Question

find using property
1/7*2/9-3/14*1/9+2/9*1/14

Answer 1

1/7×2/9-3/14×2/9+2/9×1/14
=2/9(1/7-3/14+1/14)
=2/9{(2-3+1)/14}
=2/9×0/14
=0

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Answer 2

Answer:

$\frac{1}{7}\times \frac{2}{9}- \frac{3}{14}\times \frac{1}{9}+ \frac{2}{9}\times \frac{1}{14}=\frac{1}{42}$

Step-by-step explanation:

Given : Expression  $\frac{1}{7}\times \frac{2}{9}- \frac{3}{14}\times \frac{1}{9}+ \frac{2}{9}\times \frac{1}{14}$

To find : Solve the expression using identities?

Solution :

Expression  $\frac{1}{7}\times \frac{2}{9}- \frac{3}{14}\times \frac{1}{9}+ \frac{2}{9}\times \frac{1}{14}$

Applying distributive identity, $ab+ac=a(b+c)$

Taking $\frac{1}{9}$ common from whole expression,

$=\frac{1}{9}[\frac{2}{7}- \frac{3}{14}+\frac{2}{14}]$

Taking LCM,

$=\frac{1}{9}[\frac{4-3+2}{14}]$

$=\frac{1}{9}\times \frac{3}{14}$  

$=\frac{1}{3\times14}$

$=\frac{1}{42}$    

Therefore, $\frac{1}{7}\times \frac{2}{9}- \frac{3}{14}\times \frac{1}{9}+ \frac{2}{9}\times \frac{1}{14}=\frac{1}{42}$