Solve (1/1*4+1/4*7+1/7*1+1/10*13+frac{1}{13-16})=

$$( \frac { 1 } { 1 \cdot 4 } + \frac { 1 } { 4 \cdot 7 } + \frac { 1 } { 7 \cdot 1 } + \frac { 1 } { 10 \cdot 13 } + \frac { 1 } { 13 - 16 } ) =$$

Evaluate

$$\frac{281}{2730}\approx 0.102930403$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{1}{4}+\frac{1}{4\times 7}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Multiply 4 and 7 to get 28.

$$\frac{1}{4}+\frac{1}{28}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Least common multiple of 4 and 28 is 28. Convert \frac{1}{4} and \frac{1}{28} to fractions with denominator 28.

$$\frac{7}{28}+\frac{1}{28}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Since \frac{7}{28} and \frac{1}{28} have the same denominator, add them by adding their numerators.

$$\frac{7+1}{28}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Add 7 and 1 to get 8.

$$\frac{8}{28}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Reduce the fraction \frac{8}{28} to lowest terms by extracting and canceling out 4.

$$\frac{2}{7}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Multiply 7 and 1 to get 7.

$$\frac{2}{7}+\frac{1}{7}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Since \frac{2}{7} and \frac{1}{7} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{7}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Add 2 and 1 to get 3.

$$\frac{3}{7}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Multiply 10 and 13 to get 130.

$$\frac{3}{7}+\frac{1}{130}+\frac{1}{13-16}$$

Least common multiple of 7 and 130 is 910. Convert \frac{3}{7} and \frac{1}{130} to fractions with denominator 910.

$$\frac{390}{910}+\frac{7}{910}+\frac{1}{13-16}$$

Since \frac{390}{910} and \frac{7}{910} have the same denominator, add them by adding their numerators.

$$\frac{390+7}{910}+\frac{1}{13-16}$$

Add 390 and 7 to get 397.

$$\frac{397}{910}+\frac{1}{13-16}$$

Subtract 16 from 13 to get -3.

$$\frac{397}{910}+\frac{1}{-3}$$

Fraction \frac{1}{-3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$\frac{397}{910}-\frac{1}{3}$$

Least common multiple of 910 and 3 is 2730. Convert \frac{397}{910} and \frac{1}{3} to fractions with denominator 2730.

$$\frac{1191}{2730}-\frac{910}{2730}$$

Since \frac{1191}{2730} and \frac{910}{2730} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1191-910}{2730}$$

Subtract 910 from 1191 to get 281.

$$\frac{281}{2730}$$

Factor

$$\frac{281}{2 \cdot 3 \cdot 5 \cdot 7 \cdot 13} = 0.10293040293040293$$