Solve (2a/3b)(4b/5)+a/2b+frac{b{4}}

$$\frac { ( \frac { 2 a } { 3 b } ) ( \frac { 4 b } { 5 } ) + a } { 2 b + \frac { b } { 4 } }$$

Evaluate

$$\frac{92a}{135b}$$

Short Solution Steps

Multiply \frac{2a}{3b} times \frac{4b}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2a\times 4b}{3b\times 5}+a}{2b+\frac{b}{4}}$$

Cancel out b in both numerator and denominator.

$$\frac{\frac{2\times 4a}{3\times 5}+a}{2b+\frac{b}{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{3\times 5}{3\times 5}.

$$\frac{\frac{2\times 4a}{3\times 5}+\frac{a\times 3\times 5}{3\times 5}}{2b+\frac{b}{4}}$$

Since \frac{2\times 4a}{3\times 5} and \frac{a\times 3\times 5}{3\times 5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2\times 4a+a\times 3\times 5}{3\times 5}}{2b+\frac{b}{4}}$$

Do the multiplications in 2\times 4a+a\times 3\times 5.

$$\frac{\frac{8a+15a}{3\times 5}}{2b+\frac{b}{4}}$$

Combine like terms in 8a+15a.

$$\frac{\frac{23a}{3\times 5}}{2b+\frac{b}{4}}$$

Combine 2b and \frac{b}{4} to get \frac{9}{4}b.

$$\frac{\frac{23a}{3\times 5}}{\frac{9}{4}b}$$

Express \frac{\frac{23a}{3\times 5}}{\frac{9}{4}b} as a single fraction.

$$\frac{23a}{3\times 5\times \frac{9}{4}b}$$

Multiply 3 and 5 to get 15.

$$\frac{23a}{15\times \frac{9}{4}b}$$

Express 15\times \frac{9}{4} as a single fraction.

$$\frac{23a}{\frac{15\times 9}{4}b}$$

Multiply 15 and 9 to get 135.

$$\frac{23a}{\frac{135}{4}b}$$

Expand

$$\frac{92a}{135b}$$

Short Solution Steps

Multiply \frac{2a}{3b} times \frac{4b}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2a\times 4b}{3b\times 5}+a}{2b+\frac{b}{4}}$$

Cancel out b in both numerator and denominator.

$$\frac{\frac{2\times 4a}{3\times 5}+a}{2b+\frac{b}{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{3\times 5}{3\times 5}.

$$\frac{\frac{2\times 4a}{3\times 5}+\frac{a\times 3\times 5}{3\times 5}}{2b+\frac{b}{4}}$$

Since \frac{2\times 4a}{3\times 5} and \frac{a\times 3\times 5}{3\times 5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2\times 4a+a\times 3\times 5}{3\times 5}}{2b+\frac{b}{4}}$$

Do the multiplications in 2\times 4a+a\times 3\times 5.

$$\frac{\frac{8a+15a}{3\times 5}}{2b+\frac{b}{4}}$$

Combine like terms in 8a+15a.

$$\frac{\frac{23a}{3\times 5}}{2b+\frac{b}{4}}$$

Combine 2b and \frac{b}{4} to get \frac{9}{4}b.

$$\frac{\frac{23a}{3\times 5}}{\frac{9}{4}b}$$

Express \frac{\frac{23a}{3\times 5}}{\frac{9}{4}b} as a single fraction.

$$\frac{23a}{3\times 5\times \frac{9}{4}b}$$

Multiply 3 and 5 to get 15.

$$\frac{23a}{15\times \frac{9}{4}b}$$

Express 15\times \frac{9}{4} as a single fraction.

$$\frac{23a}{\frac{15\times 9}{4}b}$$

Multiply 15 and 9 to get 135.

$$\frac{23a}{\frac{135}{4}b}$$