Solve [(2-3/5)*(3-1/3)]/[(4-1/4)+(5-1/5)]*(frac{1}{2}+24)

$$[ ( 2 - \frac { 3 } { 5 } ) \times ( 3 - \frac { 1 } { 3 } ) ] / [ ( 4 - \frac { 1 } { 4 } ) + ( 5 - \frac { 1 } { 5 } ) ] * ( \frac { 1 } { 2 } + 24 )$$

Evaluate

$$\frac{5488}{513}\approx 10.69785575$$

Solution Steps

Convert 2 to fraction \frac{10}{5}.

$$\frac{\left(\frac{10}{5}-\frac{3}{5}\right)\left(3-\frac{1}{3}\right)}{4-\frac{1}{4}+5-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Since \frac{10}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-3}{5}\left(3-\frac{1}{3}\right)}{4-\frac{1}{4}+5-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Subtract 3 from 10 to get 7.

$$\frac{\frac{7}{5}\left(3-\frac{1}{3}\right)}{4-\frac{1}{4}+5-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{\frac{7}{5}\left(\frac{9}{3}-\frac{1}{3}\right)}{4-\frac{1}{4}+5-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Since \frac{9}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{5}\times \frac{9-1}{3}}{4-\frac{1}{4}+5-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Subtract 1 from 9 to get 8.

$$\frac{\frac{7}{5}\times \frac{8}{3}}{4-\frac{1}{4}+5-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Multiply \frac{7}{5} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7\times 8}{5\times 3}}{4-\frac{1}{4}+5-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Do the multiplications in the fraction \frac{7\times 8}{5\times 3}.

$$\frac{\frac{56}{15}}{4-\frac{1}{4}+5-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Convert 4 to fraction \frac{16}{4}.

$$\frac{\frac{56}{15}}{\frac{16}{4}-\frac{1}{4}+5-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Since \frac{16}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{56}{15}}{\frac{16-1}{4}+5-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Subtract 1 from 16 to get 15.

$$\frac{\frac{56}{15}}{\frac{15}{4}+5-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Convert 5 to fraction \frac{20}{4}.

$$\frac{\frac{56}{15}}{\frac{15}{4}+\frac{20}{4}-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Since \frac{15}{4} and \frac{20}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{56}{15}}{\frac{15+20}{4}-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Add 15 and 20 to get 35.

$$\frac{\frac{56}{15}}{\frac{35}{4}-\frac{1}{5}}\left(\frac{1}{2}+24\right)$$

Least common multiple of 4 and 5 is 20. Convert \frac{35}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{\frac{56}{15}}{\frac{175}{20}-\frac{4}{20}}\left(\frac{1}{2}+24\right)$$

Since \frac{175}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{56}{15}}{\frac{175-4}{20}}\left(\frac{1}{2}+24\right)$$

Subtract 4 from 175 to get 171.

$$\frac{\frac{56}{15}}{\frac{171}{20}}\left(\frac{1}{2}+24\right)$$

Divide \frac{56}{15} by \frac{171}{20} by multiplying \frac{56}{15} by the reciprocal of \frac{171}{20}.

$$\frac{56}{15}\times \frac{20}{171}\left(\frac{1}{2}+24\right)$$

Multiply \frac{56}{15} times \frac{20}{171} by multiplying numerator times numerator and denominator times denominator.

$$\frac{56\times 20}{15\times 171}\left(\frac{1}{2}+24\right)$$

Do the multiplications in the fraction \frac{56\times 20}{15\times 171}.

$$\frac{1120}{2565}\left(\frac{1}{2}+24\right)$$

Reduce the fraction \frac{1120}{2565} to lowest terms by extracting and canceling out 5.

$$\frac{224}{513}\left(\frac{1}{2}+24\right)$$

Convert 24 to fraction \frac{48}{2}.

$$\frac{224}{513}\left(\frac{1}{2}+\frac{48}{2}\right)$$

Since \frac{1}{2} and \frac{48}{2} have the same denominator, add them by adding their numerators.

$$\frac{224}{513}\times \frac{1+48}{2}$$

Add 1 and 48 to get 49.

$$\frac{224}{513}\times \frac{49}{2}$$

Multiply \frac{224}{513} times \frac{49}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{224\times 49}{513\times 2}$$

Do the multiplications in the fraction \frac{224\times 49}{513\times 2}.

$$\frac{10976}{1026}$$

Reduce the fraction \frac{10976}{1026} to lowest terms by extracting and canceling out 2.

$$\frac{5488}{513}$$

Factor

$$\frac{2 ^ {4} \cdot 7 ^ {3}}{3 ^ {3} \cdot 19} = 10\frac{358}{513} = 10.69785575048733$$