Solve i ) 3/11 - 7/22 - 5/33 - 15/44 | 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

$$\frac { 3 } { 11 } + \frac { - 7 } { 22 } - \frac { 5 } { 33 } + \frac { - 15 } { 44 }$$

Evaluate

$-\frac{71}{132}\approx -0.537878788$

Solution Steps

Fraction $\frac{-7}{22}$ can be rewritten as $-\frac{7}{22}$ by extracting the negative sign.

$$\frac{3}{11}-\frac{7}{22}-\frac{5}{33}+\frac{-15}{44}$$

Least common multiple of $11$ and $22$ is $22$. Convert $\frac{3}{11}$ and $\frac{7}{22}$ to fractions with denominator $22$.

$$\frac{6}{22}-\frac{7}{22}-\frac{5}{33}+\frac{-15}{44}$$

Since $\frac{6}{22}$ and $\frac{7}{22}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-7}{22}-\frac{5}{33}+\frac{-15}{44}$$

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

$$-\frac{1}{22}-\frac{5}{33}+\frac{-15}{44}$$

Least common multiple of $22$ and $33$ is $66$. Convert $-\frac{1}{22}$ and $\frac{5}{33}$ to fractions with denominator $66$.

$$-\frac{3}{66}-\frac{10}{66}+\frac{-15}{44}$$

Since $-\frac{3}{66}$ and $\frac{10}{66}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-10}{66}+\frac{-15}{44}$$

Subtract $10$ from $-3$ to get $-13$.

$$-\frac{13}{66}+\frac{-15}{44}$$

Fraction $\frac{-15}{44}$ can be rewritten as $-\frac{15}{44}$ by extracting the negative sign.

$$-\frac{13}{66}-\frac{15}{44}$$

Least common multiple of $66$ and $44$ is $132$. Convert $-\frac{13}{66}$ and $\frac{15}{44}$ to fractions with denominator $132$.

$$-\frac{26}{132}-\frac{45}{132}$$

Since $-\frac{26}{132}$ and $\frac{45}{132}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-26-45}{132}$$

Subtract $45$ from $-26$ to get $-71$.

$$-\frac{71}{132}$$

Factor

$-\frac{71}{132} = -0.5378787878787878$