Solve 3/4left(1+7/3right)+10/13/frac{15{26}}-1

$$\frac{ 3 }{ 4 } \left( 1+ \frac{ 7 }{ 3 } \right) + \frac{ \frac{ 10 }{ 13 } }{ \frac{ 15 }{ 26 } } -1$$

Evaluate

$$\frac{17}{6}\approx 2.833333333$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{3}{4}\left(\frac{3}{3}+\frac{7}{3}\right)+\frac{\frac{10}{13}}{\frac{15}{26}}-1$$

Since \frac{3}{3} and \frac{7}{3} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}\times \frac{3+7}{3}+\frac{\frac{10}{13}}{\frac{15}{26}}-1$$

Add 3 and 7 to get 10.

$$\frac{3}{4}\times \frac{10}{3}+\frac{\frac{10}{13}}{\frac{15}{26}}-1$$

Multiply \frac{3}{4} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 10}{4\times 3}+\frac{\frac{10}{13}}{\frac{15}{26}}-1$$

Cancel out 3 in both numerator and denominator.

$$\frac{10}{4}+\frac{\frac{10}{13}}{\frac{15}{26}}-1$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}+\frac{\frac{10}{13}}{\frac{15}{26}}-1$$

Divide \frac{10}{13} by \frac{15}{26} by multiplying \frac{10}{13} by the reciprocal of \frac{15}{26}.

$$\frac{5}{2}+\frac{10}{13}\times \frac{26}{15}-1$$

Multiply \frac{10}{13} times \frac{26}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{2}+\frac{10\times 26}{13\times 15}-1$$

Do the multiplications in the fraction \frac{10\times 26}{13\times 15}.

$$\frac{5}{2}+\frac{260}{195}-1$$

Reduce the fraction \frac{260}{195} to lowest terms by extracting and canceling out 65.

$$\frac{5}{2}+\frac{4}{3}-1$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{15}{6}+\frac{8}{6}-1$$

Since \frac{15}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{15+8}{6}-1$$

Add 15 and 8 to get 23.

$$\frac{23}{6}-1$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{23}{6}-\frac{6}{6}$$

Since \frac{23}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23-6}{6}$$

Subtract 6 from 23 to get 17.

$$\frac{17}{6}$$

Factor

$$\frac{17}{2 \cdot 3} = 2\frac{5}{6} = 2.8333333333333335$$