Solve -(2)/(5)-((1)/(5)-(4)/(5))=((2)/(5)-((1)/(2)))-(4)/(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

$$- \frac{ 2 }{ 5 } -( \frac{ 1 }{ 5 } - \frac{ 4 }{ 5 } )=( \frac{ 2 }{ 5 } -( \frac{ 1 }{ 2 } ))- \frac{ 4 }{ 5 }$$

Verify

$\text{false}$

Solution Steps

Since $\frac{1}{5}$ and $\frac{4}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{5}-\frac{1-4}{5}=\frac{2}{5}-\frac{1}{2}-\frac{4}{5}$$

Subtract $4$ from $1$ to get $-3$.

$$-\frac{2}{5}-\left(-\frac{3}{5}\right)=\frac{2}{5}-\frac{1}{2}-\frac{4}{5}$$

The opposite of $-\frac{3}{5}$ is $\frac{3}{5}$.

$$-\frac{2}{5}+\frac{3}{5}=\frac{2}{5}-\frac{1}{2}-\frac{4}{5}$$

Since $-\frac{2}{5}$ and $\frac{3}{5}$ have the same denominator, add them by adding their numerators.

$$\frac{-2+3}{5}=\frac{2}{5}-\frac{1}{2}-\frac{4}{5}$$

Add $-2$ and $3$ to get $1$.

$$\frac{1}{5}=\frac{2}{5}-\frac{1}{2}-\frac{4}{5}$$

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

$$\frac{1}{5}=\frac{4}{10}-\frac{5}{10}-\frac{4}{5}$$

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

$$\frac{1}{5}=\frac{4-5}{10}-\frac{4}{5}$$

Subtract $5$ from $4$ to get $-1$.

$$\frac{1}{5}=-\frac{1}{10}-\frac{4}{5}$$

Least common multiple of $10$ and $5$ is $10$. Convert $-\frac{1}{10}$ and $\frac{4}{5}$ to fractions with denominator $10$.

$$\frac{1}{5}=-\frac{1}{10}-\frac{8}{10}$$

Since $-\frac{1}{10}$ and $\frac{8}{10}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}=\frac{-1-8}{10}$$

Subtract $8$ from $-1$ to get $-9$.

$$\frac{1}{5}=-\frac{9}{10}$$

Least common multiple of $5$ and $10$ is $10$. Convert $\frac{1}{5}$ and $-\frac{9}{10}$ to fractions with denominator $10$.

$$\frac{2}{10}=-\frac{9}{10}$$

Compare $\frac{2}{10}$ and $-\frac{9}{10}$.

$$\text{false}$$