Solve (13/4-2/13)(9/7+12/75)

$$( \frac { 13 } { 4 } - \frac { 2 } { 13 } ) ( \frac { 9 } { 7 } + \frac { 12 } { 75 } )$$

Evaluate

$$\frac{5819}{1300}\approx 4.476153846$$

Solution Steps

Least common multiple of 4 and 13 is 52. Convert \frac{13}{4} and \frac{2}{13} to fractions with denominator 52.

$$\left(\frac{169}{52}-\frac{8}{52}\right)\left(\frac{9}{7}+\frac{12}{75}\right)$$

Since \frac{169}{52} and \frac{8}{52} have the same denominator, subtract them by subtracting their numerators.

$$\frac{169-8}{52}\left(\frac{9}{7}+\frac{12}{75}\right)$$

Subtract 8 from 169 to get 161.

$$\frac{161}{52}\left(\frac{9}{7}+\frac{12}{75}\right)$$

Reduce the fraction \frac{12}{75} to lowest terms by extracting and canceling out 3.

$$\frac{161}{52}\left(\frac{9}{7}+\frac{4}{25}\right)$$

Least common multiple of 7 and 25 is 175. Convert \frac{9}{7} and \frac{4}{25} to fractions with denominator 175.

$$\frac{161}{52}\left(\frac{225}{175}+\frac{28}{175}\right)$$

Since \frac{225}{175} and \frac{28}{175} have the same denominator, add them by adding their numerators.

$$\frac{161}{52}\times \frac{225+28}{175}$$

Add 225 and 28 to get 253.

$$\frac{161}{52}\times \frac{253}{175}$$

Multiply \frac{161}{52} times \frac{253}{175} by multiplying numerator times numerator and denominator times denominator.

$$\frac{161\times 253}{52\times 175}$$

Do the multiplications in the fraction \frac{161\times 253}{52\times 175}.

$$\frac{40733}{9100}$$

Reduce the fraction \frac{40733}{9100} to lowest terms by extracting and canceling out 7.

$$\frac{5819}{1300}$$

Factor

$$\frac{11 \cdot 23 ^ {2}}{2 ^ {2} \cdot 5 ^ {2} \cdot 13} = 4\frac{619}{1300} = 4.476153846153847$$