Solve (1)/(2)+1(1)/(2)\div1(1)/(2)\times(2)/(3)-(1)/(4)

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Question

$$\frac{ 1 }{ 2 } +1 \frac{ 1 }{ 2 } \div 1 \frac{ 1 }{ 2 } \times \frac{ 2 }{ 3 } - \frac{ 1 }{ 4 }$$

Evaluate

$\frac{11}{12}\approx 0.916666667$

Solution Steps

Divide $\frac{1\times 2+1}{2}$ by $\frac{1\times 2+1}{2}$ to get $1$.

$$\frac{1}{2}+1\times \frac{2}{3}-\frac{1}{4}$$

Multiply $1$ and $\frac{2}{3}$ to get $\frac{2}{3}$.

$$\frac{1}{2}+\frac{2}{3}-\frac{1}{4}$$

Least common multiple of $2$ and $3$ is $6$. Convert $\frac{1}{2}$ and $\frac{2}{3}$ to fractions with denominator $6$.

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

Since $\frac{3}{6}$ and $\frac{4}{6}$ have the same denominator, add them by adding their numerators.

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

Add $3$ and $4$ to get $7$.

$$\frac{7}{6}-\frac{1}{4}$$

Least common multiple of $6$ and $4$ is $12$. Convert $\frac{7}{6}$ and $\frac{1}{4}$ to fractions with denominator $12$.

$$\frac{14}{12}-\frac{3}{12}$$

Since $\frac{14}{12}$ and $\frac{3}{12}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-3}{12}$$

Subtract $3$ from $14$ to get $11$.

$$\frac{11}{12}$$

Show Solution

Factor

$\frac{11}{2 ^ {2} \cdot 3} = 0.9166666666666666$