Solve (5/2+2/3)x(3/2+5/3)

$$( \frac { 5 } { 2 } + \frac { 2 } { 3 } ) x ( \frac { 3 } { 2 } + \frac { 5 } { 3 } )$$

Evaluate

$$\frac{361x}{36}$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{2}{3} to fractions with denominator 6.

$$\left(\frac{15}{6}+\frac{4}{6}\right)x\left(\frac{3}{2}+\frac{5}{3}\right)$$

Since \frac{15}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{15+4}{6}x\left(\frac{3}{2}+\frac{5}{3}\right)$$

Add 15 and 4 to get 19.

$$\frac{19}{6}x\left(\frac{3}{2}+\frac{5}{3}\right)$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{5}{3} to fractions with denominator 6.

$$\frac{19}{6}x\left(\frac{9}{6}+\frac{10}{6}\right)$$

Since \frac{9}{6} and \frac{10}{6} have the same denominator, add them by adding their numerators.

$$\frac{19}{6}x\times \frac{9+10}{6}$$

Add 9 and 10 to get 19.

$$\frac{19}{6}x\times \frac{19}{6}$$

Multiply \frac{19}{6} times \frac{19}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\times 19}{6\times 6}x$$

Do the multiplications in the fraction \frac{19\times 19}{6\times 6}.

$$\frac{361}{36}x$$

Expand

$$\frac{361x}{36}$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{2}{3} to fractions with denominator 6.

$$\left(\frac{15}{6}+\frac{4}{6}\right)x\left(\frac{3}{2}+\frac{5}{3}\right)$$

Since \frac{15}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{15+4}{6}x\left(\frac{3}{2}+\frac{5}{3}\right)$$

Add 15 and 4 to get 19.

$$\frac{19}{6}x\left(\frac{3}{2}+\frac{5}{3}\right)$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{5}{3} to fractions with denominator 6.

$$\frac{19}{6}x\left(\frac{9}{6}+\frac{10}{6}\right)$$

Since \frac{9}{6} and \frac{10}{6} have the same denominator, add them by adding their numerators.

$$\frac{19}{6}x\times \frac{9+10}{6}$$

Add 9 and 10 to get 19.

$$\frac{19}{6}x\times \frac{19}{6}$$

Multiply \frac{19}{6} times \frac{19}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\times 19}{6\times 6}x$$

Do the multiplications in the fraction \frac{19\times 19}{6\times 6}.

$$\frac{361}{36}x$$