Solve (2)/(3)=(4)/(6)-(1)/(2)=(3)/(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

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

Verify

$\text{false}$

Solution Steps

Reduce the fraction $\frac{4}{6}$ to lowest terms by extracting and canceling out $2$.

$$\frac{2}{3}=\frac{2}{3}-\frac{1}{2}\text{ and }\frac{4}{6}-\frac{1}{2}=\frac{3}{6}$$

Least common multiple of $3$ and $2$ is $6$. Convert $\frac{2}{3}$ and $\frac{1}{2}$ to fractions with denominator $6$.

$$\frac{2}{3}=\frac{4}{6}-\frac{3}{6}\text{ and }\frac{4}{6}-\frac{1}{2}=\frac{3}{6}$$

Since $\frac{4}{6}$ and $\frac{3}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}=\frac{4-3}{6}\text{ and }\frac{4}{6}-\frac{1}{2}=\frac{3}{6}$$

Subtract $3$ from $4$ to get $1$.

$$\frac{2}{3}=\frac{1}{6}\text{ and }\frac{4}{6}-\frac{1}{2}=\frac{3}{6}$$

Least common multiple of $3$ and $6$ is $6$. Convert $\frac{2}{3}$ and $\frac{1}{6}$ to fractions with denominator $6$.

$$\frac{4}{6}=\frac{1}{6}\text{ and }\frac{4}{6}-\frac{1}{2}=\frac{3}{6}$$

Compare $\frac{4}{6}$ and $\frac{1}{6}$.

$$\text{false}\text{ and }\frac{4}{6}-\frac{1}{2}=\frac{3}{6}$$

Reduce the fraction $\frac{4}{6}$ to lowest terms by extracting and canceling out $2$.

$$\text{false}\text{ and }\frac{2}{3}-\frac{1}{2}=\frac{3}{6}$$

Least common multiple of $3$ and $2$ is $6$. Convert $\frac{2}{3}$ and $\frac{1}{2}$ to fractions with denominator $6$.

$$\text{false}\text{ and }\frac{4}{6}-\frac{3}{6}=\frac{3}{6}$$

Since $\frac{4}{6}$ and $\frac{3}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\text{false}\text{ and }\frac{4-3}{6}=\frac{3}{6}$$

Subtract $3$ from $4$ to get $1$.

$$\text{false}\text{ and }\frac{1}{6}=\frac{3}{6}$$

Compare $\frac{1}{6}$ and $\frac{3}{6}$.

$$\text{false}\text{ and }\text{false}$$

The conjunction of $\text{false}$ and $\text{false}$ is $\text{false}$.

$$\text{false}$$