Solve (ii) - 3/7 - 4/9 = - 4/9 - 3/7 | 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

$$\frac { - 3 } { 7 } + \frac { - 4 } { 9 } = \frac { - 4 } { 9 } + \frac { - 3 } { 7 }$$

Verify

$\text{true}$

Solution Steps

Fraction $\frac{-3}{7}$ can be rewritten as $-\frac{3}{7}$ by extracting the negative sign.

$$-\frac{3}{7}+\frac{-4}{9}=\frac{-4}{9}+\frac{-3}{7}$$

Fraction $\frac{-4}{9}$ can be rewritten as $-\frac{4}{9}$ by extracting the negative sign.

$$-\frac{3}{7}-\frac{4}{9}=\frac{-4}{9}+\frac{-3}{7}$$

Least common multiple of $7$ and $9$ is $63$. Convert $-\frac{3}{7}$ and $\frac{4}{9}$ to fractions with denominator $63$.

$$-\frac{27}{63}-\frac{28}{63}=\frac{-4}{9}+\frac{-3}{7}$$

Since $-\frac{27}{63}$ and $\frac{28}{63}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-27-28}{63}=\frac{-4}{9}+\frac{-3}{7}$$

Subtract $28$ from $-27$ to get $-55$.

$$-\frac{55}{63}=\frac{-4}{9}+\frac{-3}{7}$$

Fraction $\frac{-4}{9}$ can be rewritten as $-\frac{4}{9}$ by extracting the negative sign.

$$-\frac{55}{63}=-\frac{4}{9}+\frac{-3}{7}$$

Fraction $\frac{-3}{7}$ can be rewritten as $-\frac{3}{7}$ by extracting the negative sign.

$$-\frac{55}{63}=-\frac{4}{9}-\frac{3}{7}$$

Least common multiple of $9$ and $7$ is $63$. Convert $-\frac{4}{9}$ and $\frac{3}{7}$ to fractions with denominator $63$.

$$-\frac{55}{63}=-\frac{28}{63}-\frac{27}{63}$$

Since $-\frac{28}{63}$ and $\frac{27}{63}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{55}{63}=\frac{-28-27}{63}$$

Subtract $27$ from $-28$ to get $-55$.

$$-\frac{55}{63}=-\frac{55}{63}$$

Compare $-\frac{55}{63}$ and $-\frac{55}{63}$.

$$\text{true}$$