Solve 2*3/1*4+5*6/4*7+8*4/7*10

$$\frac { 2 \times 3 } { 1 \times 4 } + \frac { 5 \times 6 } { 4 \times 7 } + \frac { 8 \times 4 } { 7 \times 10 }$$

Evaluate

$$\frac{106}{35}\approx 3.028571429$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{3}{2}+\frac{5\times 6}{4\times 7}+\frac{8\times 4}{7\times 10}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3}{2}+\frac{3\times 5}{2\times 7}+\frac{8\times 4}{7\times 10}$$

Multiply 3 and 5 to get 15.

$$\frac{3}{2}+\frac{15}{2\times 7}+\frac{8\times 4}{7\times 10}$$

Multiply 2 and 7 to get 14.

$$\frac{3}{2}+\frac{15}{14}+\frac{8\times 4}{7\times 10}$$

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

$$\frac{21}{14}+\frac{15}{14}+\frac{8\times 4}{7\times 10}$$

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

$$\frac{21+15}{14}+\frac{8\times 4}{7\times 10}$$

Add 21 and 15 to get 36.

$$\frac{36}{14}+\frac{8\times 4}{7\times 10}$$

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

$$\frac{18}{7}+\frac{8\times 4}{7\times 10}$$

Cancel out 2 in both numerator and denominator.

$$\frac{18}{7}+\frac{4\times 4}{5\times 7}$$

Multiply 4 and 4 to get 16.

$$\frac{18}{7}+\frac{16}{5\times 7}$$

Multiply 5 and 7 to get 35.

$$\frac{18}{7}+\frac{16}{35}$$

Least common multiple of 7 and 35 is 35. Convert \frac{18}{7} and \frac{16}{35} to fractions with denominator 35.

$$\frac{90}{35}+\frac{16}{35}$$

Since \frac{90}{35} and \frac{16}{35} have the same denominator, add them by adding their numerators.

$$\frac{90+16}{35}$$

Add 90 and 16 to get 106.

$$\frac{106}{35}$$

Factor

$$\frac{2 \cdot 53}{5 \cdot 7} = 3\frac{1}{35} = 3.0285714285714285$$