Solve (3/8 - 2/3) - 7/12 = 3/8 + (- 2/3 - 7/12) | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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

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Question

$$(\frac{3}{8}+\frac{-2}{3})+\frac{-7}{12}=\frac{3}{8}+(\frac{-2}{3}+\frac{-7}{12})$$

Verify

$\text{true}$

Solution Steps

Fraction $\frac{-2}{3}$ can be rewritten as $-\frac{2}{3}$ by extracting the negative sign.

$$\frac{3}{8}-\frac{2}{3}+\frac{-7}{12}=\frac{3}{8}+\frac{-2}{3}+\frac{-7}{12}$$

Least common multiple of $8$ and $3$ is $24$. Convert $\frac{3}{8}$ and $\frac{2}{3}$ to fractions with denominator $24$.

$$\frac{9}{24}-\frac{16}{24}+\frac{-7}{12}=\frac{3}{8}+\frac{-2}{3}+\frac{-7}{12}$$

Since $\frac{9}{24}$ and $\frac{16}{24}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-16}{24}+\frac{-7}{12}=\frac{3}{8}+\frac{-2}{3}+\frac{-7}{12}$$

Subtract $16$ from $9$ to get $-7$.

$$-\frac{7}{24}+\frac{-7}{12}=\frac{3}{8}+\frac{-2}{3}+\frac{-7}{12}$$

Fraction $\frac{-7}{12}$ can be rewritten as $-\frac{7}{12}$ by extracting the negative sign.

$$-\frac{7}{24}-\frac{7}{12}=\frac{3}{8}+\frac{-2}{3}+\frac{-7}{12}$$

Least common multiple of $24$ and $12$ is $24$. Convert $-\frac{7}{24}$ and $\frac{7}{12}$ to fractions with denominator $24$.

$$-\frac{7}{24}-\frac{14}{24}=\frac{3}{8}+\frac{-2}{3}+\frac{-7}{12}$$

Since $-\frac{7}{24}$ and $\frac{14}{24}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-14}{24}=\frac{3}{8}+\frac{-2}{3}+\frac{-7}{12}$$

Subtract $14$ from $-7$ to get $-21$.

$$\frac{-21}{24}=\frac{3}{8}+\frac{-2}{3}+\frac{-7}{12}$$

Reduce the fraction $\frac{-21}{24}$ to lowest terms by extracting and canceling out $3$.

$$-\frac{7}{8}=\frac{3}{8}+\frac{-2}{3}+\frac{-7}{12}$$

Fraction $\frac{-2}{3}$ can be rewritten as $-\frac{2}{3}$ by extracting the negative sign.

$$-\frac{7}{8}=\frac{3}{8}-\frac{2}{3}+\frac{-7}{12}$$

Least common multiple of $8$ and $3$ is $24$. Convert $\frac{3}{8}$ and $\frac{2}{3}$ to fractions with denominator $24$.

$$-\frac{7}{8}=\frac{9}{24}-\frac{16}{24}+\frac{-7}{12}$$

Since $\frac{9}{24}$ and $\frac{16}{24}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{7}{8}=\frac{9-16}{24}+\frac{-7}{12}$$

Subtract $16$ from $9$ to get $-7$.

$$-\frac{7}{8}=-\frac{7}{24}+\frac{-7}{12}$$

Fraction $\frac{-7}{12}$ can be rewritten as $-\frac{7}{12}$ by extracting the negative sign.

$$-\frac{7}{8}=-\frac{7}{24}-\frac{7}{12}$$

Least common multiple of $24$ and $12$ is $24$. Convert $-\frac{7}{24}$ and $\frac{7}{12}$ to fractions with denominator $24$.

$$-\frac{7}{8}=-\frac{7}{24}-\frac{14}{24}$$

Since $-\frac{7}{24}$ and $\frac{14}{24}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{7}{8}=\frac{-7-14}{24}$$

Subtract $14$ from $-7$ to get $-21$.

$$-\frac{7}{8}=\frac{-21}{24}$$

Reduce the fraction $\frac{-21}{24}$ to lowest terms by extracting and canceling out $3$.

$$-\frac{7}{8}=-\frac{7}{8}$$

Compare $-\frac{7}{8}$ and $-\frac{7}{8}$.

$$\text{true}$$