Solve \{1/3 + (3/4 - 5/6)\} + \{1/5 - (1/6 - 1/2)\}

Question

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

Evaluate

$\frac{47}{60}\approx 0.783333333$

Solution Steps

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

$$\frac{4}{12}+\frac{9}{12}-\frac{5}{6}+\frac{1}{5}-\left(\frac{1}{6}-\frac{1}{2}\right)$$

Since $\frac{4}{12}$ and $\frac{9}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{4+9}{12}-\frac{5}{6}+\frac{1}{5}-\left(\frac{1}{6}-\frac{1}{2}\right)$$

Add $4$ and $9$ to get $13$.

$$\frac{13}{12}-\frac{5}{6}+\frac{1}{5}-\left(\frac{1}{6}-\frac{1}{2}\right)$$

Least common multiple of $12$ and $6$ is $12$. Convert $\frac{13}{12}$ and $\frac{5}{6}$ to fractions with denominator $12$.

$$\frac{13}{12}-\frac{10}{12}+\frac{1}{5}-\left(\frac{1}{6}-\frac{1}{2}\right)$$

Since $\frac{13}{12}$ and $\frac{10}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{13-10}{12}+\frac{1}{5}-\left(\frac{1}{6}-\frac{1}{2}\right)$$

Subtract $10$ from $13$ to get $3$.

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

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

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

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

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

Since $\frac{1}{6}$ and $\frac{3}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}+\frac{1}{5}-\frac{1-3}{6}$$

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

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

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

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

The opposite of $-\frac{1}{3}$ is $\frac{1}{3}$.

$$\frac{1}{4}+\frac{1}{5}+\frac{1}{3}$$

Least common multiple of $5$ and $3$ is $15$. Convert $\frac{1}{5}$ and $\frac{1}{3}$ to fractions with denominator $15$.

$$\frac{1}{4}+\frac{3}{15}+\frac{5}{15}$$

Since $\frac{3}{15}$ and $\frac{5}{15}$ have the same denominator, add them by adding their numerators.

$$\frac{1}{4}+\frac{3+5}{15}$$

Add $3$ and $5$ to get $8$.

$$\frac{1}{4}+\frac{8}{15}$$

Least common multiple of $4$ and $15$ is $60$. Convert $\frac{1}{4}$ and $\frac{8}{15}$ to fractions with denominator $60$.

$$\frac{15}{60}+\frac{32}{60}$$

Since $\frac{15}{60}$ and $\frac{32}{60}$ have the same denominator, add them by adding their numerators.

$$\frac{15+32}{60}$$

Add $15$ and $32$ to get $47$.

$$\frac{47}{60}$$

Show Solution

Factor

$\frac{47}{2 ^ {2} \cdot 3 \cdot 5} = 0.7833333333333333$

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Evaluate

Solution Steps

Factor