Solve (5p/2q)(p/3)+p^2/8q/4p+frac{p{12}}

$$\frac { ( \frac { 5 p } { 2 q } ) ( \frac { p } { 3 } ) + \frac { p ^ { 2 } } { 8 q } } { 4 p + \frac { p } { 12 } }$$

Evaluate

$$\frac{23p}{98q}$$

Short Solution Steps

Multiply \frac{5p}{2q} times \frac{p}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5pp}{2q\times 3}+\frac{p^{2}}{8q}}{4p+\frac{p}{12}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2q\times 3 and 8q is 24q. Multiply \frac{5pp}{2q\times 3} times \frac{4}{4}. Multiply \frac{p^{2}}{8q} times \frac{3}{3}.

$$\frac{\frac{4\times 5pp}{24q}+\frac{3p^{2}}{24q}}{4p+\frac{p}{12}}$$

Since \frac{4\times 5pp}{24q} and \frac{3p^{2}}{24q} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4\times 5pp+3p^{2}}{24q}}{4p+\frac{p}{12}}$$

Do the multiplications in 4\times 5pp+3p^{2}.

$$\frac{\frac{20p^{2}+3p^{2}}{24q}}{4p+\frac{p}{12}}$$

Combine like terms in 20p^{2}+3p^{2}.

$$\frac{\frac{23p^{2}}{24q}}{4p+\frac{p}{12}}$$

Combine 4p and \frac{p}{12} to get \frac{49}{12}p.

$$\frac{\frac{23p^{2}}{24q}}{\frac{49}{12}p}$$

Express \frac{\frac{23p^{2}}{24q}}{\frac{49}{12}p} as a single fraction.

$$\frac{23p^{2}}{24q\times \frac{49}{12}p}$$

Cancel out p in both numerator and denominator.

$$\frac{23p}{\frac{49}{12}\times 24q}$$

Multiply \frac{49}{12} and 24 to get 98.

$$\frac{23p}{98q}$$

Expand

$$\frac{23p}{98q}$$

Short Solution Steps

Multiply \frac{5p}{2q} times \frac{p}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5pp}{2q\times 3}+\frac{p^{2}}{8q}}{4p+\frac{p}{12}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2q\times 3 and 8q is 24q. Multiply \frac{5pp}{2q\times 3} times \frac{4}{4}. Multiply \frac{p^{2}}{8q} times \frac{3}{3}.

$$\frac{\frac{4\times 5pp}{24q}+\frac{3p^{2}}{24q}}{4p+\frac{p}{12}}$$

Since \frac{4\times 5pp}{24q} and \frac{3p^{2}}{24q} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4\times 5pp+3p^{2}}{24q}}{4p+\frac{p}{12}}$$

Do the multiplications in 4\times 5pp+3p^{2}.

$$\frac{\frac{20p^{2}+3p^{2}}{24q}}{4p+\frac{p}{12}}$$

Combine like terms in 20p^{2}+3p^{2}.

$$\frac{\frac{23p^{2}}{24q}}{4p+\frac{p}{12}}$$

Combine 4p and \frac{p}{12} to get \frac{49}{12}p.

$$\frac{\frac{23p^{2}}{24q}}{\frac{49}{12}p}$$

Express \frac{\frac{23p^{2}}{24q}}{\frac{49}{12}p} as a single fraction.

$$\frac{23p^{2}}{24q\times \frac{49}{12}p}$$

Cancel out p in both numerator and denominator.

$$\frac{23p}{\frac{49}{12}\times 24q}$$

Multiply \frac{49}{12} and 24 to get 98.

$$\frac{23p}{98q}$$