Solve [15/7-8/49*2/7]*28/3

$$[ \frac { 15 } { 7 } - \frac { 8 } { 49 } \times \frac { 2 } { 7 } ] \times \frac { 28 } { 3 }$$

Evaluate

$$\frac{2876}{147}\approx 19.56462585$$

Solution Steps

Multiply \frac{8}{49} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{15}{7}-\frac{8\times 2}{49\times 7}\right)\times \frac{28}{3}$$

Do the multiplications in the fraction \frac{8\times 2}{49\times 7}.

$$\left(\frac{15}{7}-\frac{16}{343}\right)\times \frac{28}{3}$$

Least common multiple of 7 and 343 is 343. Convert \frac{15}{7} and \frac{16}{343} to fractions with denominator 343.

$$\left(\frac{735}{343}-\frac{16}{343}\right)\times \frac{28}{3}$$

Since \frac{735}{343} and \frac{16}{343} have the same denominator, subtract them by subtracting their numerators.

$$\frac{735-16}{343}\times \frac{28}{3}$$

Subtract 16 from 735 to get 719.

$$\frac{719}{343}\times \frac{28}{3}$$

Multiply \frac{719}{343} times \frac{28}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{719\times 28}{343\times 3}$$

Do the multiplications in the fraction \frac{719\times 28}{343\times 3}.

$$\frac{20132}{1029}$$

Reduce the fraction \frac{20132}{1029} to lowest terms by extracting and canceling out 7.

$$\frac{2876}{147}$$

Factor

$$\frac{2 ^ {2} \cdot 719}{3 \cdot 7 ^ {2}} = 19\frac{83}{147} = 19.564625850340136$$