Solve 15/9div21/3-(-3.25)*5/13

$$1 \frac { 5 } { 9 } \div 2 \frac { 1 } { 3 } - ( - 3.25 ) \times \frac { 5 } { 13 }$$

Evaluate

$$\frac{23}{12}\approx 1.916666667$$

Solution Steps

Divide \frac{1\times 9+5}{9} by \frac{2\times 3+1}{3} by multiplying \frac{1\times 9+5}{9} by the reciprocal of \frac{2\times 3+1}{3}.

$$\frac{\left(1\times 9+5\right)\times 3}{9\left(2\times 3+1\right)}-\left(-3.25\times \frac{5}{13}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{5+9}{3\left(1+2\times 3\right)}-\left(-3.25\times \frac{5}{13}\right)$$

Add 5 and 9 to get 14.

$$\frac{14}{3\left(1+2\times 3\right)}-\left(-3.25\times \frac{5}{13}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{14}{3\left(1+6\right)}-\left(-3.25\times \frac{5}{13}\right)$$

Add 1 and 6 to get 7.

$$\frac{14}{3\times 7}-\left(-3.25\times \frac{5}{13}\right)$$

Multiply 3 and 7 to get 21.

$$\frac{14}{21}-\left(-3.25\times \frac{5}{13}\right)$$

Reduce the fraction \frac{14}{21} to lowest terms by extracting and canceling out 7.

$$\frac{2}{3}-\left(-3.25\times \frac{5}{13}\right)$$

Convert decimal number -3.25 to fraction -\frac{325}{100}. Reduce the fraction -\frac{325}{100} to lowest terms by extracting and canceling out 25.

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

Multiply -\frac{13}{4} times \frac{5}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}-\frac{-13\times 5}{4\times 13}$$

Do the multiplications in the fraction \frac{-13\times 5}{4\times 13}.

$$\frac{2}{3}-\frac{-65}{52}$$

Reduce the fraction \frac{-65}{52} to lowest terms by extracting and canceling out 13.

$$\frac{2}{3}-\left(-\frac{5}{4}\right)$$

The opposite of -\frac{5}{4} is \frac{5}{4}.

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

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{8}{12}+\frac{15}{12}$$

Since \frac{8}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+15}{12}$$

Add 8 and 15 to get 23.

$$\frac{23}{12}$$

Factor

$$\frac{23}{3 \cdot 2 ^ {2}} = 1\frac{11}{12} = 1.9166666666666667$$