Solve 0+1/4+1/2+3/4+1+frac{5/4+frac{6}{4}}{7}

$$\frac { 0 + \frac { 1 } { 4 } + \frac { 1 } { 2 } + \frac { 3 } { 4 } + 1 + \frac { 5 } { 4 } + \frac { 6 } { 4 } } { 7 }$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Add 0 and \frac{1}{4} to get \frac{1}{4}.

$$\frac{\frac{1}{4}+\frac{1}{2}+\frac{3}{4}+1+\frac{5}{4}+\frac{6}{4}}{7}$$

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

$$\frac{\frac{1}{4}+\frac{2}{4}+\frac{3}{4}+1+\frac{5}{4}+\frac{6}{4}}{7}$$

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

$$\frac{\frac{1+2}{4}+\frac{3}{4}+1+\frac{5}{4}+\frac{6}{4}}{7}$$

Add 1 and 2 to get 3.

$$\frac{\frac{3}{4}+\frac{3}{4}+1+\frac{5}{4}+\frac{6}{4}}{7}$$

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

$$\frac{\frac{3+3}{4}+1+\frac{5}{4}+\frac{6}{4}}{7}$$

Add 3 and 3 to get 6.

$$\frac{\frac{6}{4}+1+\frac{5}{4}+\frac{6}{4}}{7}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{2}+1+\frac{5}{4}+\frac{6}{4}}{7}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{\frac{3}{2}+\frac{2}{2}+\frac{5}{4}+\frac{6}{4}}{7}$$

Since \frac{3}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+2}{2}+\frac{5}{4}+\frac{6}{4}}{7}$$

Add 3 and 2 to get 5.

$$\frac{\frac{5}{2}+\frac{5}{4}+\frac{6}{4}}{7}$$

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{5}{4} to fractions with denominator 4.

$$\frac{\frac{10}{4}+\frac{5}{4}+\frac{6}{4}}{7}$$

Since \frac{10}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10+5}{4}+\frac{6}{4}}{7}$$

Add 10 and 5 to get 15.

$$\frac{\frac{15}{4}+\frac{6}{4}}{7}$$

Since \frac{15}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15+6}{4}}{7}$$

Add 15 and 6 to get 21.

$$\frac{\frac{21}{4}}{7}$$

Express \frac{\frac{21}{4}}{7} as a single fraction.

$$\frac{21}{4\times 7}$$

Multiply 4 and 7 to get 28.

$$\frac{21}{28}$$

Reduce the fraction \frac{21}{28} to lowest terms by extracting and canceling out 7.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$