Solve 2*3/1*4+5*6/4*7+8*9/7*10+11*12/10*13+frac{14*15}{13*16}=

$$\frac { 2 \times 3 } { 1 \times 4 } + \frac { 5 \times 6 } { 4 \times 7 } + \frac { 8 \times 9 } { 7 \times 10 } + \frac { 11 \times 12 } { 10 \times 13 } + \frac { 14 \times 15 } { 13 \times 16 } =$$

Evaluate

$$\frac{45}{8}=5.625$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{3}{2}+\frac{5\times 6}{4\times 7}+\frac{8\times 9}{7\times 10}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3}{2}+\frac{3\times 5}{2\times 7}+\frac{8\times 9}{7\times 10}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Multiply 3 and 5 to get 15.

$$\frac{3}{2}+\frac{15}{2\times 7}+\frac{8\times 9}{7\times 10}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Multiply 2 and 7 to get 14.

$$\frac{3}{2}+\frac{15}{14}+\frac{8\times 9}{7\times 10}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Least common multiple of 2 and 14 is 14. Convert \frac{3}{2} and \frac{15}{14} to fractions with denominator 14.

$$\frac{21}{14}+\frac{15}{14}+\frac{8\times 9}{7\times 10}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Since \frac{21}{14} and \frac{15}{14} have the same denominator, add them by adding their numerators.

$$\frac{21+15}{14}+\frac{8\times 9}{7\times 10}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Add 21 and 15 to get 36.

$$\frac{36}{14}+\frac{8\times 9}{7\times 10}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Reduce the fraction \frac{36}{14} to lowest terms by extracting and canceling out 2.

$$\frac{18}{7}+\frac{8\times 9}{7\times 10}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Cancel out 2 in both numerator and denominator.

$$\frac{18}{7}+\frac{4\times 9}{5\times 7}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Multiply 4 and 9 to get 36.

$$\frac{18}{7}+\frac{36}{5\times 7}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Multiply 5 and 7 to get 35.

$$\frac{18}{7}+\frac{36}{35}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Least common multiple of 7 and 35 is 35. Convert \frac{18}{7} and \frac{36}{35} to fractions with denominator 35.

$$\frac{90}{35}+\frac{36}{35}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Since \frac{90}{35} and \frac{36}{35} have the same denominator, add them by adding their numerators.

$$\frac{90+36}{35}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Add 90 and 36 to get 126.

$$\frac{126}{35}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Reduce the fraction \frac{126}{35} to lowest terms by extracting and canceling out 7.

$$\frac{18}{5}+\frac{11\times 12}{10\times 13}+\frac{14\times 15}{13\times 16}$$

Cancel out 2 in both numerator and denominator.

$$\frac{18}{5}+\frac{6\times 11}{5\times 13}+\frac{14\times 15}{13\times 16}$$

Multiply 6 and 11 to get 66.

$$\frac{18}{5}+\frac{66}{5\times 13}+\frac{14\times 15}{13\times 16}$$

Multiply 5 and 13 to get 65.

$$\frac{18}{5}+\frac{66}{65}+\frac{14\times 15}{13\times 16}$$

Least common multiple of 5 and 65 is 65. Convert \frac{18}{5} and \frac{66}{65} to fractions with denominator 65.

$$\frac{234}{65}+\frac{66}{65}+\frac{14\times 15}{13\times 16}$$

Since \frac{234}{65} and \frac{66}{65} have the same denominator, add them by adding their numerators.

$$\frac{234+66}{65}+\frac{14\times 15}{13\times 16}$$

Add 234 and 66 to get 300.

$$\frac{300}{65}+\frac{14\times 15}{13\times 16}$$

Reduce the fraction \frac{300}{65} to lowest terms by extracting and canceling out 5.

$$\frac{60}{13}+\frac{14\times 15}{13\times 16}$$

Cancel out 2 in both numerator and denominator.

$$\frac{60}{13}+\frac{7\times 15}{8\times 13}$$

Multiply 7 and 15 to get 105.

$$\frac{60}{13}+\frac{105}{8\times 13}$$

Multiply 8 and 13 to get 104.

$$\frac{60}{13}+\frac{105}{104}$$

Least common multiple of 13 and 104 is 104. Convert \frac{60}{13} and \frac{105}{104} to fractions with denominator 104.

$$\frac{480}{104}+\frac{105}{104}$$

Since \frac{480}{104} and \frac{105}{104} have the same denominator, add them by adding their numerators.

$$\frac{480+105}{104}$$

Add 480 and 105 to get 585.

$$\frac{585}{104}$$

Reduce the fraction \frac{585}{104} to lowest terms by extracting and canceling out 13.

$$\frac{45}{8}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{2 ^ {3}} = 5\frac{5}{8} = 5.625$$