Solve (1+(7)/(3)-(16)/(27)+(75)/(18)+12-17+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

$$(1+ \frac{ 7 }{ 3 } - \frac{ 16 }{ 27 } + \frac{ 75 }{ 18 } +12-17+5)$$

Evaluate

$\frac{373}{54}\approx 6.907407407$

Solution Steps

Convert $1$ to fraction $\frac{3}{3}$.

$$\frac{3}{3}+\frac{7}{3}-\frac{16}{27}+\frac{75}{18}+12-17+5$$

Since $\frac{3}{3}$ and $\frac{7}{3}$ have the same denominator, add them by adding their numerators.

$$\frac{3+7}{3}-\frac{16}{27}+\frac{75}{18}+12-17+5$$

Add $3$ and $7$ to get $10$.

$$\frac{10}{3}-\frac{16}{27}+\frac{75}{18}+12-17+5$$

Least common multiple of $3$ and $27$ is $27$. Convert $\frac{10}{3}$ and $\frac{16}{27}$ to fractions with denominator $27$.

$$\frac{90}{27}-\frac{16}{27}+\frac{75}{18}+12-17+5$$

Since $\frac{90}{27}$ and $\frac{16}{27}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{90-16}{27}+\frac{75}{18}+12-17+5$$

Subtract $16$ from $90$ to get $74$.

$$\frac{74}{27}+\frac{75}{18}+12-17+5$$

Reduce the fraction $\frac{75}{18}$ to lowest terms by extracting and canceling out $3$.

$$\frac{74}{27}+\frac{25}{6}+12-17+5$$

Least common multiple of $27$ and $6$ is $54$. Convert $\frac{74}{27}$ and $\frac{25}{6}$ to fractions with denominator $54$.

$$\frac{148}{54}+\frac{225}{54}+12-17+5$$

Since $\frac{148}{54}$ and $\frac{225}{54}$ have the same denominator, add them by adding their numerators.

$$\frac{148+225}{54}+12-17+5$$

Add $148$ and $225$ to get $373$.

$$\frac{373}{54}+12-17+5$$

Convert $12$ to fraction $\frac{648}{54}$.

$$\frac{373}{54}+\frac{648}{54}-17+5$$

Since $\frac{373}{54}$ and $\frac{648}{54}$ have the same denominator, add them by adding their numerators.

$$\frac{373+648}{54}-17+5$$

Add $373$ and $648$ to get $1021$.

$$\frac{1021}{54}-17+5$$

Convert $17$ to fraction $\frac{918}{54}$.

$$\frac{1021}{54}-\frac{918}{54}+5$$

Since $\frac{1021}{54}$ and $\frac{918}{54}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1021-918}{54}+5$$

Subtract $918$ from $1021$ to get $103$.

$$\frac{103}{54}+5$$

Convert $5$ to fraction $\frac{270}{54}$.

$$\frac{103}{54}+\frac{270}{54}$$

Since $\frac{103}{54}$ and $\frac{270}{54}$ have the same denominator, add them by adding their numerators.

$$\frac{103+270}{54}$$

Add $103$ and $270$ to get $373$.

$$\frac{373}{54}$$

Factor

$\frac{373}{2 \cdot 3 ^ {3}} = 6\frac{49}{54} = 6.907407407407407$