Solve 121/99/(4-frac{1{3})}+sqrt{55/99*5}

$$\frac { \frac { 121 } { 99 } } { ( 4 - \frac { 1 } { 3 } ) } + \sqrt { \frac { 55 } { 99 } \cdot 5 }$$

Evaluate

$$2$$

Solution Steps

Reduce the fraction \frac{121}{99} to lowest terms by extracting and canceling out 11.

$$\frac{\frac{11}{9}}{4-\frac{1}{3}}+\sqrt{\frac{55}{99}\times 5}$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{\frac{11}{9}}{\frac{12}{3}-\frac{1}{3}}+\sqrt{\frac{55}{99}\times 5}$$

Since \frac{12}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{9}}{\frac{12-1}{3}}+\sqrt{\frac{55}{99}\times 5}$$

Subtract 1 from 12 to get 11.

$$\frac{\frac{11}{9}}{\frac{11}{3}}+\sqrt{\frac{55}{99}\times 5}$$

Divide \frac{11}{9} by \frac{11}{3} by multiplying \frac{11}{9} by the reciprocal of \frac{11}{3}.

$$\frac{11}{9}\times \frac{3}{11}+\sqrt{\frac{55}{99}\times 5}$$

Multiply \frac{11}{9} times \frac{3}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 3}{9\times 11}+\sqrt{\frac{55}{99}\times 5}$$

Cancel out 11 in both numerator and denominator.

$$\frac{3}{9}+\sqrt{\frac{55}{99}\times 5}$$

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

$$\frac{1}{3}+\sqrt{\frac{55}{99}\times 5}$$

Reduce the fraction \frac{55}{99} to lowest terms by extracting and canceling out 11.

$$\frac{1}{3}+\sqrt{\frac{5}{9}\times 5}$$

Express \frac{5}{9}\times 5 as a single fraction.

$$\frac{1}{3}+\sqrt{\frac{5\times 5}{9}}$$

Multiply 5 and 5 to get 25.

$$\frac{1}{3}+\sqrt{\frac{25}{9}}$$

Rewrite the square root of the division \frac{25}{9} as the division of square roots \frac{\sqrt{25}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{1}{3}+\frac{5}{3}$$

Since \frac{1}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$\frac{1+5}{3}$$

Add 1 and 5 to get 6.

$$\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$2$$

Factor

$$2$$