Solve 5(3/2)^2+40(3/2)

$$5 ( \frac { 3 } { 2 } ) ^ { 2 } + 40 ( \frac { 3 } { 2 } )$$

Evaluate

$$\frac{285}{4}=71.25$$

Solution Steps

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$5\times \frac{9}{4}+40\times \frac{3}{2}$$

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

$$\frac{5\times 9}{4}+40\times \frac{3}{2}$$

Multiply 5 and 9 to get 45.

$$\frac{45}{4}+40\times \frac{3}{2}$$

Express 40\times \frac{3}{2} as a single fraction.

$$\frac{45}{4}+\frac{40\times 3}{2}$$

Multiply 40 and 3 to get 120.

$$\frac{45}{4}+\frac{120}{2}$$

Divide 120 by 2 to get 60.

$$\frac{45}{4}+60$$

Convert 60 to fraction \frac{240}{4}.

$$\frac{45}{4}+\frac{240}{4}$$

Since \frac{45}{4} and \frac{240}{4} have the same denominator, add them by adding their numerators.

$$\frac{45+240}{4}$$

Add 45 and 240 to get 285.

$$\frac{285}{4}$$

Factor

$$\frac{3 \cdot 5 \cdot 19}{2 ^ {2}} = 71\frac{1}{4} = 71.25$$