Solve ( D) 10 65 . ((3 1/5 + 3/5) + 8/5)/(1 1/7 + \{6/7 - (1/7 + 1/5)\}) का सरलीकृत मान

Question

$$\frac { ( 3 \frac { 1 } { 5 } + \frac { 3 } { 5 } ) \div \frac { 8 } { 5 } } { 1 \frac { 1 } { 7 } \div \{ \frac { 6 } { 7 } - ( \frac { 1 } { 7 } \div \frac { 1 } { 5 } ) \} }$$

Evaluate

$\frac{19}{64}=0.296875$

Solution Steps

Divide $\frac{\frac{3\times 5+1}{5}+\frac{3}{5}}{\frac{8}{5}}$ by $\frac{\frac{1\times 7+1}{7}}{\frac{6}{7}-\frac{\frac{1}{7}}{\frac{1}{5}}}$ by multiplying $\frac{\frac{3\times 5+1}{5}+\frac{3}{5}}{\frac{8}{5}}$ by the reciprocal of $\frac{\frac{1\times 7+1}{7}}{\frac{6}{7}-\frac{\frac{1}{7}}{\frac{1}{5}}}$.

$$\frac{\left(\frac{3\times 5+1}{5}+\frac{3}{5}\right)\left(\frac{6}{7}-\frac{\frac{1}{7}}{\frac{1}{5}}\right)}{\frac{8}{5}\times \frac{1\times 7+1}{7}}$$

Multiply $3$ and $5$ to get $15$.

$$\frac{\left(\frac{15+1}{5}+\frac{3}{5}\right)\left(\frac{6}{7}-\frac{\frac{1}{7}}{\frac{1}{5}}\right)}{\frac{8}{5}\times \frac{1\times 7+1}{7}}$$

Add $15$ and $1$ to get $16$.

$$\frac{\left(\frac{16}{5}+\frac{3}{5}\right)\left(\frac{6}{7}-\frac{\frac{1}{7}}{\frac{1}{5}}\right)}{\frac{8}{5}\times \frac{1\times 7+1}{7}}$$

Since $\frac{16}{5}$ and $\frac{3}{5}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{16+3}{5}\left(\frac{6}{7}-\frac{\frac{1}{7}}{\frac{1}{5}}\right)}{\frac{8}{5}\times \frac{1\times 7+1}{7}}$$

Add $16$ and $3$ to get $19$.

$$\frac{\frac{19}{5}\left(\frac{6}{7}-\frac{\frac{1}{7}}{\frac{1}{5}}\right)}{\frac{8}{5}\times \frac{1\times 7+1}{7}}$$

Divide $\frac{1}{7}$ by $\frac{1}{5}$ by multiplying $\frac{1}{7}$ by the reciprocal of $\frac{1}{5}$.

$$\frac{\frac{19}{5}\left(\frac{6}{7}-\frac{1}{7}\times 5\right)}{\frac{8}{5}\times \frac{1\times 7+1}{7}}$$

Multiply $\frac{1}{7}$ and $5$ to get $\frac{5}{7}$.

$$\frac{\frac{19}{5}\left(\frac{6}{7}-\frac{5}{7}\right)}{\frac{8}{5}\times \frac{1\times 7+1}{7}}$$

Since $\frac{6}{7}$ and $\frac{5}{7}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{19}{5}\times \frac{6-5}{7}}{\frac{8}{5}\times \frac{1\times 7+1}{7}}$$

Subtract $5$ from $6$ to get $1$.

$$\frac{\frac{19}{5}\times \frac{1}{7}}{\frac{8}{5}\times \frac{1\times 7+1}{7}}$$

Multiply $\frac{19}{5}$ times $\frac{1}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{19\times 1}{5\times 7}}{\frac{8}{5}\times \frac{1\times 7+1}{7}}$$

Do the multiplications in the fraction $\frac{19\times 1}{5\times 7}$.

$$\frac{\frac{19}{35}}{\frac{8}{5}\times \frac{1\times 7+1}{7}}$$

Multiply $1$ and $7$ to get $7$.

$$\frac{\frac{19}{35}}{\frac{8}{5}\times \frac{7+1}{7}}$$

Add $7$ and $1$ to get $8$.

$$\frac{\frac{19}{35}}{\frac{8}{5}\times \frac{8}{7}}$$

Multiply $\frac{8}{5}$ times $\frac{8}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{19}{35}}{\frac{8\times 8}{5\times 7}}$$

Do the multiplications in the fraction $\frac{8\times 8}{5\times 7}$.

$$\frac{\frac{19}{35}}{\frac{64}{35}}$$

Divide $\frac{19}{35}$ by $\frac{64}{35}$ by multiplying $\frac{19}{35}$ by the reciprocal of $\frac{64}{35}$.

$$\frac{19}{35}\times \frac{35}{64}$$

Multiply $\frac{19}{35}$ times $\frac{35}{64}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\times 35}{35\times 64}$$

Cancel out $35$ in both numerator and denominator.

$$\frac{19}{64}$$

Show Solution

Factor

$\frac{19}{2 ^ {6}} = 0.296875$

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