Solve (1)/(5)-{(2)/(5)+(4)/(15)\times(1)/(2)-((1)/(2)+(2)/(5))} | 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

$$\frac{ 1 }{ 5 } - \{ \frac{ 2 }{ 5 } + \frac{ 4 }{ 15 } \times \frac{ 1 }{ 2 } -( \frac{ 1 }{ 2 } + \frac{ 2 }{ 5 } ) \}$$

Evaluate

$\frac{17}{30}\approx 0.566666667$

Solution Steps

Multiply $\frac{4}{15}$ times $\frac{1}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{5}-\left(\frac{2}{5}+\frac{4\times 1}{15\times 2}-\left(\frac{1}{2}+\frac{2}{5}\right)\right)$$

Do the multiplications in the fraction $\frac{4\times 1}{15\times 2}$.

$$\frac{1}{5}-\left(\frac{2}{5}+\frac{4}{30}-\left(\frac{1}{2}+\frac{2}{5}\right)\right)$$

Reduce the fraction $\frac{4}{30}$ to lowest terms by extracting and canceling out $2$.

$$\frac{1}{5}-\left(\frac{2}{5}+\frac{2}{15}-\left(\frac{1}{2}+\frac{2}{5}\right)\right)$$

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

$$\frac{1}{5}-\left(\frac{6}{15}+\frac{2}{15}-\left(\frac{1}{2}+\frac{2}{5}\right)\right)$$

Since $\frac{6}{15}$ and $\frac{2}{15}$ have the same denominator, add them by adding their numerators.

$$\frac{1}{5}-\left(\frac{6+2}{15}-\left(\frac{1}{2}+\frac{2}{5}\right)\right)$$

Add $6$ and $2$ to get $8$.

$$\frac{1}{5}-\left(\frac{8}{15}-\left(\frac{1}{2}+\frac{2}{5}\right)\right)$$

Least common multiple of $2$ and $5$ is $10$. Convert $\frac{1}{2}$ and $\frac{2}{5}$ to fractions with denominator $10$.

$$\frac{1}{5}-\left(\frac{8}{15}-\left(\frac{5}{10}+\frac{4}{10}\right)\right)$$

Since $\frac{5}{10}$ and $\frac{4}{10}$ have the same denominator, add them by adding their numerators.

$$\frac{1}{5}-\left(\frac{8}{15}-\frac{5+4}{10}\right)$$

Add $5$ and $4$ to get $9$.

$$\frac{1}{5}-\left(\frac{8}{15}-\frac{9}{10}\right)$$

Least common multiple of $15$ and $10$ is $30$. Convert $\frac{8}{15}$ and $\frac{9}{10}$ to fractions with denominator $30$.

$$\frac{1}{5}-\left(\frac{16}{30}-\frac{27}{30}\right)$$

Since $\frac{16}{30}$ and $\frac{27}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}-\frac{16-27}{30}$$

Subtract $27$ from $16$ to get $-11$.

$$\frac{1}{5}-\left(-\frac{11}{30}\right)$$

The opposite of $-\frac{11}{30}$ is $\frac{11}{30}$.

$$\frac{1}{5}+\frac{11}{30}$$

Least common multiple of $5$ and $30$ is $30$. Convert $\frac{1}{5}$ and $\frac{11}{30}$ to fractions with denominator $30$.

$$\frac{6}{30}+\frac{11}{30}$$

Since $\frac{6}{30}$ and $\frac{11}{30}$ have the same denominator, add them by adding their numerators.

$$\frac{6+11}{30}$$

Add $6$ and $11$ to get $17$.

$$\frac{17}{30}$$

Factor

$\frac{17}{2 \cdot 3 \cdot 5} = 0.5666666666666667$