Solve 13/16*(9/13*17-9/13)-(124/5-3frac{8}{13}-2frac{8}{13})

$$\frac{ 13 }{ 16 } \times ( \frac{ 9 }{ 13 } \times 17- \frac{ 9 }{ 13 } )-( 12 \frac { 4 } { 5 } - 3 \frac { 8 } { 13 } - 2 \frac { 8 } { 13 } )$$

Evaluate

$$\frac{158}{65}\approx 2.430769231$$

Solution Steps

Express \frac{9}{13}\times 17 as a single fraction.

$$\frac{13}{16}\left(\frac{9\times 17}{13}-\frac{9}{13}\right)-\left(\frac{12\times 5+4}{5}-\frac{3\times 13+8}{13}-\frac{2\times 13+8}{13}\right)$$

Multiply 9 and 17 to get 153.

$$\frac{13}{16}\left(\frac{153}{13}-\frac{9}{13}\right)-\left(\frac{12\times 5+4}{5}-\frac{3\times 13+8}{13}-\frac{2\times 13+8}{13}\right)$$

Since \frac{153}{13} and \frac{9}{13} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{16}\times \frac{153-9}{13}-\left(\frac{12\times 5+4}{5}-\frac{3\times 13+8}{13}-\frac{2\times 13+8}{13}\right)$$

Subtract 9 from 153 to get 144.

$$\frac{13}{16}\times \frac{144}{13}-\left(\frac{12\times 5+4}{5}-\frac{3\times 13+8}{13}-\frac{2\times 13+8}{13}\right)$$

Multiply \frac{13}{16} times \frac{144}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 144}{16\times 13}-\left(\frac{12\times 5+4}{5}-\frac{3\times 13+8}{13}-\frac{2\times 13+8}{13}\right)$$

Cancel out 13 in both numerator and denominator.

$$\frac{144}{16}-\left(\frac{12\times 5+4}{5}-\frac{3\times 13+8}{13}-\frac{2\times 13+8}{13}\right)$$

Divide 144 by 16 to get 9.

$$9-\left(\frac{12\times 5+4}{5}-\frac{3\times 13+8}{13}-\frac{2\times 13+8}{13}\right)$$

Multiply 12 and 5 to get 60.

$$9-\left(\frac{60+4}{5}-\frac{3\times 13+8}{13}-\frac{2\times 13+8}{13}\right)$$

Add 60 and 4 to get 64.

$$9-\left(\frac{64}{5}-\frac{3\times 13+8}{13}-\frac{2\times 13+8}{13}\right)$$

Multiply 3 and 13 to get 39.

$$9-\left(\frac{64}{5}-\frac{39+8}{13}-\frac{2\times 13+8}{13}\right)$$

Add 39 and 8 to get 47.

$$9-\left(\frac{64}{5}-\frac{47}{13}-\frac{2\times 13+8}{13}\right)$$

Least common multiple of 5 and 13 is 65. Convert \frac{64}{5} and \frac{47}{13} to fractions with denominator 65.

$$9-\left(\frac{832}{65}-\frac{235}{65}-\frac{2\times 13+8}{13}\right)$$

Since \frac{832}{65} and \frac{235}{65} have the same denominator, subtract them by subtracting their numerators.

$$9-\left(\frac{832-235}{65}-\frac{2\times 13+8}{13}\right)$$

Subtract 235 from 832 to get 597.

$$9-\left(\frac{597}{65}-\frac{2\times 13+8}{13}\right)$$

Multiply 2 and 13 to get 26.

$$9-\left(\frac{597}{65}-\frac{26+8}{13}\right)$$

Add 26 and 8 to get 34.

$$9-\left(\frac{597}{65}-\frac{34}{13}\right)$$

Least common multiple of 65 and 13 is 65. Convert \frac{597}{65} and \frac{34}{13} to fractions with denominator 65.

$$9-\left(\frac{597}{65}-\frac{170}{65}\right)$$

Since \frac{597}{65} and \frac{170}{65} have the same denominator, subtract them by subtracting their numerators.

$$9-\frac{597-170}{65}$$

Subtract 170 from 597 to get 427.

$$9-\frac{427}{65}$$

Convert 9 to fraction \frac{585}{65}.

$$\frac{585}{65}-\frac{427}{65}$$

Since \frac{585}{65} and \frac{427}{65} have the same denominator, subtract them by subtracting their numerators.

$$\frac{585-427}{65}$$

Subtract 427 from 585 to get 158.

$$\frac{158}{65}$$

Factor

$$\frac{2 \cdot 79}{5 \cdot 13} = 2\frac{28}{65} = 2.4307692307692306$$