Solve - 20 + (3/- 5 - 7/- 10) = (- 20 + 3/- 5) - 7/- 10 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

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Question

$$-20+(\frac{3}{-5}+\frac{-7}{-10})=(-20+\frac{3}{-5})+\frac{-7}{-10}$$

Verify

$\text{true}$

Solution Steps

Fraction $\frac{3}{-5}$ can be rewritten as $-\frac{3}{5}$ by extracting the negative sign.

$$-20-\frac{3}{5}+\frac{-7}{-10}=-20+\frac{3}{-5}+\frac{-7}{-10}$$

Convert $-20$ to fraction $-\frac{100}{5}$.

$$-\frac{100}{5}-\frac{3}{5}+\frac{-7}{-10}=-20+\frac{3}{-5}+\frac{-7}{-10}$$

Since $-\frac{100}{5}$ and $\frac{3}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-100-3}{5}+\frac{-7}{-10}=-20+\frac{3}{-5}+\frac{-7}{-10}$$

Subtract $3$ from $-100$ to get $-103$.

$$-\frac{103}{5}+\frac{-7}{-10}=-20+\frac{3}{-5}+\frac{-7}{-10}$$

Fraction $\frac{-7}{-10}$ can be simplified to $\frac{7}{10}$ by removing the negative sign from both the numerator and the denominator.

$$-\frac{103}{5}+\frac{7}{10}=-20+\frac{3}{-5}+\frac{-7}{-10}$$

Least common multiple of $5$ and $10$ is $10$. Convert $-\frac{103}{5}$ and $\frac{7}{10}$ to fractions with denominator $10$.

$$-\frac{206}{10}+\frac{7}{10}=-20+\frac{3}{-5}+\frac{-7}{-10}$$

Since $-\frac{206}{10}$ and $\frac{7}{10}$ have the same denominator, add them by adding their numerators.

$$\frac{-206+7}{10}=-20+\frac{3}{-5}+\frac{-7}{-10}$$

Add $-206$ and $7$ to get $-199$.

$$-\frac{199}{10}=-20+\frac{3}{-5}+\frac{-7}{-10}$$

Fraction $\frac{3}{-5}$ can be rewritten as $-\frac{3}{5}$ by extracting the negative sign.

$$-\frac{199}{10}=-20-\frac{3}{5}+\frac{-7}{-10}$$

Convert $-20$ to fraction $-\frac{100}{5}$.

$$-\frac{199}{10}=-\frac{100}{5}-\frac{3}{5}+\frac{-7}{-10}$$

Since $-\frac{100}{5}$ and $\frac{3}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{199}{10}=\frac{-100-3}{5}+\frac{-7}{-10}$$

Subtract $3$ from $-100$ to get $-103$.

$$-\frac{199}{10}=-\frac{103}{5}+\frac{-7}{-10}$$

Fraction $\frac{-7}{-10}$ can be simplified to $\frac{7}{10}$ by removing the negative sign from both the numerator and the denominator.

$$-\frac{199}{10}=-\frac{103}{5}+\frac{7}{10}$$

Least common multiple of $5$ and $10$ is $10$. Convert $-\frac{103}{5}$ and $\frac{7}{10}$ to fractions with denominator $10$.

$$-\frac{199}{10}=-\frac{206}{10}+\frac{7}{10}$$

Since $-\frac{206}{10}$ and $\frac{7}{10}$ have the same denominator, add them by adding their numerators.

$$-\frac{199}{10}=\frac{-206+7}{10}$$

Add $-206$ and $7$ to get $-199$.

$$-\frac{199}{10}=-\frac{199}{10}$$

Compare $-\frac{199}{10}$ and $-\frac{199}{10}$.

$$\text{true}$$