Solve 27/36div(63/4+23/16)

$$2 \frac { 7 } { 36 } \div ( 6 \frac { 3 } { 4 } + 2 \frac { 3 } { 16 } )$$

Evaluate

$$\frac{316}{1287}\approx 0.245532246$$

Solution Steps

Multiply 2 and 36 to get 72.

$$\frac{\frac{72+7}{36}}{\frac{6\times 4+3}{4}+\frac{2\times 16+3}{16}}$$

Add 72 and 7 to get 79.

$$\frac{\frac{79}{36}}{\frac{6\times 4+3}{4}+\frac{2\times 16+3}{16}}$$

Multiply 6 and 4 to get 24.

$$\frac{\frac{79}{36}}{\frac{24+3}{4}+\frac{2\times 16+3}{16}}$$

Add 24 and 3 to get 27.

$$\frac{\frac{79}{36}}{\frac{27}{4}+\frac{2\times 16+3}{16}}$$

Multiply 2 and 16 to get 32.

$$\frac{\frac{79}{36}}{\frac{27}{4}+\frac{32+3}{16}}$$

Add 32 and 3 to get 35.

$$\frac{\frac{79}{36}}{\frac{27}{4}+\frac{35}{16}}$$

Least common multiple of 4 and 16 is 16. Convert \frac{27}{4} and \frac{35}{16} to fractions with denominator 16.

$$\frac{\frac{79}{36}}{\frac{108}{16}+\frac{35}{16}}$$

Since \frac{108}{16} and \frac{35}{16} have the same denominator, add them by adding their numerators.

$$\frac{\frac{79}{36}}{\frac{108+35}{16}}$$

Add 108 and 35 to get 143.

$$\frac{\frac{79}{36}}{\frac{143}{16}}$$

Divide \frac{79}{36} by \frac{143}{16} by multiplying \frac{79}{36} by the reciprocal of \frac{143}{16}.

$$\frac{79}{36}\times \frac{16}{143}$$

Multiply \frac{79}{36} times \frac{16}{143} by multiplying numerator times numerator and denominator times denominator.

$$\frac{79\times 16}{36\times 143}$$

Do the multiplications in the fraction \frac{79\times 16}{36\times 143}.

$$\frac{1264}{5148}$$

Reduce the fraction \frac{1264}{5148} to lowest terms by extracting and canceling out 4.

$$\frac{316}{1287}$$

Factor

$$\frac{2 ^ {2} \cdot 79}{3 ^ {2} \cdot 11 \cdot 13} = 0.24553224553224554$$