Solve Date: - 3/4 + [- 5/6 + 7/8) = (3/9 - 5/6] + 7/3 | 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

$$\frac { - 3 } { 4 } + [ \frac { - 5 } { 6 } + \frac { 7 } { 3 } ) = ( \frac { 3 } { 9 } + \frac { - 5 } { 6 } ) + \frac { 7 } { 3 }$$

Verify

$\text{false}$

Solution Steps

Fraction $\frac{-3}{4}$ can be rewritten as $-\frac{3}{4}$ by extracting the negative sign.

$$-\frac{3}{4}+\frac{-5}{6}+\frac{7}{3}=\frac{3}{9}+\frac{-5}{6}+\frac{7}{3}$$

Fraction $\frac{-5}{6}$ can be rewritten as $-\frac{5}{6}$ by extracting the negative sign.

$$-\frac{3}{4}-\frac{5}{6}+\frac{7}{3}=\frac{3}{9}+\frac{-5}{6}+\frac{7}{3}$$

Least common multiple of $4$ and $6$ is $12$. Convert $-\frac{3}{4}$ and $\frac{5}{6}$ to fractions with denominator $12$.

$$-\frac{9}{12}-\frac{10}{12}+\frac{7}{3}=\frac{3}{9}+\frac{-5}{6}+\frac{7}{3}$$

Since $-\frac{9}{12}$ and $\frac{10}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-10}{12}+\frac{7}{3}=\frac{3}{9}+\frac{-5}{6}+\frac{7}{3}$$

Subtract $10$ from $-9$ to get $-19$.

$$-\frac{19}{12}+\frac{7}{3}=\frac{3}{9}+\frac{-5}{6}+\frac{7}{3}$$

Least common multiple of $12$ and $3$ is $12$. Convert $-\frac{19}{12}$ and $\frac{7}{3}$ to fractions with denominator $12$.

$$-\frac{19}{12}+\frac{28}{12}=\frac{3}{9}+\frac{-5}{6}+\frac{7}{3}$$

Since $-\frac{19}{12}$ and $\frac{28}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{-19+28}{12}=\frac{3}{9}+\frac{-5}{6}+\frac{7}{3}$$

Add $-19$ and $28$ to get $9$.

$$\frac{9}{12}=\frac{3}{9}+\frac{-5}{6}+\frac{7}{3}$$

Reduce the fraction $\frac{9}{12}$ to lowest terms by extracting and canceling out $3$.

$$\frac{3}{4}=\frac{3}{9}+\frac{-5}{6}+\frac{7}{3}$$

Reduce the fraction $\frac{3}{9}$ to lowest terms by extracting and canceling out $3$.

$$\frac{3}{4}=\frac{1}{3}+\frac{-5}{6}+\frac{7}{3}$$

Fraction $\frac{-5}{6}$ can be rewritten as $-\frac{5}{6}$ by extracting the negative sign.

$$\frac{3}{4}=\frac{1}{3}-\frac{5}{6}+\frac{7}{3}$$

Least common multiple of $3$ and $6$ is $6$. Convert $\frac{1}{3}$ and $\frac{5}{6}$ to fractions with denominator $6$.

$$\frac{3}{4}=\frac{2}{6}-\frac{5}{6}+\frac{7}{3}$$

Since $\frac{2}{6}$ and $\frac{5}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}=\frac{2-5}{6}+\frac{7}{3}$$

Subtract $5$ from $2$ to get $-3$.

$$\frac{3}{4}=\frac{-3}{6}+\frac{7}{3}$$

Reduce the fraction $\frac{-3}{6}$ to lowest terms by extracting and canceling out $3$.

$$\frac{3}{4}=-\frac{1}{2}+\frac{7}{3}$$

Least common multiple of $2$ and $3$ is $6$. Convert $-\frac{1}{2}$ and $\frac{7}{3}$ to fractions with denominator $6$.

$$\frac{3}{4}=-\frac{3}{6}+\frac{14}{6}$$

Since $-\frac{3}{6}$ and $\frac{14}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{3}{4}=\frac{-3+14}{6}$$

Add $-3$ and $14$ to get $11$.

$$\frac{3}{4}=\frac{11}{6}$$

Least common multiple of $4$ and $6$ is $12$. Convert $\frac{3}{4}$ and $\frac{11}{6}$ to fractions with denominator $12$.

$$\frac{9}{12}=\frac{22}{12}$$

Compare $\frac{9}{12}$ and $\frac{22}{12}$.

$$\text{false}$$