Solve 2/5+3/4+3/4:9/8=

$$\frac { 2 } { 5 } + \frac { 3 } { 4 } + \frac { 3 } { 4 } : \frac { 9 } { 8 } =$$

Evaluate

$$\frac{109}{60}\approx 1.816666667$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{2}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{8}{20}+\frac{15}{20}+\frac{\frac{3}{4}}{\frac{9}{8}}$$

Since \frac{8}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{8+15}{20}+\frac{\frac{3}{4}}{\frac{9}{8}}$$

Add 8 and 15 to get 23.

$$\frac{23}{20}+\frac{\frac{3}{4}}{\frac{9}{8}}$$

Divide \frac{3}{4} by \frac{9}{8} by multiplying \frac{3}{4} by the reciprocal of \frac{9}{8}.

$$\frac{23}{20}+\frac{3}{4}\times \frac{8}{9}$$

Multiply \frac{3}{4} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23}{20}+\frac{3\times 8}{4\times 9}$$

Do the multiplications in the fraction \frac{3\times 8}{4\times 9}.

$$\frac{23}{20}+\frac{24}{36}$$

Reduce the fraction \frac{24}{36} to lowest terms by extracting and canceling out 12.

$$\frac{23}{20}+\frac{2}{3}$$

Least common multiple of 20 and 3 is 60. Convert \frac{23}{20} and \frac{2}{3} to fractions with denominator 60.

$$\frac{69}{60}+\frac{40}{60}$$

Since \frac{69}{60} and \frac{40}{60} have the same denominator, add them by adding their numerators.

$$\frac{69+40}{60}$$

Add 69 and 40 to get 109.

$$\frac{109}{60}$$

Factor

$$\frac{109}{2 ^ {2} \cdot 3 \cdot 5} = 1\frac{49}{60} = 1.8166666666666667$$