Solve 1/2+3/8+11/2+17/8+frac{3}{4}

$$\frac{ 1 }{ 2 } + \frac{ 3 }{ 8 } +1 \frac{ 1 }{ 2 } +1 \frac{ 7 }{ 8 } + \frac{ 3 }{ 4 }$$

Evaluate

$$5$$

Solution Steps

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{3}{8} to fractions with denominator 8.

$$\frac{4}{8}+\frac{3}{8}+\frac{1\times 2+1}{2}+\frac{1\times 8+7}{8}+\frac{3}{4}$$

Since \frac{4}{8} and \frac{3}{8} have the same denominator, add them by adding their numerators.

$$\frac{4+3}{8}+\frac{1\times 2+1}{2}+\frac{1\times 8+7}{8}+\frac{3}{4}$$

Add 4 and 3 to get 7.

$$\frac{7}{8}+\frac{1\times 2+1}{2}+\frac{1\times 8+7}{8}+\frac{3}{4}$$

Multiply 1 and 2 to get 2.

$$\frac{7}{8}+\frac{2+1}{2}+\frac{1\times 8+7}{8}+\frac{3}{4}$$

Add 2 and 1 to get 3.

$$\frac{7}{8}+\frac{3}{2}+\frac{1\times 8+7}{8}+\frac{3}{4}$$

Least common multiple of 8 and 2 is 8. Convert \frac{7}{8} and \frac{3}{2} to fractions with denominator 8.

$$\frac{7}{8}+\frac{12}{8}+\frac{1\times 8+7}{8}+\frac{3}{4}$$

Since \frac{7}{8} and \frac{12}{8} have the same denominator, add them by adding their numerators.

$$\frac{7+12}{8}+\frac{1\times 8+7}{8}+\frac{3}{4}$$

Add 7 and 12 to get 19.

$$\frac{19}{8}+\frac{1\times 8+7}{8}+\frac{3}{4}$$

Multiply 1 and 8 to get 8.

$$\frac{19}{8}+\frac{8+7}{8}+\frac{3}{4}$$

Add 8 and 7 to get 15.

$$\frac{19}{8}+\frac{15}{8}+\frac{3}{4}$$

Since \frac{19}{8} and \frac{15}{8} have the same denominator, add them by adding their numerators.

$$\frac{19+15}{8}+\frac{3}{4}$$

Add 19 and 15 to get 34.

$$\frac{34}{8}+\frac{3}{4}$$

Reduce the fraction \frac{34}{8} to lowest terms by extracting and canceling out 2.

$$\frac{17}{4}+\frac{3}{4}$$

Since \frac{17}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{17+3}{4}$$

Add 17 and 3 to get 20.

$$\frac{20}{4}$$

Divide 20 by 4 to get 5.

$$5$$

Factor

$$5$$