Solve (225)-3/2\times(243)-3/5/(81)-5/4\times(27)-4/3 | 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

$$(225)-3/2 \times (243)-3/5/(81)-5/4 \times (27)-4/3$$

Evaluate

$-\frac{94279}{540}\approx -174.590740741$

Solution Steps

Express $\frac{3}{2}\times 243$ as a single fraction.

$$225-\frac{3\times 243}{2}-\frac{\frac{3}{5}}{81}-\frac{5}{4}\times 27-\frac{4}{3}$$

Multiply $3$ and $243$ to get $729$.

$$225-\frac{729}{2}-\frac{\frac{3}{5}}{81}-\frac{5}{4}\times 27-\frac{4}{3}$$

Convert $225$ to fraction $\frac{450}{2}$.

$$\frac{450}{2}-\frac{729}{2}-\frac{\frac{3}{5}}{81}-\frac{5}{4}\times 27-\frac{4}{3}$$

Since $\frac{450}{2}$ and $\frac{729}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{450-729}{2}-\frac{\frac{3}{5}}{81}-\frac{5}{4}\times 27-\frac{4}{3}$$

Subtract $729$ from $450$ to get $-279$.

$$-\frac{279}{2}-\frac{\frac{3}{5}}{81}-\frac{5}{4}\times 27-\frac{4}{3}$$

Express $\frac{\frac{3}{5}}{81}$ as a single fraction.

$$-\frac{279}{2}-\frac{3}{5\times 81}-\frac{5}{4}\times 27-\frac{4}{3}$$

Multiply $5$ and $81$ to get $405$.

$$-\frac{279}{2}-\frac{3}{405}-\frac{5}{4}\times 27-\frac{4}{3}$$

Reduce the fraction $\frac{3}{405}$ to lowest terms by extracting and canceling out $3$.

$$-\frac{279}{2}-\frac{1}{135}-\frac{5}{4}\times 27-\frac{4}{3}$$

Least common multiple of $2$ and $135$ is $270$. Convert $-\frac{279}{2}$ and $\frac{1}{135}$ to fractions with denominator $270$.

$$-\frac{37665}{270}-\frac{2}{270}-\frac{5}{4}\times 27-\frac{4}{3}$$

Since $-\frac{37665}{270}$ and $\frac{2}{270}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-37665-2}{270}-\frac{5}{4}\times 27-\frac{4}{3}$$

Subtract $2$ from $-37665$ to get $-37667$.

$$-\frac{37667}{270}-\frac{5}{4}\times 27-\frac{4}{3}$$

Express $\frac{5}{4}\times 27$ as a single fraction.

$$-\frac{37667}{270}-\frac{5\times 27}{4}-\frac{4}{3}$$

Multiply $5$ and $27$ to get $135$.

$$-\frac{37667}{270}-\frac{135}{4}-\frac{4}{3}$$

Least common multiple of $270$ and $4$ is $540$. Convert $-\frac{37667}{270}$ and $\frac{135}{4}$ to fractions with denominator $540$.

$$-\frac{75334}{540}-\frac{18225}{540}-\frac{4}{3}$$

Since $-\frac{75334}{540}$ and $\frac{18225}{540}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-75334-18225}{540}-\frac{4}{3}$$

Subtract $18225$ from $-75334$ to get $-93559$.

$$-\frac{93559}{540}-\frac{4}{3}$$

Least common multiple of $540$ and $3$ is $540$. Convert $-\frac{93559}{540}$ and $\frac{4}{3}$ to fractions with denominator $540$.

$$-\frac{93559}{540}-\frac{720}{540}$$

Since $-\frac{93559}{540}$ and $\frac{720}{540}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-93559-720}{540}$$

Subtract $720$ from $-93559$ to get $-94279$.

$$-\frac{94279}{540}$$

Factor

$-\frac{94279}{540} = -174\frac{319}{540} = -174.59074074074073$