Solve ((5)/(6)-(3)/(5)+(7)/(6))\times(2(2)/(3)+(3)/(4)-2(1)/(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

$$( \frac{ 5 }{ 6 } - \frac{ 3 }{ 5 } + \frac{ 7 }{ 6 } ) \times (2 \frac{ 2 }{ 3 } + \frac{ 3 }{ 4 } -2 \frac{ 1 }{ 5 } )$$

Evaluate

$\frac{511}{300}\approx 1.703333333$

Solution Steps

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

$$\left(\frac{25}{30}-\frac{18}{30}+\frac{7}{6}\right)\left(\frac{2\times 3+2}{3}+\frac{3}{4}-\frac{2\times 5+1}{5}\right)$$

Since $\frac{25}{30}$ and $\frac{18}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{25-18}{30}+\frac{7}{6}\right)\left(\frac{2\times 3+2}{3}+\frac{3}{4}-\frac{2\times 5+1}{5}\right)$$

Subtract $18$ from $25$ to get $7$.

$$\left(\frac{7}{30}+\frac{7}{6}\right)\left(\frac{2\times 3+2}{3}+\frac{3}{4}-\frac{2\times 5+1}{5}\right)$$

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

$$\left(\frac{7}{30}+\frac{35}{30}\right)\left(\frac{2\times 3+2}{3}+\frac{3}{4}-\frac{2\times 5+1}{5}\right)$$

Since $\frac{7}{30}$ and $\frac{35}{30}$ have the same denominator, add them by adding their numerators.

$$\frac{7+35}{30}\left(\frac{2\times 3+2}{3}+\frac{3}{4}-\frac{2\times 5+1}{5}\right)$$

Add $7$ and $35$ to get $42$.

$$\frac{42}{30}\left(\frac{2\times 3+2}{3}+\frac{3}{4}-\frac{2\times 5+1}{5}\right)$$

Reduce the fraction $\frac{42}{30}$ to lowest terms by extracting and canceling out $6$.

$$\frac{7}{5}\left(\frac{2\times 3+2}{3}+\frac{3}{4}-\frac{2\times 5+1}{5}\right)$$

Multiply $2$ and $3$ to get $6$.

$$\frac{7}{5}\left(\frac{6+2}{3}+\frac{3}{4}-\frac{2\times 5+1}{5}\right)$$

Add $6$ and $2$ to get $8$.

$$\frac{7}{5}\left(\frac{8}{3}+\frac{3}{4}-\frac{2\times 5+1}{5}\right)$$

Least common multiple of $3$ and $4$ is $12$. Convert $\frac{8}{3}$ and $\frac{3}{4}$ to fractions with denominator $12$.

$$\frac{7}{5}\left(\frac{32}{12}+\frac{9}{12}-\frac{2\times 5+1}{5}\right)$$

Since $\frac{32}{12}$ and $\frac{9}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{7}{5}\left(\frac{32+9}{12}-\frac{2\times 5+1}{5}\right)$$

Add $32$ and $9$ to get $41$.

$$\frac{7}{5}\left(\frac{41}{12}-\frac{2\times 5+1}{5}\right)$$

Multiply $2$ and $5$ to get $10$.

$$\frac{7}{5}\left(\frac{41}{12}-\frac{10+1}{5}\right)$$

Add $10$ and $1$ to get $11$.

$$\frac{7}{5}\left(\frac{41}{12}-\frac{11}{5}\right)$$

Least common multiple of $12$ and $5$ is $60$. Convert $\frac{41}{12}$ and $\frac{11}{5}$ to fractions with denominator $60$.

$$\frac{7}{5}\left(\frac{205}{60}-\frac{132}{60}\right)$$

Since $\frac{205}{60}$ and $\frac{132}{60}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{5}\times \frac{205-132}{60}$$

Subtract $132$ from $205$ to get $73$.

$$\frac{7}{5}\times \frac{73}{60}$$

Multiply $\frac{7}{5}$ times $\frac{73}{60}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 73}{5\times 60}$$

Do the multiplications in the fraction $\frac{7\times 73}{5\times 60}$.

$$\frac{511}{300}$$

Factor

$\frac{7 \cdot 73}{2 ^ {2} \cdot 3 \cdot 5 ^ {2}} = 1\frac{211}{300} = 1.7033333333333334$