Solve (3)/(2)\times(9)/(4)-((1)/(3))^(3)((7)/(6))^(1)+(5)/(2) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{ 3 }{ 2 } \times \frac{ 9 }{ 4 } - { \left( \frac{ 1 }{ 3 } \right) }^{ 3 } { \left( \frac{ 7 }{ 6 } \right) }^{ 1 } + \frac{ 5 }{ 2 }$$

Evaluate

$\frac{3779}{648}\approx 5.831790123$

Solution Steps

Multiply $\frac{3}{2}$ times $\frac{9}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 9}{2\times 4}-\left(\frac{1}{3}\right)^{3}\times \left(\frac{7}{6}\right)^{1}+\frac{5}{2}$$

Do the multiplications in the fraction $\frac{3\times 9}{2\times 4}$.

$$\frac{27}{8}-\left(\frac{1}{3}\right)^{3}\times \left(\frac{7}{6}\right)^{1}+\frac{5}{2}$$

Calculate $\frac{1}{3}$ to the power of $3$ and get $\frac{1}{27}$.

$$\frac{27}{8}-\frac{1}{27}\times \left(\frac{7}{6}\right)^{1}+\frac{5}{2}$$

Calculate $\frac{7}{6}$ to the power of $1$ and get $\frac{7}{6}$.

$$\frac{27}{8}-\frac{1}{27}\times \frac{7}{6}+\frac{5}{2}$$

Multiply $\frac{1}{27}$ times $\frac{7}{6}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{27}{8}-\frac{1\times 7}{27\times 6}+\frac{5}{2}$$

Do the multiplications in the fraction $\frac{1\times 7}{27\times 6}$.

$$\frac{27}{8}-\frac{7}{162}+\frac{5}{2}$$

Least common multiple of $8$ and $162$ is $648$. Convert $\frac{27}{8}$ and $\frac{7}{162}$ to fractions with denominator $648$.

$$\frac{2187}{648}-\frac{28}{648}+\frac{5}{2}$$

Since $\frac{2187}{648}$ and $\frac{28}{648}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{2187-28}{648}+\frac{5}{2}$$

Subtract $28$ from $2187$ to get $2159$.

$$\frac{2159}{648}+\frac{5}{2}$$

Least common multiple of $648$ and $2$ is $648$. Convert $\frac{2159}{648}$ and $\frac{5}{2}$ to fractions with denominator $648$.

$$\frac{2159}{648}+\frac{1620}{648}$$

Since $\frac{2159}{648}$ and $\frac{1620}{648}$ have the same denominator, add them by adding their numerators.

$$\frac{2159+1620}{648}$$

Add $2159$ and $1620$ to get $3779$.

$$\frac{3779}{648}$$

Factor

$\frac{3779}{2 ^ {3} \cdot 3 ^ {4}} = 5\frac{539}{648} = 5.83179012345679$