Solve left(3/4+1/3right)13/3/3frac{1{4}}

$$\frac{ \left( \frac{ 3 }{ 4 } + \frac{ 1 }{ 3 } \right) \frac{ 13 }{ 3 } }{ 3 \frac{ 1 }{ 4 } }$$

Evaluate

$$\frac{13}{9}\approx 1.444444444$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{\left(\frac{9}{12}+\frac{4}{12}\right)\times \frac{13}{3}}{\frac{3\times 4+1}{4}}$$

Since \frac{9}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+4}{12}\times \frac{13}{3}}{\frac{3\times 4+1}{4}}$$

Add 9 and 4 to get 13.

$$\frac{\frac{13}{12}\times \frac{13}{3}}{\frac{3\times 4+1}{4}}$$

Multiply \frac{13}{12} times \frac{13}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13\times 13}{12\times 3}}{\frac{3\times 4+1}{4}}$$

Do the multiplications in the fraction \frac{13\times 13}{12\times 3}.

$$\frac{\frac{169}{36}}{\frac{3\times 4+1}{4}}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{169}{36}}{\frac{12+1}{4}}$$

Add 12 and 1 to get 13.

$$\frac{\frac{169}{36}}{\frac{13}{4}}$$

Divide \frac{169}{36} by \frac{13}{4} by multiplying \frac{169}{36} by the reciprocal of \frac{13}{4}.

$$\frac{169}{36}\times \frac{4}{13}$$

Multiply \frac{169}{36} times \frac{4}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{169\times 4}{36\times 13}$$

Do the multiplications in the fraction \frac{169\times 4}{36\times 13}.

$$\frac{676}{468}$$

Reduce the fraction \frac{676}{468} to lowest terms by extracting and canceling out 52.

$$\frac{13}{9}$$

Factor

$$\frac{13}{3 ^ {2}} = 1\frac{4}{9} = 1.4444444444444444$$