Solve - 2/7 + [3/7 - 5/9] = [- 2/7 + 3/7] - 5/9 | Equatix - Math Solver

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Example

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a⋅(b-2)=3b

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

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Question

$$\frac{-2}{7}+[\frac{3}{7}+\frac{-5}{9}]=[\frac{-2}{7}+\frac{3}{7}]+\frac{-5}{9}$$

Verify

$\text{true}$

Solution Steps

Fraction $\frac{-2}{7}$ can be rewritten as $-\frac{2}{7}$ by extracting the negative sign.

$$-\frac{2}{7}+\frac{3}{7}+\frac{-5}{9}=\frac{-2}{7}+\frac{3}{7}+\frac{-5}{9}$$

Since $-\frac{2}{7}$ and $\frac{3}{7}$ have the same denominator, add them by adding their numerators.

$$\frac{-2+3}{7}+\frac{-5}{9}=\frac{-2}{7}+\frac{3}{7}+\frac{-5}{9}$$

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

$$\frac{1}{7}+\frac{-5}{9}=\frac{-2}{7}+\frac{3}{7}+\frac{-5}{9}$$

Fraction $\frac{-5}{9}$ can be rewritten as $-\frac{5}{9}$ by extracting the negative sign.

$$\frac{1}{7}-\frac{5}{9}=\frac{-2}{7}+\frac{3}{7}+\frac{-5}{9}$$

Least common multiple of $7$ and $9$ is $63$. Convert $\frac{1}{7}$ and $\frac{5}{9}$ to fractions with denominator $63$.

$$\frac{9}{63}-\frac{35}{63}=\frac{-2}{7}+\frac{3}{7}+\frac{-5}{9}$$

Since $\frac{9}{63}$ and $\frac{35}{63}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-35}{63}=\frac{-2}{7}+\frac{3}{7}+\frac{-5}{9}$$

Subtract $35$ from $9$ to get $-26$.

$$-\frac{26}{63}=\frac{-2}{7}+\frac{3}{7}+\frac{-5}{9}$$

Fraction $\frac{-2}{7}$ can be rewritten as $-\frac{2}{7}$ by extracting the negative sign.

$$-\frac{26}{63}=-\frac{2}{7}+\frac{3}{7}+\frac{-5}{9}$$

Since $-\frac{2}{7}$ and $\frac{3}{7}$ have the same denominator, add them by adding their numerators.

$$-\frac{26}{63}=\frac{-2+3}{7}+\frac{-5}{9}$$

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

$$-\frac{26}{63}=\frac{1}{7}+\frac{-5}{9}$$

Fraction $\frac{-5}{9}$ can be rewritten as $-\frac{5}{9}$ by extracting the negative sign.

$$-\frac{26}{63}=\frac{1}{7}-\frac{5}{9}$$

Least common multiple of $7$ and $9$ is $63$. Convert $\frac{1}{7}$ and $\frac{5}{9}$ to fractions with denominator $63$.

$$-\frac{26}{63}=\frac{9}{63}-\frac{35}{63}$$

Since $\frac{9}{63}$ and $\frac{35}{63}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{26}{63}=\frac{9-35}{63}$$

Subtract $35$ from $9$ to get $-26$.

$$-\frac{26}{63}=-\frac{26}{63}$$

Compare $-\frac{26}{63}$ and $-\frac{26}{63}$.

$$\text{true}$$