Solve |(1)/(5)|+|(-2)/(15)|+|(1)/(5)|+|(-4)/(15)|+|(1)/(3)|is | 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

$$| \frac{ 1 }{ 5 } |+| \frac{ -2 }{ 15 } |+| \frac{ 1 }{ 5 } |+| \frac{ -4 }{ 15 } |+| \frac{ 1 }{ 3 } |is$$

Evaluate

$\frac{is}{3}+\frac{4}{5}$

Solution Steps

The modulus of a complex number $a+bi$ is $\sqrt{a^{2}+b^{2}}$. The modulus of $\frac{1}{5}$ is $\frac{1}{5}$.

$$\frac{1}{5}+|\frac{-2}{15}|+|\frac{1}{5}|+|\frac{-4}{15}|+|\frac{1}{3}|is$$

Fraction $\frac{-2}{15}$ can be rewritten as $-\frac{2}{15}$ by extracting the negative sign.

$$\frac{1}{5}+|-\frac{2}{15}|+|\frac{1}{5}|+|\frac{-4}{15}|+|\frac{1}{3}|is$$

The modulus of a complex number $a+bi$ is $\sqrt{a^{2}+b^{2}}$. The modulus of $-\frac{2}{15}$ is $\frac{2}{15}$.

$$\frac{1}{5}+\frac{2}{15}+|\frac{1}{5}|+|\frac{-4}{15}|+|\frac{1}{3}|is$$

Least common multiple of $5$ and $15$ is $15$. Convert $\frac{1}{5}$ and $\frac{2}{15}$ to fractions with denominator $15$.

$$\frac{3}{15}+\frac{2}{15}+|\frac{1}{5}|+|\frac{-4}{15}|+|\frac{1}{3}|is$$

Since $\frac{3}{15}$ and $\frac{2}{15}$ have the same denominator, add them by adding their numerators.

$$\frac{3+2}{15}+|\frac{1}{5}|+|\frac{-4}{15}|+|\frac{1}{3}|is$$

Add $3$ and $2$ to get $5$.

$$\frac{5}{15}+|\frac{1}{5}|+|\frac{-4}{15}|+|\frac{1}{3}|is$$

Reduce the fraction $\frac{5}{15}$ to lowest terms by extracting and canceling out $5$.

$$\frac{1}{3}+|\frac{1}{5}|+|\frac{-4}{15}|+|\frac{1}{3}|is$$

The modulus of a complex number $a+bi$ is $\sqrt{a^{2}+b^{2}}$. The modulus of $\frac{1}{5}$ is $\frac{1}{5}$.

$$\frac{1}{3}+\frac{1}{5}+|\frac{-4}{15}|+|\frac{1}{3}|is$$

Least common multiple of $3$ and $5$ is $15$. Convert $\frac{1}{3}$ and $\frac{1}{5}$ to fractions with denominator $15$.

$$\frac{5}{15}+\frac{3}{15}+|\frac{-4}{15}|+|\frac{1}{3}|is$$

Since $\frac{5}{15}$ and $\frac{3}{15}$ have the same denominator, add them by adding their numerators.

$$\frac{5+3}{15}+|\frac{-4}{15}|+|\frac{1}{3}|is$$

Add $5$ and $3$ to get $8$.

$$\frac{8}{15}+|\frac{-4}{15}|+|\frac{1}{3}|is$$

Fraction $\frac{-4}{15}$ can be rewritten as $-\frac{4}{15}$ by extracting the negative sign.

$$\frac{8}{15}+|-\frac{4}{15}|+|\frac{1}{3}|is$$

The modulus of a complex number $a+bi$ is $\sqrt{a^{2}+b^{2}}$. The modulus of $-\frac{4}{15}$ is $\frac{4}{15}$.

$$\frac{8}{15}+\frac{4}{15}+|\frac{1}{3}|is$$

Since $\frac{8}{15}$ and $\frac{4}{15}$ have the same denominator, add them by adding their numerators.

$$\frac{8+4}{15}+|\frac{1}{3}|is$$

Add $8$ and $4$ to get $12$.

$$\frac{12}{15}+|\frac{1}{3}|is$$

Reduce the fraction $\frac{12}{15}$ to lowest terms by extracting and canceling out $3$.

$$\frac{4}{5}+|\frac{1}{3}|is$$

The modulus of a complex number $a+bi$ is $\sqrt{a^{2}+b^{2}}$. The modulus of $\frac{1}{3}$ is $\frac{1}{3}$.

$$\frac{4}{5}+\frac{1}{3}is$$