Solve 1/2+1/3*sqrt{16/9}-1/12+sqrt{frac{25}{16}}*frac{8}{3}=

$$\frac { 1 } { 2 } + \frac { 1 } { 3 } \cdot \sqrt { \frac { 16 } { 9 } } - \frac { 1 } { 12 } + \sqrt { \frac { 25 } { 16 } } \cdot \frac { 8 } { 3 } =$$

Evaluate

$$\frac{151}{36}\approx 4.194444444$$

Solution Steps

Rewrite the square root of the division \frac{16}{9} as the division of square roots \frac{\sqrt{16}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{1}{2}+\frac{1}{3}\times \frac{4}{3}-\frac{1}{12}+\sqrt{\frac{25}{16}}\times \frac{8}{3}$$

Multiply \frac{1}{3} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{1\times 4}{3\times 3}-\frac{1}{12}+\sqrt{\frac{25}{16}}\times \frac{8}{3}$$

Do the multiplications in the fraction \frac{1\times 4}{3\times 3}.

$$\frac{1}{2}+\frac{4}{9}-\frac{1}{12}+\sqrt{\frac{25}{16}}\times \frac{8}{3}$$

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{4}{9} to fractions with denominator 18.

$$\frac{9}{18}+\frac{8}{18}-\frac{1}{12}+\sqrt{\frac{25}{16}}\times \frac{8}{3}$$

Since \frac{9}{18} and \frac{8}{18} have the same denominator, add them by adding their numerators.

$$\frac{9+8}{18}-\frac{1}{12}+\sqrt{\frac{25}{16}}\times \frac{8}{3}$$

Add 9 and 8 to get 17.

$$\frac{17}{18}-\frac{1}{12}+\sqrt{\frac{25}{16}}\times \frac{8}{3}$$

Least common multiple of 18 and 12 is 36. Convert \frac{17}{18} and \frac{1}{12} to fractions with denominator 36.

$$\frac{34}{36}-\frac{3}{36}+\sqrt{\frac{25}{16}}\times \frac{8}{3}$$

Since \frac{34}{36} and \frac{3}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{34-3}{36}+\sqrt{\frac{25}{16}}\times \frac{8}{3}$$

Subtract 3 from 34 to get 31.

$$\frac{31}{36}+\sqrt{\frac{25}{16}}\times \frac{8}{3}$$

Rewrite the square root of the division \frac{25}{16} as the division of square roots \frac{\sqrt{25}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{31}{36}+\frac{5}{4}\times \frac{8}{3}$$

Multiply \frac{5}{4} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31}{36}+\frac{5\times 8}{4\times 3}$$

Do the multiplications in the fraction \frac{5\times 8}{4\times 3}.

$$\frac{31}{36}+\frac{40}{12}$$

Reduce the fraction \frac{40}{12} to lowest terms by extracting and canceling out 4.

$$\frac{31}{36}+\frac{10}{3}$$

Least common multiple of 36 and 3 is 36. Convert \frac{31}{36} and \frac{10}{3} to fractions with denominator 36.

$$\frac{31}{36}+\frac{120}{36}$$

Since \frac{31}{36} and \frac{120}{36} have the same denominator, add them by adding their numerators.

$$\frac{31+120}{36}$$

Add 31 and 120 to get 151.

$$\frac{151}{36}$$

Factor

$$\frac{151}{2 ^ {2} \cdot 3 ^ {2}} = 4\frac{7}{36} = 4.194444444444445$$