Solve C = (1/2 + 2/3 - 3/5)/(2/3 + 1/2 - 4/5) | 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

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

Solve for C

$C = \frac{17}{11} = 1\frac{6}{11} \approx 1.545454545$

Steps for Solving Linear Equation

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

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

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

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

Add $3$ and $4$ to get $7$.

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

Least common multiple of $6$ and $5$ is $30$. Convert $\frac{7}{6}$ and $\frac{3}{5}$ to fractions with denominator $30$.

$$C=\frac{\frac{35}{30}-\frac{18}{30}}{\frac{2}{3}+\frac{1}{2}-\frac{4}{5}}$$

Since $\frac{35}{30}$ and $\frac{18}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$C=\frac{\frac{35-18}{30}}{\frac{2}{3}+\frac{1}{2}-\frac{4}{5}}$$

Subtract $18$ from $35$ to get $17$.

$$C=\frac{\frac{17}{30}}{\frac{2}{3}+\frac{1}{2}-\frac{4}{5}}$$

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

$$C=\frac{\frac{17}{30}}{\frac{4}{6}+\frac{3}{6}-\frac{4}{5}}$$

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

$$C=\frac{\frac{17}{30}}{\frac{4+3}{6}-\frac{4}{5}}$$

Add $4$ and $3$ to get $7$.

$$C=\frac{\frac{17}{30}}{\frac{7}{6}-\frac{4}{5}}$$

Least common multiple of $6$ and $5$ is $30$. Convert $\frac{7}{6}$ and $\frac{4}{5}$ to fractions with denominator $30$.

$$C=\frac{\frac{17}{30}}{\frac{35}{30}-\frac{24}{30}}$$

Since $\frac{35}{30}$ and $\frac{24}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$C=\frac{\frac{17}{30}}{\frac{35-24}{30}}$$

Subtract $24$ from $35$ to get $11$.

$$C=\frac{\frac{17}{30}}{\frac{11}{30}}$$

Divide $\frac{17}{30}$ by $\frac{11}{30}$ by multiplying $\frac{17}{30}$ by the reciprocal of $\frac{11}{30}$.

$$C=\frac{17}{30}\times \frac{30}{11}$$

Multiply $\frac{17}{30}$ times $\frac{30}{11}$ by multiplying numerator times numerator and denominator times denominator.

$$C=\frac{17\times 30}{30\times 11}$$

Cancel out $30$ in both numerator and denominator.

$$C=\frac{17}{11}$$

Assign C

$C≔\frac{17}{11}$