Solve 190/[(1+156:4+3-2^2*3^2)+(112*8-39*3+5*4)]:(7

$$\frac { 190 } { [ ( 1 + 156 : 4 + 3 - 2 ^ { 2 } \cdot 3 ^ { 2 } ) + ( 112 \cdot 8 - 39 \cdot 3 + 5 \cdot 4 ) ] : ( 7 }$$

Evaluate

$$\frac{665}{403}\approx 1.650124069$$

Solution Steps

Divide 190 by \frac{1+\frac{156}{4}+3-2^{2}\times 3^{2}+112\times 8-39\times 3+5\times 4}{7} by multiplying 190 by the reciprocal of \frac{1+\frac{156}{4}+3-2^{2}\times 3^{2}+112\times 8-39\times 3+5\times 4}{7}.

$$\frac{190\times 7}{1+\frac{156}{4}+3-2^{2}\times 3^{2}+112\times 8-39\times 3+5\times 4}$$

Multiply 190 and 7 to get 1330.

$$\frac{1330}{1+\frac{156}{4}+3-2^{2}\times 3^{2}+112\times 8-39\times 3+5\times 4}$$

Divide 156 by 4 to get 39.

$$\frac{1330}{1+39+3-2^{2}\times 3^{2}+112\times 8-39\times 3+5\times 4}$$

Add 1 and 39 to get 40.

$$\frac{1330}{40+3-2^{2}\times 3^{2}+112\times 8-39\times 3+5\times 4}$$

Add 40 and 3 to get 43.

$$\frac{1330}{43-2^{2}\times 3^{2}+112\times 8-39\times 3+5\times 4}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1330}{43-4\times 3^{2}+112\times 8-39\times 3+5\times 4}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{1330}{43-4\times 9+112\times 8-39\times 3+5\times 4}$$

Multiply 4 and 9 to get 36.

$$\frac{1330}{43-36+112\times 8-39\times 3+5\times 4}$$

Subtract 36 from 43 to get 7.

$$\frac{1330}{7+112\times 8-39\times 3+5\times 4}$$

Multiply 112 and 8 to get 896.

$$\frac{1330}{7+896-39\times 3+5\times 4}$$

Multiply 39 and 3 to get 117.

$$\frac{1330}{7+896-117+5\times 4}$$

Subtract 117 from 896 to get 779.

$$\frac{1330}{7+779+5\times 4}$$

Add 7 and 779 to get 786.

$$\frac{1330}{786+5\times 4}$$

Multiply 5 and 4 to get 20.

$$\frac{1330}{786+20}$$

Add 786 and 20 to get 806.

$$\frac{1330}{806}$$

Reduce the fraction \frac{1330}{806} to lowest terms by extracting and canceling out 2.

$$\frac{665}{403}$$

Factor

$$\frac{5 \cdot 7 \cdot 19}{13 \cdot 31} = 1\frac{262}{403} = 1.650124069478908$$