Solve Associative ) 1 2 +[( -3 4 + 5 6 )]=( 1 2 - 3 4 )+ 5 6 =Prare-lhc Teacher's Signature :. | 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

$$\frac { 1 } { 2 } + [ ( \frac { - 3 } { 4 } + \frac { 5 } { 6 } ) ] = ( \frac { 1 } { 2 } - \frac { 3 } { 4 } ) + \frac { 5 } { 6 } =$$

Verify

$\text{true}$

Solution Steps

Fraction $\frac{-3}{4}$ can be rewritten as $-\frac{3}{4}$ by extracting the negative sign.

$$\frac{1}{2}-\frac{3}{4}+\frac{5}{6}=\frac{1}{2}-\frac{3}{4}+\frac{5}{6}$$

Least common multiple of $2$ and $4$ is $4$. Convert $\frac{1}{2}$ and $\frac{3}{4}$ to fractions with denominator $4$.

$$\frac{2}{4}-\frac{3}{4}+\frac{5}{6}=\frac{1}{2}-\frac{3}{4}+\frac{5}{6}$$

Since $\frac{2}{4}$ and $\frac{3}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-3}{4}+\frac{5}{6}=\frac{1}{2}-\frac{3}{4}+\frac{5}{6}$$

Subtract $3$ from $2$ to get $-1$.

$$-\frac{1}{4}+\frac{5}{6}=\frac{1}{2}-\frac{3}{4}+\frac{5}{6}$$

Least common multiple of $4$ and $6$ is $12$. Convert $-\frac{1}{4}$ and $\frac{5}{6}$ to fractions with denominator $12$.

$$-\frac{3}{12}+\frac{10}{12}=\frac{1}{2}-\frac{3}{4}+\frac{5}{6}$$

Since $-\frac{3}{12}$ and $\frac{10}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{-3+10}{12}=\frac{1}{2}-\frac{3}{4}+\frac{5}{6}$$

Add $-3$ and $10$ to get $7$.

$$\frac{7}{12}=\frac{1}{2}-\frac{3}{4}+\frac{5}{6}$$

Least common multiple of $2$ and $4$ is $4$. Convert $\frac{1}{2}$ and $\frac{3}{4}$ to fractions with denominator $4$.

$$\frac{7}{12}=\frac{2}{4}-\frac{3}{4}+\frac{5}{6}$$

Since $\frac{2}{4}$ and $\frac{3}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{12}=\frac{2-3}{4}+\frac{5}{6}$$

Subtract $3$ from $2$ to get $-1$.

$$\frac{7}{12}=-\frac{1}{4}+\frac{5}{6}$$

Least common multiple of $4$ and $6$ is $12$. Convert $-\frac{1}{4}$ and $\frac{5}{6}$ to fractions with denominator $12$.

$$\frac{7}{12}=-\frac{3}{12}+\frac{10}{12}$$

Since $-\frac{3}{12}$ and $\frac{10}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{7}{12}=\frac{-3+10}{12}$$

Add $-3$ and $10$ to get $7$.

$$\frac{7}{12}=\frac{7}{12}$$

Compare $\frac{7}{12}$ and $\frac{7}{12}$.

$$\text{true}$$