Solve (3/4+6/9+182/90):39/9=

$$( \frac { 3 } { 4 } + \frac { 6 } { 9 } + \frac { 182 } { 90 } ) : \frac { 39 } { 9 } =$$

Evaluate

$$\frac{619}{780}\approx 0.793589744$$

Solution Steps

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{3}{4}+\frac{2}{3}+\frac{182}{90}}{\frac{39}{9}}$$

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

$$\frac{\frac{9}{12}+\frac{8}{12}+\frac{182}{90}}{\frac{39}{9}}$$

Since \frac{9}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+8}{12}+\frac{182}{90}}{\frac{39}{9}}$$

Add 9 and 8 to get 17.

$$\frac{\frac{17}{12}+\frac{182}{90}}{\frac{39}{9}}$$

Reduce the fraction \frac{182}{90} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{17}{12}+\frac{91}{45}}{\frac{39}{9}}$$

Least common multiple of 12 and 45 is 180. Convert \frac{17}{12} and \frac{91}{45} to fractions with denominator 180.

$$\frac{\frac{255}{180}+\frac{364}{180}}{\frac{39}{9}}$$

Since \frac{255}{180} and \frac{364}{180} have the same denominator, add them by adding their numerators.

$$\frac{\frac{255+364}{180}}{\frac{39}{9}}$$

Add 255 and 364 to get 619.

$$\frac{\frac{619}{180}}{\frac{39}{9}}$$

Reduce the fraction \frac{39}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{619}{180}}{\frac{13}{3}}$$

Divide \frac{619}{180} by \frac{13}{3} by multiplying \frac{619}{180} by the reciprocal of \frac{13}{3}.

$$\frac{619}{180}\times \frac{3}{13}$$

Multiply \frac{619}{180} times \frac{3}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{619\times 3}{180\times 13}$$

Do the multiplications in the fraction \frac{619\times 3}{180\times 13}.

$$\frac{1857}{2340}$$

Reduce the fraction \frac{1857}{2340} to lowest terms by extracting and canceling out 3.

$$\frac{619}{780}$$

Factor

$$\frac{619}{2 ^ {2} \cdot 3 \cdot 5 \cdot 13} = 0.7935897435897435$$