Solve 1/4*43/4*16/57+(41/4+1frac{2}{3})*frac{16}{71}+frac{2}{27}*4frac{1}{2}

$$\frac { 1 } { 4 } \cdot 4 \frac { 3 } { 4 } \cdot \frac { 16 } { 57 } + ( 4 \frac { 1 } { 4 } + 1 \frac { 2 } { 3 } ) \cdot \frac { 16 } { 71 } + \frac { 2 } { 27 } \cdot 4 \frac { 1 } { 2 }$$

Evaluate

$$2$$

Solution Steps

Multiply 4 and 4 to get 16.

$$\frac{1}{4}\times \frac{16+3}{4}\times \frac{16}{57}+\left(\frac{4\times 4+1}{4}+\frac{1\times 3+2}{3}\right)\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Add 16 and 3 to get 19.

$$\frac{1}{4}\times \frac{19}{4}\times \frac{16}{57}+\left(\frac{4\times 4+1}{4}+\frac{1\times 3+2}{3}\right)\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Multiply \frac{1}{4} times \frac{19}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 19}{4\times 4}\times \frac{16}{57}+\left(\frac{4\times 4+1}{4}+\frac{1\times 3+2}{3}\right)\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Do the multiplications in the fraction \frac{1\times 19}{4\times 4}.

$$\frac{19}{16}\times \frac{16}{57}+\left(\frac{4\times 4+1}{4}+\frac{1\times 3+2}{3}\right)\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Multiply \frac{19}{16} times \frac{16}{57} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\times 16}{16\times 57}+\left(\frac{4\times 4+1}{4}+\frac{1\times 3+2}{3}\right)\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Cancel out 16 in both numerator and denominator.

$$\frac{19}{57}+\left(\frac{4\times 4+1}{4}+\frac{1\times 3+2}{3}\right)\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Reduce the fraction \frac{19}{57} to lowest terms by extracting and canceling out 19.

$$\frac{1}{3}+\left(\frac{4\times 4+1}{4}+\frac{1\times 3+2}{3}\right)\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Multiply 4 and 4 to get 16.

$$\frac{1}{3}+\left(\frac{16+1}{4}+\frac{1\times 3+2}{3}\right)\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Add 16 and 1 to get 17.

$$\frac{1}{3}+\left(\frac{17}{4}+\frac{1\times 3+2}{3}\right)\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Multiply 1 and 3 to get 3.

$$\frac{1}{3}+\left(\frac{17}{4}+\frac{3+2}{3}\right)\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Add 3 and 2 to get 5.

$$\frac{1}{3}+\left(\frac{17}{4}+\frac{5}{3}\right)\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Least common multiple of 4 and 3 is 12. Convert \frac{17}{4} and \frac{5}{3} to fractions with denominator 12.

$$\frac{1}{3}+\left(\frac{51}{12}+\frac{20}{12}\right)\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Since \frac{51}{12} and \frac{20}{12} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}+\frac{51+20}{12}\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Add 51 and 20 to get 71.

$$\frac{1}{3}+\frac{71}{12}\times \frac{16}{71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Multiply \frac{71}{12} times \frac{16}{71} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}+\frac{71\times 16}{12\times 71}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Cancel out 71 in both numerator and denominator.

$$\frac{1}{3}+\frac{16}{12}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Reduce the fraction \frac{16}{12} to lowest terms by extracting and canceling out 4.

$$\frac{1}{3}+\frac{4}{3}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Since \frac{1}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{1+4}{3}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Add 1 and 4 to get 5.

$$\frac{5}{3}+\frac{2}{27}\times \frac{4\times 2+1}{2}$$

Multiply 4 and 2 to get 8.

$$\frac{5}{3}+\frac{2}{27}\times \frac{8+1}{2}$$

Add 8 and 1 to get 9.

$$\frac{5}{3}+\frac{2}{27}\times \frac{9}{2}$$

Multiply \frac{2}{27} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{3}+\frac{2\times 9}{27\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5}{3}+\frac{9}{27}$$

Reduce the fraction \frac{9}{27} to lowest terms by extracting and canceling out 9.

$$\frac{5}{3}+\frac{1}{3}$$

Since \frac{5}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{5+1}{3}$$

Add 5 and 1 to get 6.

$$\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$2$$

Factor

$$2$$