Question

$\huge\bold{ᴘʀᴏᴠᴇ \: ᴛʜᴀᴛ }$
$9 \times \frac{2}{7} + \frac{2}{9} = \frac{176}{63}$
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Answer 1

Given:

• Equation: $\tt 9 \times \frac{2}{7} + \frac{2}{9} = \frac{176}{63}$

Exigency:

• To prove that the following condition is true.

Solution:

➱ Here,

• We have 3 fractions with different operators between them. Now, using bodmas rule let's evaluate the right hand side and check weather it equals the left hand side.

As we know that,

• BODMAS stands for

↝ Bracket

↝Of

↝Division

↝Multiplication

↝Addition

↝Subtraction

Now, let's start evaluating

$\longrightarrow \tt \: \frac{9}{1} \times \frac{2}{7} + \frac{2}{9} \\ \\ \\ \longrightarrow \tt \frac{18}{7} + \frac{2}{9} \: \: \: \: \: \: \: \: \:$

• Now, let's find the l.c.m of 7 and 9

$\tt \: 7 = { \boxed{ \pink{ \tt{ 7}}}} \times { \boxed{ \pink{ \tt{ 1}}}} \\ \\ 9 = { \boxed{ \pink{ \tt{ 9}}}} \times { \boxed{ \pink{ \tt{ 1}}}}$

• LCM = 9 × 7 = 63

$\longrightarrow \tt\frac{18 \times 9}{7 \times 9} + \frac{2 \times 7}{9 \times 7} \\ \\ \\ \longrightarrow \tt \frac{162}{63} + \frac{14}{63} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \frac{176}{63} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• L.H.S = R.H.S hence proved.!!