Solve - 6/7 - 5/6 - 4/9 - 15/7 | 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

$$\frac{-6}{7}+\frac{-5}{6}+\frac{-4}{9}+\frac{-15}{7}$$

Evaluate

$-\frac{77}{18}\approx -4.277777778$

Solution Steps

Fraction $\frac{-6}{7}$ can be rewritten as $-\frac{6}{7}$ by extracting the negative sign.

$$-\frac{6}{7}+\frac{-5}{6}+\frac{-4}{9}+\frac{-15}{7}$$

Fraction $\frac{-5}{6}$ can be rewritten as $-\frac{5}{6}$ by extracting the negative sign.

$$-\frac{6}{7}-\frac{5}{6}+\frac{-4}{9}+\frac{-15}{7}$$

Least common multiple of $7$ and $6$ is $42$. Convert $-\frac{6}{7}$ and $\frac{5}{6}$ to fractions with denominator $42$.

$$-\frac{36}{42}-\frac{35}{42}+\frac{-4}{9}+\frac{-15}{7}$$

Since $-\frac{36}{42}$ and $\frac{35}{42}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-36-35}{42}+\frac{-4}{9}+\frac{-15}{7}$$

Subtract $35$ from $-36$ to get $-71$.

$$-\frac{71}{42}+\frac{-4}{9}+\frac{-15}{7}$$

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

$$-\frac{71}{42}-\frac{4}{9}+\frac{-15}{7}$$

Least common multiple of $42$ and $9$ is $126$. Convert $-\frac{71}{42}$ and $\frac{4}{9}$ to fractions with denominator $126$.

$$-\frac{213}{126}-\frac{56}{126}+\frac{-15}{7}$$

Since $-\frac{213}{126}$ and $\frac{56}{126}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-213-56}{126}+\frac{-15}{7}$$

Subtract $56$ from $-213$ to get $-269$.

$$-\frac{269}{126}+\frac{-15}{7}$$

Fraction $\frac{-15}{7}$ can be rewritten as $-\frac{15}{7}$ by extracting the negative sign.

$$-\frac{269}{126}-\frac{15}{7}$$

Least common multiple of $126$ and $7$ is $126$. Convert $-\frac{269}{126}$ and $\frac{15}{7}$ to fractions with denominator $126$.

$$-\frac{269}{126}-\frac{270}{126}$$

Since $-\frac{269}{126}$ and $\frac{270}{126}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-269-270}{126}$$

Subtract $270$ from $-269$ to get $-539$.

$$\frac{-539}{126}$$

Reduce the fraction $\frac{-539}{126}$ to lowest terms by extracting and canceling out $7$.

$$-\frac{77}{18}$$

Factor

$-\frac{77}{18} = -4\frac{5}{18} = -4.277777777777778$