \: 3 }$

=> x = $\frac{ 9 }{ 27 } \: - \: \frac{ 60 }{ 27 }$

=> x = $\frac{ 9 \: - \: 60 }{ 27 }$

=> x = $\frac{ -51 }{ 27 }$

Proof :-

LHS

• $\frac{-51}{27} \: + \: \frac{5}{9} \: × \: \frac{4}{9}$ = ⅓

• $\frac{ -51 }{ 27 } \: + \: \frac{ 20 }{ 9 }$ = ⅓

• $\frac{ -51 \: × \: 9 }{ 27 \: × \: 9 } \: + \: \frac{ 20 \: × \: 27 }{ 9 \: × \: 27 }$ = ⅓

• $\frac{ -459 }{ 243 } \: + \: \frac{ 540 }{ 243 }$ = ⅓

• $\frac{ -459 \: + \: 540 }{ 243 }$ = ⅓

• $\frac{ 81 }{ 243 }$ = ⅓

81 → 9 × 9 → (3 × 3) (3 × 3)

243 → 3 × 3 × 3 × 3 × 3

• $\frac{ (3 \: × \: 3 \: × \: 3 \: × \: 3) }{(3 \: × \: 3 \: × \: 3 \: × \: 3 \: × \: 3)}$ = ⅓

• ⅓ = ⅓

:. LHS = RHS