Solve 4,4:11+1/5-3^0+3,4/(16:frac{4{7}-132/3):43}=

$$\frac { 4,4 : 11 + \frac { 1 } { 5 } - 3 ^ { 0 } + 3,4 } { ( 16 : \frac { 4 } { 7 } - 13 \frac { 2 } { 3 } ) : 43 } =$$

Evaluate

$$9$$

Solution Steps

Expand \frac{4,4}{11} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{44}{110}+\frac{1}{5}-3^{0}+3,4}{\frac{\frac{16}{\frac{4}{7}}-\frac{13\times 3+2}{3}}{43}}$$

Reduce the fraction \frac{44}{110} to lowest terms by extracting and canceling out 22.

$$\frac{\frac{2}{5}+\frac{1}{5}-3^{0}+3,4}{\frac{\frac{16}{\frac{4}{7}}-\frac{13\times 3+2}{3}}{43}}$$

Add \frac{2}{5} and \frac{1}{5} to get \frac{3}{5}.

$$\frac{\frac{3}{5}-3^{0}+3,4}{\frac{\frac{16}{\frac{4}{7}}-\frac{13\times 3+2}{3}}{43}}$$

Calculate 3 to the power of 0 and get 1.

$$\frac{\frac{3}{5}-1+3,4}{\frac{\frac{16}{\frac{4}{7}}-\frac{13\times 3+2}{3}}{43}}$$

Subtract 1 from \frac{3}{5} to get -\frac{2}{5}.

$$\frac{-\frac{2}{5}+3,4}{\frac{\frac{16}{\frac{4}{7}}-\frac{13\times 3+2}{3}}{43}}$$

Add -\frac{2}{5} and 3,4 to get 3.

$$\frac{3}{\frac{\frac{16}{\frac{4}{7}}-\frac{13\times 3+2}{3}}{43}}$$

Divide 16 by \frac{4}{7} by multiplying 16 by the reciprocal of \frac{4}{7}.

$$\frac{3}{\frac{16\times \frac{7}{4}-\frac{13\times 3+2}{3}}{43}}$$

Multiply 16 and \frac{7}{4} to get 28.

$$\frac{3}{\frac{28-\frac{13\times 3+2}{3}}{43}}$$

Multiply 13 and 3 to get 39.

$$\frac{3}{\frac{28-\frac{39+2}{3}}{43}}$$

Add 39 and 2 to get 41.

$$\frac{3}{\frac{28-\frac{41}{3}}{43}}$$

Subtract \frac{41}{3} from 28 to get \frac{43}{3}.

$$\frac{3}{\frac{\frac{43}{3}}{43}}$$

Express \frac{\frac{43}{3}}{43} as a single fraction.

$$\frac{3}{\frac{43}{3\times 43}}$$

Cancel out 43 in both numerator and denominator.

$$\frac{3}{\frac{1}{3}}$$

Divide 3 by \frac{1}{3} by multiplying 3 by the reciprocal of \frac{1}{3}.

$$3\times 3$$

Multiply 3 and 3 to get 9.

$$9$$

Factor

$$3^{2}$$