Solve 3/4+(4/5div51/3)

$$\frac { 3 } { 4 } + ( \frac { 4 } { 5 } \div 5 \frac { 1 } { 3 } )$$

Evaluate

$$\frac{9}{10}=0.9$$

Solution Steps

Divide \frac{4}{5} by \frac{5\times 3+1}{3} by multiplying \frac{4}{5} by the reciprocal of \frac{5\times 3+1}{3}.

$$\frac{3}{4}+\frac{4\times 3}{5\left(5\times 3+1\right)}$$

Multiply 4 and 3 to get 12.

$$\frac{3}{4}+\frac{12}{5\left(5\times 3+1\right)}$$

Multiply 5 and 3 to get 15.

$$\frac{3}{4}+\frac{12}{5\left(15+1\right)}$$

Add 15 and 1 to get 16.

$$\frac{3}{4}+\frac{12}{5\times 16}$$

Multiply 5 and 16 to get 80.

$$\frac{3}{4}+\frac{12}{80}$$

Reduce the fraction \frac{12}{80} to lowest terms by extracting and canceling out 4.

$$\frac{3}{4}+\frac{3}{20}$$

Least common multiple of 4 and 20 is 20. Convert \frac{3}{4} and \frac{3}{20} to fractions with denominator 20.

$$\frac{15}{20}+\frac{3}{20}$$

Since \frac{15}{20} and \frac{3}{20} have the same denominator, add them by adding their numerators.

$$\frac{15+3}{20}$$

Add 15 and 3 to get 18.

$$\frac{18}{20}$$

Reduce the fraction \frac{18}{20} to lowest terms by extracting and canceling out 2.

$$\frac{9}{10}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 5} = 0.9$$