Solve - 8/9 * (39/18 + 13/- 36) = (- 8/9 * 39/18) + 13/- 36 | Equatix - Math Solver

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Question

$$\frac{-8}{9}\times(\frac{39}{18}+\frac{13}{-36})=(\frac{-8}{9}\times\frac{39}{18})+\frac{13}{-36}$$

Verify

$\text{false}$

Solution Steps

Fraction $\frac{-8}{9}$ can be rewritten as $-\frac{8}{9}$ by extracting the negative sign.

$$-\frac{8}{9}\left(\frac{39}{18}+\frac{13}{-36}\right)=\frac{-8}{9}\times \frac{39}{18}+\frac{13}{-36}$$

Reduce the fraction $\frac{39}{18}$ to lowest terms by extracting and canceling out $3$.

$$-\frac{8}{9}\left(\frac{13}{6}+\frac{13}{-36}\right)=\frac{-8}{9}\times \frac{39}{18}+\frac{13}{-36}$$

Fraction $\frac{13}{-36}$ can be rewritten as $-\frac{13}{36}$ by extracting the negative sign.

$$-\frac{8}{9}\left(\frac{13}{6}-\frac{13}{36}\right)=\frac{-8}{9}\times \frac{39}{18}+\frac{13}{-36}$$

Least common multiple of $6$ and $36$ is $36$. Convert $\frac{13}{6}$ and $\frac{13}{36}$ to fractions with denominator $36$.

$$-\frac{8}{9}\left(\frac{78}{36}-\frac{13}{36}\right)=\frac{-8}{9}\times \frac{39}{18}+\frac{13}{-36}$$

Since $\frac{78}{36}$ and $\frac{13}{36}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{8}{9}\times \frac{78-13}{36}=\frac{-8}{9}\times \frac{39}{18}+\frac{13}{-36}$$

Subtract $13$ from $78$ to get $65$.

$$-\frac{8}{9}\times \frac{65}{36}=\frac{-8}{9}\times \frac{39}{18}+\frac{13}{-36}$$

Multiply $-\frac{8}{9}$ times $\frac{65}{36}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-8\times 65}{9\times 36}=\frac{-8}{9}\times \frac{39}{18}+\frac{13}{-36}$$

Do the multiplications in the fraction $\frac{-8\times 65}{9\times 36}$.

$$\frac{-520}{324}=\frac{-8}{9}\times \frac{39}{18}+\frac{13}{-36}$$

Reduce the fraction $\frac{-520}{324}$ to lowest terms by extracting and canceling out $4$.

$$-\frac{130}{81}=\frac{-8}{9}\times \frac{39}{18}+\frac{13}{-36}$$

Fraction $\frac{-8}{9}$ can be rewritten as $-\frac{8}{9}$ by extracting the negative sign.

$$-\frac{130}{81}=-\frac{8}{9}\times \frac{39}{18}+\frac{13}{-36}$$

Reduce the fraction $\frac{39}{18}$ to lowest terms by extracting and canceling out $3$.

$$-\frac{130}{81}=-\frac{8}{9}\times \frac{13}{6}+\frac{13}{-36}$$

Multiply $-\frac{8}{9}$ times $\frac{13}{6}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{130}{81}=\frac{-8\times 13}{9\times 6}+\frac{13}{-36}$$

Do the multiplications in the fraction $\frac{-8\times 13}{9\times 6}$.

$$-\frac{130}{81}=\frac{-104}{54}+\frac{13}{-36}$$

Reduce the fraction $\frac{-104}{54}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{130}{81}=-\frac{52}{27}+\frac{13}{-36}$$

Fraction $\frac{13}{-36}$ can be rewritten as $-\frac{13}{36}$ by extracting the negative sign.

$$-\frac{130}{81}=-\frac{52}{27}-\frac{13}{36}$$

Least common multiple of $27$ and $36$ is $108$. Convert $-\frac{52}{27}$ and $\frac{13}{36}$ to fractions with denominator $108$.

$$-\frac{130}{81}=-\frac{208}{108}-\frac{39}{108}$$

Since $-\frac{208}{108}$ and $\frac{39}{108}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{130}{81}=\frac{-208-39}{108}$$

Subtract $39$ from $-208$ to get $-247$.

$$-\frac{130}{81}=-\frac{247}{108}$$

Least common multiple of $81$ and $108$ is $324$. Convert $-\frac{130}{81}$ and $-\frac{247}{108}$ to fractions with denominator $324$.

$$-\frac{520}{324}=-\frac{741}{324}$$

Compare $-\frac{520}{324}$ and $-\frac{741}{324}$.

$$\text{false}$$