Solve 2/4+4/16+6/36+8/64

$$\frac{ 2 }{ 4 } + \frac{ 4 }{ 16 } + \frac{ 6 }{ 36 } + \frac{ 8 }{ 64 }$$

Evaluate

$$\frac{25}{24}\approx 1.041666667$$

Solution Steps

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}+\frac{4}{16}+\frac{6}{36}+\frac{8}{64}$$

Reduce the fraction \frac{4}{16} to lowest terms by extracting and canceling out 4.

$$\frac{1}{2}+\frac{1}{4}+\frac{6}{36}+\frac{8}{64}$$

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

$$\frac{2}{4}+\frac{1}{4}+\frac{6}{36}+\frac{8}{64}$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{4}+\frac{6}{36}+\frac{8}{64}$$

Add 2 and 1 to get 3.

$$\frac{3}{4}+\frac{6}{36}+\frac{8}{64}$$

Reduce the fraction \frac{6}{36} to lowest terms by extracting and canceling out 6.

$$\frac{3}{4}+\frac{1}{6}+\frac{8}{64}$$

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{9}{12}+\frac{2}{12}+\frac{8}{64}$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{9+2}{12}+\frac{8}{64}$$

Add 9 and 2 to get 11.

$$\frac{11}{12}+\frac{8}{64}$$

Reduce the fraction \frac{8}{64} to lowest terms by extracting and canceling out 8.

$$\frac{11}{12}+\frac{1}{8}$$

Least common multiple of 12 and 8 is 24. Convert \frac{11}{12} and \frac{1}{8} to fractions with denominator 24.

$$\frac{22}{24}+\frac{3}{24}$$

Since \frac{22}{24} and \frac{3}{24} have the same denominator, add them by adding their numerators.

$$\frac{22+3}{24}$$

Add 22 and 3 to get 25.

$$\frac{25}{24}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {3} \cdot 3} = 1\frac{1}{24} = 1.0416666666666667$$