Solve 2(2)/(3)-(-(7)/(9)-(3)/(7))+(-(6)/(7)+(5)/(7))-3(2)/(3)((3)/(4)-(5)/(7)) | 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

$$2 \frac{ 2 }{ 3 } -(- \frac{ 7 }{ 9 } - \frac{ 3 }{ 7 } )+(- \frac{ 6 }{ 7 } + \frac{ 5 }{ 7 } )-3 \frac{ 2 }{ 3 } ( \frac{ 3 }{ 4 } - \frac{ 5 }{ 7 } )$$

Evaluate

$\frac{907}{252}\approx 3.599206349$

Solution Steps

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

$$\frac{6+2}{3}-\left(-\frac{7}{9}-\frac{3}{7}\right)-\frac{6}{7}+\frac{5}{7}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

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

$$\frac{8}{3}-\left(-\frac{7}{9}-\frac{3}{7}\right)-\frac{6}{7}+\frac{5}{7}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Least common multiple of $9$ and $7$ is $63$. Convert $-\frac{7}{9}$ and $\frac{3}{7}$ to fractions with denominator $63$.

$$\frac{8}{3}-\left(-\frac{49}{63}-\frac{27}{63}\right)-\frac{6}{7}+\frac{5}{7}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Since $-\frac{49}{63}$ and $\frac{27}{63}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{3}-\frac{-49-27}{63}-\frac{6}{7}+\frac{5}{7}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Subtract $27$ from $-49$ to get $-76$.

$$\frac{8}{3}-\left(-\frac{76}{63}\right)-\frac{6}{7}+\frac{5}{7}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

The opposite of $-\frac{76}{63}$ is $\frac{76}{63}$.

$$\frac{8}{3}+\frac{76}{63}-\frac{6}{7}+\frac{5}{7}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Least common multiple of $3$ and $63$ is $63$. Convert $\frac{8}{3}$ and $\frac{76}{63}$ to fractions with denominator $63$.

$$\frac{168}{63}+\frac{76}{63}-\frac{6}{7}+\frac{5}{7}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Since $\frac{168}{63}$ and $\frac{76}{63}$ have the same denominator, add them by adding their numerators.

$$\frac{168+76}{63}-\frac{6}{7}+\frac{5}{7}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Add $168$ and $76$ to get $244$.

$$\frac{244}{63}-\frac{6}{7}+\frac{5}{7}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Least common multiple of $63$ and $7$ is $63$. Convert $\frac{244}{63}$ and $\frac{6}{7}$ to fractions with denominator $63$.

$$\frac{244}{63}-\frac{54}{63}+\frac{5}{7}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Since $\frac{244}{63}$ and $\frac{54}{63}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{244-54}{63}+\frac{5}{7}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Subtract $54$ from $244$ to get $190$.

$$\frac{190}{63}+\frac{5}{7}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Least common multiple of $63$ and $7$ is $63$. Convert $\frac{190}{63}$ and $\frac{5}{7}$ to fractions with denominator $63$.

$$\frac{190}{63}+\frac{45}{63}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Since $\frac{190}{63}$ and $\frac{45}{63}$ have the same denominator, add them by adding their numerators.

$$\frac{190+45}{63}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Add $190$ and $45$ to get $235$.

$$\frac{235}{63}-\frac{3\times 3+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Multiply $3$ and $3$ to get $9$.

$$\frac{235}{63}-\frac{9+2}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Add $9$ and $2$ to get $11$.

$$\frac{235}{63}-\frac{11}{3}\left(\frac{3}{4}-\frac{5}{7}\right)$$

Least common multiple of $4$ and $7$ is $28$. Convert $\frac{3}{4}$ and $\frac{5}{7}$ to fractions with denominator $28$.

$$\frac{235}{63}-\frac{11}{3}\left(\frac{21}{28}-\frac{20}{28}\right)$$

Since $\frac{21}{28}$ and $\frac{20}{28}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{235}{63}-\frac{11}{3}\times \frac{21-20}{28}$$

Subtract $20$ from $21$ to get $1$.

$$\frac{235}{63}-\frac{11}{3}\times \frac{1}{28}$$

Multiply $\frac{11}{3}$ times $\frac{1}{28}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{235}{63}-\frac{11\times 1}{3\times 28}$$

Do the multiplications in the fraction $\frac{11\times 1}{3\times 28}$.

$$\frac{235}{63}-\frac{11}{84}$$

Least common multiple of $63$ and $84$ is $252$. Convert $\frac{235}{63}$ and $\frac{11}{84}$ to fractions with denominator $252$.

$$\frac{940}{252}-\frac{33}{252}$$

Since $\frac{940}{252}$ and $\frac{33}{252}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{940-33}{252}$$

Subtract $33$ from $940$ to get $907$.

$$\frac{907}{252}$$

Factor

$\frac{907}{2 ^ {2} \cdot 3 ^ {2} \cdot 7} = 3\frac{151}{252} = 3.5992063492063493$