Question

simplify 2/3+5/6-1/9

Answer 1

2/3+5/6-1/9

LCM OF 3, 6, 9=18

12/18+15/18-2/18=25/18

Answer 2

Answer:

Required answer is $1 \frac{7}{18}$

Step-by-step explanation:

Given,

$\frac{2}{3} + \frac{5}{6} - \frac{1}{9}$

This is a problem of fraction.We can solve this problem by fraction's addition and subtraction rule.

First we are adding $\frac{2}{3} \: and \: \frac{5}{6}$

So,

$\frac{2}{3} + \frac{5}{6} \\ = \frac{2 \times 2 + 5}{6} \\ = \frac{4 + 5}{6} \\ = \frac{9}{6}$

Now we are Subtracting $\frac{1}{9}$from $\frac{9}{6}$

So,

$\frac{9}{6} - \frac{1}{9} \\ = \frac{9 \times 3 - 2}{18} \\ = \frac{27 - 2}{18} \\ = \frac{25}{18}$

Therefore,

$\frac{2}{3} + \frac{5}{6} - \frac{1}{9} = \frac{25}{18} = 1 \frac{7}{18}$

This is a problem of Algebra.

Some important formulas of Algebra,

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

${a}^{2} - {b}^{2} = (a + b)(a - b)\\{a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab\\{a}^{2} + {b}^{2} = {(a - b)}^{2} + 2ab\\{a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )\\{a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$