Solve -1/7*-1/10+2/7*31/80-frac{2}{7}*-frac{43}{320}

$$- \frac{ 1 }{ 7 } \times - \frac{ 1 }{ 10 } + \frac{ 2 }{ 7 } \times \frac{ 31 }{ 80 } - \frac{ 2 }{ 7 } \times - \frac{ 43 }{ 320 }$$

Evaluate

$$\frac{183}{1120}\approx 0.163392857$$

Solution Steps

Multiply -\frac{1}{7} times -\frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-1\right)}{7\times 10}+\frac{2}{7}\times \frac{31}{80}-\frac{2}{7}\left(-\frac{43}{320}\right)$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{7\times 10}.

$$\frac{1}{70}+\frac{2}{7}\times \frac{31}{80}-\frac{2}{7}\left(-\frac{43}{320}\right)$$

Multiply \frac{2}{7} times \frac{31}{80} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{70}+\frac{2\times 31}{7\times 80}-\frac{2}{7}\left(-\frac{43}{320}\right)$$

Do the multiplications in the fraction \frac{2\times 31}{7\times 80}.

$$\frac{1}{70}+\frac{62}{560}-\frac{2}{7}\left(-\frac{43}{320}\right)$$

Reduce the fraction \frac{62}{560} to lowest terms by extracting and canceling out 2.

$$\frac{1}{70}+\frac{31}{280}-\frac{2}{7}\left(-\frac{43}{320}\right)$$

Least common multiple of 70 and 280 is 280. Convert \frac{1}{70} and \frac{31}{280} to fractions with denominator 280.

$$\frac{4}{280}+\frac{31}{280}-\frac{2}{7}\left(-\frac{43}{320}\right)$$

Since \frac{4}{280} and \frac{31}{280} have the same denominator, add them by adding their numerators.

$$\frac{4+31}{280}-\frac{2}{7}\left(-\frac{43}{320}\right)$$

Add 4 and 31 to get 35.

$$\frac{35}{280}-\frac{2}{7}\left(-\frac{43}{320}\right)$$

Reduce the fraction \frac{35}{280} to lowest terms by extracting and canceling out 35.

$$\frac{1}{8}-\frac{2}{7}\left(-\frac{43}{320}\right)$$

Multiply \frac{2}{7} times -\frac{43}{320} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{8}-\frac{2\left(-43\right)}{7\times 320}$$

Do the multiplications in the fraction \frac{2\left(-43\right)}{7\times 320}.

$$\frac{1}{8}-\frac{-86}{2240}$$

Reduce the fraction \frac{-86}{2240} to lowest terms by extracting and canceling out 2.

$$\frac{1}{8}-\left(-\frac{43}{1120}\right)$$

The opposite of -\frac{43}{1120} is \frac{43}{1120}.

$$\frac{1}{8}+\frac{43}{1120}$$

Least common multiple of 8 and 1120 is 1120. Convert \frac{1}{8} and \frac{43}{1120} to fractions with denominator 1120.

$$\frac{140}{1120}+\frac{43}{1120}$$

Since \frac{140}{1120} and \frac{43}{1120} have the same denominator, add them by adding their numerators.

$$\frac{140+43}{1120}$$

Add 140 and 43 to get 183.

$$\frac{183}{1120}$$

Factor

$$\frac{3 \cdot 61}{2 ^ {5} \cdot 5 \cdot 7} = 0.16339285714285715$$