Solve 4/55/13-045/13+3/5div16

$$\frac{ 4 }{ 5 } \frac{ 5 }{ 13 } -04 \frac{ 5 }{ 13 } + \frac{ 3 }{ 5 } \div 16$$

Evaluate

$$\frac{359}{1040}\approx 0.345192308$$

Solution Steps

Multiply \frac{4}{5} times \frac{5}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 5}{5\times 13}-0\times \frac{4\times 13+5}{13}+\frac{\frac{3}{5}}{16}$$

Cancel out 5 in both numerator and denominator.

$$\frac{4}{13}-0\times \frac{4\times 13+5}{13}+\frac{\frac{3}{5}}{16}$$

Multiply 4 and 13 to get 52.

$$\frac{4}{13}-0\times \frac{52+5}{13}+\frac{\frac{3}{5}}{16}$$

Add 52 and 5 to get 57.

$$\frac{4}{13}-0\times \frac{57}{13}+\frac{\frac{3}{5}}{16}$$

Multiply 0 and \frac{57}{13} to get 0.

$$\frac{4}{13}-0+\frac{\frac{3}{5}}{16}$$

Subtract 0 from \frac{4}{13} to get \frac{4}{13}.

$$\frac{4}{13}+\frac{\frac{3}{5}}{16}$$

Express \frac{\frac{3}{5}}{16} as a single fraction.

$$\frac{4}{13}+\frac{3}{5\times 16}$$

Multiply 5 and 16 to get 80.

$$\frac{4}{13}+\frac{3}{80}$$

Least common multiple of 13 and 80 is 1040. Convert \frac{4}{13} and \frac{3}{80} to fractions with denominator 1040.

$$\frac{320}{1040}+\frac{39}{1040}$$

Since \frac{320}{1040} and \frac{39}{1040} have the same denominator, add them by adding their numerators.

$$\frac{320+39}{1040}$$

Add 320 and 39 to get 359.

$$\frac{359}{1040}$$

Factor

$$\frac{359}{2 ^ {4} \cdot 5 \cdot 13} = 0.3451923076923077$$