Solve - 9/42 + (- 5/21) + 3/84 + 1/6 | 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

$$\frac{-9}{42}+(\frac{-5}{21})+\frac{3}{84}+\frac{1}{6}$$

Evaluate

$-\frac{1}{4}=-0.25$

Solution Steps

Reduce the fraction $\frac{-9}{42}$ to lowest terms by extracting and canceling out $3$.

$$-\frac{3}{14}+\frac{-5}{21}+\frac{3}{84}+\frac{1}{6}$$

Fraction $\frac{-5}{21}$ can be rewritten as $-\frac{5}{21}$ by extracting the negative sign.

$$-\frac{3}{14}-\frac{5}{21}+\frac{3}{84}+\frac{1}{6}$$

Least common multiple of $14$ and $21$ is $42$. Convert $-\frac{3}{14}$ and $\frac{5}{21}$ to fractions with denominator $42$.

$$-\frac{9}{42}-\frac{10}{42}+\frac{3}{84}+\frac{1}{6}$$

Since $-\frac{9}{42}$ and $\frac{10}{42}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-10}{42}+\frac{3}{84}+\frac{1}{6}$$

Subtract $10$ from $-9$ to get $-19$.

$$-\frac{19}{42}+\frac{3}{84}+\frac{1}{6}$$

Reduce the fraction $\frac{3}{84}$ to lowest terms by extracting and canceling out $3$.

$$-\frac{19}{42}+\frac{1}{28}+\frac{1}{6}$$

Least common multiple of $42$ and $28$ is $84$. Convert $-\frac{19}{42}$ and $\frac{1}{28}$ to fractions with denominator $84$.

$$-\frac{38}{84}+\frac{3}{84}+\frac{1}{6}$$

Since $-\frac{38}{84}$ and $\frac{3}{84}$ have the same denominator, add them by adding their numerators.

$$\frac{-38+3}{84}+\frac{1}{6}$$

Add $-38$ and $3$ to get $-35$.

$$\frac{-35}{84}+\frac{1}{6}$$

Reduce the fraction $\frac{-35}{84}$ to lowest terms by extracting and canceling out $7$.

$$-\frac{5}{12}+\frac{1}{6}$$

Least common multiple of $12$ and $6$ is $12$. Convert $-\frac{5}{12}$ and $\frac{1}{6}$ to fractions with denominator $12$.

$$-\frac{5}{12}+\frac{2}{12}$$

Since $-\frac{5}{12}$ and $\frac{2}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{-5+2}{12}$$

Add $-5$ and $2$ to get $-3$.

$$\frac{-3}{12}$$

Reduce the fraction $\frac{-3}{12}$ to lowest terms by extracting and canceling out $3$.

$$-\frac{1}{4}$$

Factor

$-\frac{1}{4} = -0.25$