Solve 4/7+-8/9+-13/7+17/21 | 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

$$4/7+-8/9+-13/7+17/21$$

Evaluate

$-\frac{86}{63}\approx -1.365079365$

Solution Steps

Fraction $\frac{-8}{9}$ can be rewritten as $-\frac{8}{9}$ by extracting the negative sign.

$$\frac{4}{7}-\frac{8}{9}+\frac{-13}{7}+\frac{17}{21}$$

Least common multiple of $7$ and $9$ is $63$. Convert $\frac{4}{7}$ and $\frac{8}{9}$ to fractions with denominator $63$.

$$\frac{36}{63}-\frac{56}{63}+\frac{-13}{7}+\frac{17}{21}$$

Since $\frac{36}{63}$ and $\frac{56}{63}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{36-56}{63}+\frac{-13}{7}+\frac{17}{21}$$

Subtract $56$ from $36$ to get $-20$.

$$-\frac{20}{63}+\frac{-13}{7}+\frac{17}{21}$$

Fraction $\frac{-13}{7}$ can be rewritten as $-\frac{13}{7}$ by extracting the negative sign.

$$-\frac{20}{63}-\frac{13}{7}+\frac{17}{21}$$

Least common multiple of $63$ and $7$ is $63$. Convert $-\frac{20}{63}$ and $\frac{13}{7}$ to fractions with denominator $63$.

$$-\frac{20}{63}-\frac{117}{63}+\frac{17}{21}$$

Since $-\frac{20}{63}$ and $\frac{117}{63}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-20-117}{63}+\frac{17}{21}$$

Subtract $117$ from $-20$ to get $-137$.

$$-\frac{137}{63}+\frac{17}{21}$$

Least common multiple of $63$ and $21$ is $63$. Convert $-\frac{137}{63}$ and $\frac{17}{21}$ to fractions with denominator $63$.

$$-\frac{137}{63}+\frac{51}{63}$$

Since $-\frac{137}{63}$ and $\frac{51}{63}$ have the same denominator, add them by adding their numerators.

$$\frac{-137+51}{63}$$

Add $-137$ and $51$ to get $-86$.

$$-\frac{86}{63}$$

Factor

$-\frac{86}{63} = -1\frac{23}{63} = -1.3650793650793651$