Solve (3/2+2/3):(3/4+4/3)

$$( \frac { 3 } { 2 } + \frac { 2 } { 3 } ) : ( \frac { 3 } { 4 } + \frac { 4 } { 3 } )$$

Evaluate

$$\frac{26}{25}=1.04$$

Solution Steps

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

$$\frac{\frac{9}{6}+\frac{4}{6}}{\frac{3}{4}+\frac{4}{3}}$$

Since \frac{9}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+4}{6}}{\frac{3}{4}+\frac{4}{3}}$$

Add 9 and 4 to get 13.

$$\frac{\frac{13}{6}}{\frac{3}{4}+\frac{4}{3}}$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{4}{3} to fractions with denominator 12.

$$\frac{\frac{13}{6}}{\frac{9}{12}+\frac{16}{12}}$$

Since \frac{9}{12} and \frac{16}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{6}}{\frac{9+16}{12}}$$

Add 9 and 16 to get 25.

$$\frac{\frac{13}{6}}{\frac{25}{12}}$$

Divide \frac{13}{6} by \frac{25}{12} by multiplying \frac{13}{6} by the reciprocal of \frac{25}{12}.

$$\frac{13}{6}\times \frac{12}{25}$$

Multiply \frac{13}{6} times \frac{12}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 12}{6\times 25}$$

Do the multiplications in the fraction \frac{13\times 12}{6\times 25}.

$$\frac{156}{150}$$

Reduce the fraction \frac{156}{150} to lowest terms by extracting and canceling out 6.

$$\frac{26}{25}$$

Factor

$$\frac{2 \cdot 13}{5 ^ {2}} = 1\frac{1}{25} = 1.04$$