Solve 2 1/2 + [3 1/3 - \{45/6 - (1 1/3 - 1 1/2 + 5/12)\}]

Question

$$2\frac{1}{2}+[3\frac{1}{3}-\{\frac{45}{6}-(1\frac{1}{3}-1\frac{1}{2}+\frac{5}{12})\}]$$

Evaluate

$-\frac{17}{12}\approx -1.416666667$

Solution Steps

Multiply $2$ and $2$ to get $4$.

$$\frac{4+1}{2}+\frac{3\times 3+1}{3}-\left(\frac{45}{6}-\left(\frac{1\times 3+1}{3}-\frac{1\times 2+1}{2}+\frac{5}{12}\right)\right)$$

Add $4$ and $1$ to get $5$.

$$\frac{5}{2}+\frac{3\times 3+1}{3}-\left(\frac{45}{6}-\left(\frac{1\times 3+1}{3}-\frac{1\times 2+1}{2}+\frac{5}{12}\right)\right)$$

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

$$\frac{5}{2}+\frac{9+1}{3}-\left(\frac{45}{6}-\left(\frac{1\times 3+1}{3}-\frac{1\times 2+1}{2}+\frac{5}{12}\right)\right)$$

Add $9$ and $1$ to get $10$.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{45}{6}-\left(\frac{1\times 3+1}{3}-\frac{1\times 2+1}{2}+\frac{5}{12}\right)\right)$$

Reduce the fraction $\frac{45}{6}$ to lowest terms by extracting and canceling out $3$.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{15}{2}-\left(\frac{1\times 3+1}{3}-\frac{1\times 2+1}{2}+\frac{5}{12}\right)\right)$$

Multiply $1$ and $3$ to get $3$.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{15}{2}-\left(\frac{3+1}{3}-\frac{1\times 2+1}{2}+\frac{5}{12}\right)\right)$$

Add $3$ and $1$ to get $4$.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{15}{2}-\left(\frac{4}{3}-\frac{1\times 2+1}{2}+\frac{5}{12}\right)\right)$$

Multiply $1$ and $2$ to get $2$.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{15}{2}-\left(\frac{4}{3}-\frac{2+1}{2}+\frac{5}{12}\right)\right)$$

Add $2$ and $1$ to get $3$.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{15}{2}-\left(\frac{4}{3}-\frac{3}{2}+\frac{5}{12}\right)\right)$$

Least common multiple of $3$ and $2$ is $6$. Convert $\frac{4}{3}$ and $\frac{3}{2}$ to fractions with denominator $6$.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{15}{2}-\left(\frac{8}{6}-\frac{9}{6}+\frac{5}{12}\right)\right)$$

Since $\frac{8}{6}$ and $\frac{9}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{15}{2}-\left(\frac{8-9}{6}+\frac{5}{12}\right)\right)$$

Subtract $9$ from $8$ to get $-1$.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{15}{2}-\left(-\frac{1}{6}+\frac{5}{12}\right)\right)$$

Least common multiple of $6$ and $12$ is $12$. Convert $-\frac{1}{6}$ and $\frac{5}{12}$ to fractions with denominator $12$.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{15}{2}-\left(-\frac{2}{12}+\frac{5}{12}\right)\right)$$

Since $-\frac{2}{12}$ and $\frac{5}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{15}{2}-\frac{-2+5}{12}\right)$$

Add $-2$ and $5$ to get $3$.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{15}{2}-\frac{3}{12}\right)$$

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

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{15}{2}-\frac{1}{4}\right)$$

Least common multiple of $2$ and $4$ is $4$. Convert $\frac{15}{2}$ and $\frac{1}{4}$ to fractions with denominator $4$.

$$\frac{5}{2}+\frac{10}{3}-\left(\frac{30}{4}-\frac{1}{4}\right)$$

Since $\frac{30}{4}$ and $\frac{1}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{2}+\frac{10}{3}-\frac{30-1}{4}$$

Subtract $1$ from $30$ to get $29$.

$$\frac{5}{2}+\frac{10}{3}-\frac{29}{4}$$

Least common multiple of $3$ and $4$ is $12$. Convert $\frac{10}{3}$ and $\frac{29}{4}$ to fractions with denominator $12$.

$$\frac{5}{2}+\frac{40}{12}-\frac{87}{12}$$

Since $\frac{40}{12}$ and $\frac{87}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{2}+\frac{40-87}{12}$$

Subtract $87$ from $40$ to get $-47$.

$$\frac{5}{2}-\frac{47}{12}$$

Least common multiple of $2$ and $12$ is $12$. Convert $\frac{5}{2}$ and $\frac{47}{12}$ to fractions with denominator $12$.

$$\frac{30}{12}-\frac{47}{12}$$

Since $\frac{30}{12}$ and $\frac{47}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{30-47}{12}$$

Subtract $47$ from $30$ to get $-17$.

$$-\frac{17}{12}$$

Show Solution

Factor

$-\frac{17}{12} = -1\frac{5}{12} = -1.4166666666666667$

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