Solve .7/8+-1/7=-1/7+7/8. | 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

$$.7/8+-1/7=-1/7+7/8.$$

Verify

$\text{false}$

Solution Steps

Expand $\frac{0.7}{8}$ by multiplying both numerator and the denominator by $10$.

$$\frac{7}{80}+\frac{-1}{7}=\frac{-1}{7}+\frac{7}{8}$$

Fraction $\frac{-1}{7}$ can be rewritten as $-\frac{1}{7}$ by extracting the negative sign.

$$\frac{7}{80}-\frac{1}{7}=\frac{-1}{7}+\frac{7}{8}$$

Least common multiple of $80$ and $7$ is $560$. Convert $\frac{7}{80}$ and $\frac{1}{7}$ to fractions with denominator $560$.

$$\frac{49}{560}-\frac{80}{560}=\frac{-1}{7}+\frac{7}{8}$$

Since $\frac{49}{560}$ and $\frac{80}{560}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{49-80}{560}=\frac{-1}{7}+\frac{7}{8}$$

Subtract $80$ from $49$ to get $-31$.

$$-\frac{31}{560}=\frac{-1}{7}+\frac{7}{8}$$

Fraction $\frac{-1}{7}$ can be rewritten as $-\frac{1}{7}$ by extracting the negative sign.

$$-\frac{31}{560}=-\frac{1}{7}+\frac{7}{8}$$

Least common multiple of $7$ and $8$ is $56$. Convert $-\frac{1}{7}$ and $\frac{7}{8}$ to fractions with denominator $56$.

$$-\frac{31}{560}=-\frac{8}{56}+\frac{49}{56}$$

Since $-\frac{8}{56}$ and $\frac{49}{56}$ have the same denominator, add them by adding their numerators.

$$-\frac{31}{560}=\frac{-8+49}{56}$$

Add $-8$ and $49$ to get $41$.

$$-\frac{31}{560}=\frac{41}{56}$$

Least common multiple of $560$ and $56$ is $560$. Convert $-\frac{31}{560}$ and $\frac{41}{56}$ to fractions with denominator $560$.

$$-\frac{31}{560}=\frac{410}{560}$$

Compare $-\frac{31}{560}$ and $\frac{410}{560}$.

$$\text{false}$$