Solve 4*(3/2)^2+28*3/2+33/16*(frac{3{2})^2+24*3/2+36}

$$\frac { 4 \times ( \frac { 3 } { 2 } ) ^ { 2 } + 28 \times \frac { 3 } { 2 } + 33 } { 16 \times ( \frac { 3 } { 2 } ) ^ { 2 } + 24 \times \frac { 3 } { 2 } + 36 }$$

Evaluate

$$\frac{7}{9}\approx 0.777777778$$

Solution Steps

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

$$\frac{4\times \frac{9}{4}+28\times \frac{3}{2}+33}{16\times \left(\frac{3}{2}\right)^{2}+24\times \frac{3}{2}+36}$$

Cancel out 4 and 4.

$$\frac{9+28\times \frac{3}{2}+33}{16\times \left(\frac{3}{2}\right)^{2}+24\times \frac{3}{2}+36}$$

Express 28\times \frac{3}{2} as a single fraction.

$$\frac{9+\frac{28\times 3}{2}+33}{16\times \left(\frac{3}{2}\right)^{2}+24\times \frac{3}{2}+36}$$

Multiply 28 and 3 to get 84.

$$\frac{9+\frac{84}{2}+33}{16\times \left(\frac{3}{2}\right)^{2}+24\times \frac{3}{2}+36}$$

Divide 84 by 2 to get 42.

$$\frac{9+42+33}{16\times \left(\frac{3}{2}\right)^{2}+24\times \frac{3}{2}+36}$$

Add 9 and 42 to get 51.

$$\frac{51+33}{16\times \left(\frac{3}{2}\right)^{2}+24\times \frac{3}{2}+36}$$

Add 51 and 33 to get 84.

$$\frac{84}{16\times \left(\frac{3}{2}\right)^{2}+24\times \frac{3}{2}+36}$$

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

$$\frac{84}{16\times \frac{9}{4}+24\times \frac{3}{2}+36}$$

Express 16\times \frac{9}{4} as a single fraction.

$$\frac{84}{\frac{16\times 9}{4}+24\times \frac{3}{2}+36}$$

Multiply 16 and 9 to get 144.

$$\frac{84}{\frac{144}{4}+24\times \frac{3}{2}+36}$$

Divide 144 by 4 to get 36.

$$\frac{84}{36+24\times \frac{3}{2}+36}$$

Express 24\times \frac{3}{2} as a single fraction.

$$\frac{84}{36+\frac{24\times 3}{2}+36}$$

Multiply 24 and 3 to get 72.

$$\frac{84}{36+\frac{72}{2}+36}$$

Divide 72 by 2 to get 36.

$$\frac{84}{36+36+36}$$

Add 36 and 36 to get 72.

$$\frac{84}{72+36}$$

Add 72 and 36 to get 108.

$$\frac{84}{108}$$

Reduce the fraction \frac{84}{108} to lowest terms by extracting and canceling out 12.

$$\frac{7}{9}$$

Factor

$$\frac{7}{3 ^ {2}} = 0.7777777777777778$$