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

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

Evaluate

$$\frac{5}{16}=0.3125$$

Solution Steps

Multiply 1 and 4 to get 4.

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

Multiply 4 and 7 to get 28.

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

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

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

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

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

Add 7 and 1 to get 8.

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

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

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

Multiply 7 and 10 to get 70.

$$\frac{2}{7}+\frac{1}{70}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Least common multiple of 7 and 70 is 70. Convert \frac{2}{7} and \frac{1}{70} to fractions with denominator 70.

$$\frac{20}{70}+\frac{1}{70}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Since \frac{20}{70} and \frac{1}{70} have the same denominator, add them by adding their numerators.

$$\frac{20+1}{70}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Add 20 and 1 to get 21.

$$\frac{21}{70}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Reduce the fraction \frac{21}{70} to lowest terms by extracting and canceling out 7.

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

Multiply 10 and 13 to get 130.

$$\frac{3}{10}+\frac{1}{130}+\frac{1}{13\times 16}$$

Least common multiple of 10 and 130 is 130. Convert \frac{3}{10} and \frac{1}{130} to fractions with denominator 130.

$$\frac{39}{130}+\frac{1}{130}+\frac{1}{13\times 16}$$

Since \frac{39}{130} and \frac{1}{130} have the same denominator, add them by adding their numerators.

$$\frac{39+1}{130}+\frac{1}{13\times 16}$$

Add 39 and 1 to get 40.

$$\frac{40}{130}+\frac{1}{13\times 16}$$

Reduce the fraction \frac{40}{130} to lowest terms by extracting and canceling out 10.

$$\frac{4}{13}+\frac{1}{13\times 16}$$

Multiply 13 and 16 to get 208.

$$\frac{4}{13}+\frac{1}{208}$$

Least common multiple of 13 and 208 is 208. Convert \frac{4}{13} and \frac{1}{208} to fractions with denominator 208.

$$\frac{64}{208}+\frac{1}{208}$$

Since \frac{64}{208} and \frac{1}{208} have the same denominator, add them by adding their numerators.

$$\frac{64+1}{208}$$

Add 64 and 1 to get 65.

$$\frac{65}{208}$$

Reduce the fraction \frac{65}{208} to lowest terms by extracting and canceling out 13.

$$\frac{5}{16}$$

Factor

$$\frac{5}{2 ^ {4}} = 0.3125$$