Solve [(2/4 - 1/3) * 3/2 + (2/6 - 1/4)(1 - 2/5)] / (6/20) + 1 LIV | 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

$$[ ( \frac { 2 } { 4 } - \frac { 1 } { 3 } ) \cdot \frac { 3 } { 2 } + ( \frac { 2 } { 6 } - \frac { 1 } { 4 } ) \cdot ( 1 - \frac { 2 } { 5 } ) ] : \frac { 6 } { 20 } + 1$$

Evaluate

$2$

Solution Steps

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

$$\frac{\left(\frac{1}{2}-\frac{1}{3}\right)\times \frac{3}{2}+\left(\frac{2}{6}-\frac{1}{4}\right)\left(1-\frac{2}{5}\right)}{\frac{6}{20}}+1$$

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

$$\frac{\left(\frac{3}{6}-\frac{2}{6}\right)\times \frac{3}{2}+\left(\frac{2}{6}-\frac{1}{4}\right)\left(1-\frac{2}{5}\right)}{\frac{6}{20}}+1$$

Since $\frac{3}{6}$ and $\frac{2}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-2}{6}\times \frac{3}{2}+\left(\frac{2}{6}-\frac{1}{4}\right)\left(1-\frac{2}{5}\right)}{\frac{6}{20}}+1$$

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

$$\frac{\frac{1}{6}\times \frac{3}{2}+\left(\frac{2}{6}-\frac{1}{4}\right)\left(1-\frac{2}{5}\right)}{\frac{6}{20}}+1$$

Multiply $\frac{1}{6}$ times $\frac{3}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 3}{6\times 2}+\left(\frac{2}{6}-\frac{1}{4}\right)\left(1-\frac{2}{5}\right)}{\frac{6}{20}}+1$$

Do the multiplications in the fraction $\frac{1\times 3}{6\times 2}$.

$$\frac{\frac{3}{12}+\left(\frac{2}{6}-\frac{1}{4}\right)\left(1-\frac{2}{5}\right)}{\frac{6}{20}}+1$$

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

$$\frac{\frac{1}{4}+\left(\frac{2}{6}-\frac{1}{4}\right)\left(1-\frac{2}{5}\right)}{\frac{6}{20}}+1$$

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

$$\frac{\frac{1}{4}+\left(\frac{1}{3}-\frac{1}{4}\right)\left(1-\frac{2}{5}\right)}{\frac{6}{20}}+1$$

Least common multiple of $3$ and $4$ is $12$. Convert $\frac{1}{3}$ and $\frac{1}{4}$ to fractions with denominator $12$.

$$\frac{\frac{1}{4}+\left(\frac{4}{12}-\frac{3}{12}\right)\left(1-\frac{2}{5}\right)}{\frac{6}{20}}+1$$

Since $\frac{4}{12}$ and $\frac{3}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{4}+\frac{4-3}{12}\left(1-\frac{2}{5}\right)}{\frac{6}{20}}+1$$

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

$$\frac{\frac{1}{4}+\frac{1}{12}\left(1-\frac{2}{5}\right)}{\frac{6}{20}}+1$$

Convert $1$ to fraction $\frac{5}{5}$.

$$\frac{\frac{1}{4}+\frac{1}{12}\left(\frac{5}{5}-\frac{2}{5}\right)}{\frac{6}{20}}+1$$

Since $\frac{5}{5}$ and $\frac{2}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{4}+\frac{1}{12}\times \frac{5-2}{5}}{\frac{6}{20}}+1$$

Subtract $2$ from $5$ to get $3$.

$$\frac{\frac{1}{4}+\frac{1}{12}\times \frac{3}{5}}{\frac{6}{20}}+1$$

Multiply $\frac{1}{12}$ times $\frac{3}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{4}+\frac{1\times 3}{12\times 5}}{\frac{6}{20}}+1$$

Do the multiplications in the fraction $\frac{1\times 3}{12\times 5}$.

$$\frac{\frac{1}{4}+\frac{3}{60}}{\frac{6}{20}}+1$$

Reduce the fraction $\frac{3}{60}$ to lowest terms by extracting and canceling out $3$.

$$\frac{\frac{1}{4}+\frac{1}{20}}{\frac{6}{20}}+1$$

Least common multiple of $4$ and $20$ is $20$. Convert $\frac{1}{4}$ and $\frac{1}{20}$ to fractions with denominator $20$.

$$\frac{\frac{5}{20}+\frac{1}{20}}{\frac{6}{20}}+1$$

Since $\frac{5}{20}$ and $\frac{1}{20}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+1}{20}}{\frac{6}{20}}+1$$

Add $5$ and $1$ to get $6$.

$$\frac{\frac{6}{20}}{\frac{6}{20}}+1$$

Reduce the fraction $\frac{6}{20}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{3}{10}}{\frac{6}{20}}+1$$

Reduce the fraction $\frac{6}{20}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{3}{10}}{\frac{3}{10}}+1$$

Divide $\frac{3}{10}$ by $\frac{3}{10}$ to get $1$.

$$1+1$$

Add $1$ and $1$ to get $2$.

$$2$$

Factor

$2$