Solve 41/4+7/8+21/2+31/4+frac{1}{2}+5frac{1}{8}

$$4 \frac { 1 } { 4 } + \frac { 7 } { 8 } + 2 \frac { 1 } { 2 } + 3 \frac { 1 } { 4 } + \frac { 1 } { 2 } + 5 \frac { 1 } { 8 }$$

Evaluate

$$\frac{33}{2}=16.5$$

Solution Steps

Multiply 4 and 4 to get 16.

$$\frac{16+1}{4}+\frac{7}{8}+\frac{2\times 2+1}{2}+\frac{3\times 4+1}{4}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Add 16 and 1 to get 17.

$$\frac{17}{4}+\frac{7}{8}+\frac{2\times 2+1}{2}+\frac{3\times 4+1}{4}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Least common multiple of 4 and 8 is 8. Convert \frac{17}{4} and \frac{7}{8} to fractions with denominator 8.

$$\frac{34}{8}+\frac{7}{8}+\frac{2\times 2+1}{2}+\frac{3\times 4+1}{4}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Since \frac{34}{8} and \frac{7}{8} have the same denominator, add them by adding their numerators.

$$\frac{34+7}{8}+\frac{2\times 2+1}{2}+\frac{3\times 4+1}{4}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Add 34 and 7 to get 41.

$$\frac{41}{8}+\frac{2\times 2+1}{2}+\frac{3\times 4+1}{4}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Multiply 2 and 2 to get 4.

$$\frac{41}{8}+\frac{4+1}{2}+\frac{3\times 4+1}{4}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Add 4 and 1 to get 5.

$$\frac{41}{8}+\frac{5}{2}+\frac{3\times 4+1}{4}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Least common multiple of 8 and 2 is 8. Convert \frac{41}{8} and \frac{5}{2} to fractions with denominator 8.

$$\frac{41}{8}+\frac{20}{8}+\frac{3\times 4+1}{4}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Since \frac{41}{8} and \frac{20}{8} have the same denominator, add them by adding their numerators.

$$\frac{41+20}{8}+\frac{3\times 4+1}{4}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Add 41 and 20 to get 61.

$$\frac{61}{8}+\frac{3\times 4+1}{4}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Multiply 3 and 4 to get 12.

$$\frac{61}{8}+\frac{12+1}{4}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Add 12 and 1 to get 13.

$$\frac{61}{8}+\frac{13}{4}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Least common multiple of 8 and 4 is 8. Convert \frac{61}{8} and \frac{13}{4} to fractions with denominator 8.

$$\frac{61}{8}+\frac{26}{8}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Since \frac{61}{8} and \frac{26}{8} have the same denominator, add them by adding their numerators.

$$\frac{61+26}{8}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Add 61 and 26 to get 87.

$$\frac{87}{8}+\frac{1}{2}+\frac{5\times 8+1}{8}$$

Least common multiple of 8 and 2 is 8. Convert \frac{87}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{87}{8}+\frac{4}{8}+\frac{5\times 8+1}{8}$$

Since \frac{87}{8} and \frac{4}{8} have the same denominator, add them by adding their numerators.

$$\frac{87+4}{8}+\frac{5\times 8+1}{8}$$

Add 87 and 4 to get 91.

$$\frac{91}{8}+\frac{5\times 8+1}{8}$$

Multiply 5 and 8 to get 40.

$$\frac{91}{8}+\frac{40+1}{8}$$

Add 40 and 1 to get 41.

$$\frac{91}{8}+\frac{41}{8}$$

Since \frac{91}{8} and \frac{41}{8} have the same denominator, add them by adding their numerators.

$$\frac{91+41}{8}$$

Add 91 and 41 to get 132.

$$\frac{132}{8}$$

Reduce the fraction \frac{132}{8} to lowest terms by extracting and canceling out 4.

$$\frac{33}{2}$$

Factor

$$\frac{3 \cdot 11}{2} = 16\frac{1}{2} = 16.5$$