Solve 9/6+1/4+3/2+4/8+frac{8}{4}+frac{8}{4}

$$\frac{ 9 }{ 6 } + \frac{ 1 }{ 4 } + \frac{ 3 }{ 2 } + \frac{ 4 }{ 8 } + \frac{ 8 }{ 4 } + \frac{ 8 }{ 4 }$$

Evaluate

$$\frac{31}{4}=7.75$$

Solution Steps

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

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

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{6}{4}+\frac{1}{4}+\frac{3}{2}+\frac{4}{8}+\frac{8}{4}+\frac{8}{4}$$

Since \frac{6}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{6+1}{4}+\frac{3}{2}+\frac{4}{8}+\frac{8}{4}+\frac{8}{4}$$

Add 6 and 1 to get 7.

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

Least common multiple of 4 and 2 is 4. Convert \frac{7}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{7}{4}+\frac{6}{4}+\frac{4}{8}+\frac{8}{4}+\frac{8}{4}$$

Since \frac{7}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{7+6}{4}+\frac{4}{8}+\frac{8}{4}+\frac{8}{4}$$

Add 7 and 6 to get 13.

$$\frac{13}{4}+\frac{4}{8}+\frac{8}{4}+\frac{8}{4}$$

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

$$\frac{13}{4}+\frac{1}{2}+\frac{8}{4}+\frac{8}{4}$$

Least common multiple of 4 and 2 is 4. Convert \frac{13}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{13}{4}+\frac{2}{4}+\frac{8}{4}+\frac{8}{4}$$

Since \frac{13}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{13+2}{4}+\frac{8}{4}+\frac{8}{4}$$

Add 13 and 2 to get 15.

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

Since \frac{15}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

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

Add 15 and 8 to get 23.

$$\frac{23}{4}+\frac{8}{4}$$

Since \frac{23}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\frac{23+8}{4}$$

Add 23 and 8 to get 31.

$$\frac{31}{4}$$

Factor

$$\frac{31}{2 ^ {2}} = 7\frac{3}{4} = 7.75$$