Solve (3)/(7)+(-6)/(11)+(-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

$$\frac{ 3 }{ 7 } + \frac{ -6 }{ 11 } + \frac{ -8 }{ 21 } + \frac{ 5 }{ 22 } =$$

Evaluate

$-\frac{125}{462}\approx -0.270562771$

Solution Steps

Fraction $\frac{-6}{11}$ can be rewritten as $-\frac{6}{11}$ by extracting the negative sign.

$$\frac{3}{7}-\frac{6}{11}+\frac{-8}{21}+\frac{5}{22}$$

Least common multiple of $7$ and $11$ is $77$. Convert $\frac{3}{7}$ and $\frac{6}{11}$ to fractions with denominator $77$.

$$\frac{33}{77}-\frac{42}{77}+\frac{-8}{21}+\frac{5}{22}$$

Since $\frac{33}{77}$ and $\frac{42}{77}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{33-42}{77}+\frac{-8}{21}+\frac{5}{22}$$

Subtract $42$ from $33$ to get $-9$.

$$-\frac{9}{77}+\frac{-8}{21}+\frac{5}{22}$$

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

$$-\frac{9}{77}-\frac{8}{21}+\frac{5}{22}$$

Least common multiple of $77$ and $21$ is $231$. Convert $-\frac{9}{77}$ and $\frac{8}{21}$ to fractions with denominator $231$.

$$-\frac{27}{231}-\frac{88}{231}+\frac{5}{22}$$

Since $-\frac{27}{231}$ and $\frac{88}{231}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-27-88}{231}+\frac{5}{22}$$

Subtract $88$ from $-27$ to get $-115$.

$$-\frac{115}{231}+\frac{5}{22}$$

Least common multiple of $231$ and $22$ is $462$. Convert $-\frac{115}{231}$ and $\frac{5}{22}$ to fractions with denominator $462$.

$$-\frac{230}{462}+\frac{105}{462}$$

Since $-\frac{230}{462}$ and $\frac{105}{462}$ have the same denominator, add them by adding their numerators.

$$\frac{-230+105}{462}$$

Add $-230$ and $105$ to get $-125$.

$$-\frac{125}{462}$$

Factor

$-\frac{125}{462} = -0.27056277056277056$