Solve 3/7+(-6/12)+(-8/21)+(5/22) | 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

$$3/7+(-6/12)+(-8/21)+(5/22)$$

Evaluate

$-\frac{52}{231}\approx -0.225108225$

Solution Steps

Reduce the fraction $\frac{-6}{12}$ to lowest terms by extracting and canceling out $6$.

$$\frac{3}{7}-\frac{1}{2}+\frac{-8}{21}+\frac{5}{22}$$

Least common multiple of $7$ and $2$ is $14$. Convert $\frac{3}{7}$ and $\frac{1}{2}$ to fractions with denominator $14$.

$$\frac{6}{14}-\frac{7}{14}+\frac{-8}{21}+\frac{5}{22}$$

Since $\frac{6}{14}$ and $\frac{7}{14}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-7}{14}+\frac{-8}{21}+\frac{5}{22}$$

Subtract $7$ from $6$ to get $-1$.

$$-\frac{1}{14}+\frac{-8}{21}+\frac{5}{22}$$

Fraction $\frac{-8}{21}$ can be rewritten as $-\frac{8}{21}$ by extracting the negative sign.

$$-\frac{1}{14}-\frac{8}{21}+\frac{5}{22}$$

Least common multiple of $14$ and $21$ is $42$. Convert $-\frac{1}{14}$ and $\frac{8}{21}$ to fractions with denominator $42$.

$$-\frac{3}{42}-\frac{16}{42}+\frac{5}{22}$$

Since $-\frac{3}{42}$ and $\frac{16}{42}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-16}{42}+\frac{5}{22}$$

Subtract $16$ from $-3$ to get $-19$.

$$-\frac{19}{42}+\frac{5}{22}$$

Least common multiple of $42$ and $22$ is $462$. Convert $-\frac{19}{42}$ and $\frac{5}{22}$ to fractions with denominator $462$.

$$-\frac{209}{462}+\frac{105}{462}$$

Since $-\frac{209}{462}$ and $\frac{105}{462}$ have the same denominator, add them by adding their numerators.

$$\frac{-209+105}{462}$$

Add $-209$ and $105$ to get $-104$.

$$\frac{-104}{462}$$

Reduce the fraction $\frac{-104}{462}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{52}{231}$$

Factor

$-\frac{52}{231} = -0.22510822510822512$