Solve (4,25(49/16-(21/3-1/3))*frac{18/41}{0,45}):1,4+frac{1}{12}

$$( 4,25 \frac { ( 4 \frac { 9 } { 16 } - ( 2 \frac { 1 } { 3 } - \frac { 1 } { 3 } ) ) \cdot \frac { 18 } { 41 } } { 0,45 } ) : 1,4 + \frac { 1 } { 12 }$$

Evaluate

$$\frac{1289}{168}\approx 7,672619048$$

Solution Steps

Multiply 4 and 16 to get 64.

$$\frac{4,25\times \frac{\left(\frac{64+9}{16}-\left(\frac{2\times 3+1}{3}-\frac{1}{3}\right)\right)\times \frac{18}{41}}{0,45}}{1,4}+\frac{1}{12}$$

Add 64 and 9 to get 73.

$$\frac{4,25\times \frac{\left(\frac{73}{16}-\left(\frac{2\times 3+1}{3}-\frac{1}{3}\right)\right)\times \frac{18}{41}}{0,45}}{1,4}+\frac{1}{12}$$

Multiply 2 and 3 to get 6.

$$\frac{4,25\times \frac{\left(\frac{73}{16}-\left(\frac{6+1}{3}-\frac{1}{3}\right)\right)\times \frac{18}{41}}{0,45}}{1,4}+\frac{1}{12}$$

Add 6 and 1 to get 7.

$$\frac{4,25\times \frac{\left(\frac{73}{16}-\left(\frac{7}{3}-\frac{1}{3}\right)\right)\times \frac{18}{41}}{0,45}}{1,4}+\frac{1}{12}$$

Since \frac{7}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4,25\times \frac{\left(\frac{73}{16}-\frac{7-1}{3}\right)\times \frac{18}{41}}{0,45}}{1,4}+\frac{1}{12}$$

Subtract 1 from 7 to get 6.

$$\frac{4,25\times \frac{\left(\frac{73}{16}-\frac{6}{3}\right)\times \frac{18}{41}}{0,45}}{1,4}+\frac{1}{12}$$

Divide 6 by 3 to get 2.

$$\frac{4,25\times \frac{\left(\frac{73}{16}-2\right)\times \frac{18}{41}}{0,45}}{1,4}+\frac{1}{12}$$

Convert 2 to fraction \frac{32}{16}.

$$\frac{4,25\times \frac{\left(\frac{73}{16}-\frac{32}{16}\right)\times \frac{18}{41}}{0,45}}{1,4}+\frac{1}{12}$$

Since \frac{73}{16} and \frac{32}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4,25\times \frac{\frac{73-32}{16}\times \frac{18}{41}}{0,45}}{1,4}+\frac{1}{12}$$

Subtract 32 from 73 to get 41.

$$\frac{4,25\times \frac{\frac{41}{16}\times \frac{18}{41}}{0,45}}{1,4}+\frac{1}{12}$$

Multiply \frac{41}{16} times \frac{18}{41} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4,25\times \frac{\frac{41\times 18}{16\times 41}}{0,45}}{1,4}+\frac{1}{12}$$

Cancel out 41 in both numerator and denominator.

$$\frac{4,25\times \frac{\frac{18}{16}}{0,45}}{1,4}+\frac{1}{12}$$

Reduce the fraction \frac{18}{16} to lowest terms by extracting and canceling out 2.

$$\frac{4,25\times \frac{\frac{9}{8}}{0,45}}{1,4}+\frac{1}{12}$$

Express \frac{\frac{9}{8}}{0,45} as a single fraction.

$$\frac{4,25\times \frac{9}{8\times 0,45}}{1,4}+\frac{1}{12}$$

Multiply 8 and 0,45 to get 3,6.

$$\frac{4,25\times \frac{9}{3,6}}{1,4}+\frac{1}{12}$$

Expand \frac{9}{3,6} by multiplying both numerator and the denominator by 10.

$$\frac{4,25\times \frac{90}{36}}{1,4}+\frac{1}{12}$$

Reduce the fraction \frac{90}{36} to lowest terms by extracting and canceling out 18.

$$\frac{4,25\times \frac{5}{2}}{1,4}+\frac{1}{12}$$

Convert decimal number 4,25 to fraction \frac{425}{100}. Reduce the fraction \frac{425}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{17}{4}\times \frac{5}{2}}{1,4}+\frac{1}{12}$$

Multiply \frac{17}{4} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{17\times 5}{4\times 2}}{1,4}+\frac{1}{12}$$

Do the multiplications in the fraction \frac{17\times 5}{4\times 2}.

$$\frac{\frac{85}{8}}{1,4}+\frac{1}{12}$$

Express \frac{\frac{85}{8}}{1,4} as a single fraction.

$$\frac{85}{8\times 1,4}+\frac{1}{12}$$

Multiply 8 and 1,4 to get 11,2.

$$\frac{85}{11,2}+\frac{1}{12}$$

Expand \frac{85}{11,2} by multiplying both numerator and the denominator by 10.

$$\frac{850}{112}+\frac{1}{12}$$

Reduce the fraction \frac{850}{112} to lowest terms by extracting and canceling out 2.

$$\frac{425}{56}+\frac{1}{12}$$

Least common multiple of 56 and 12 is 168. Convert \frac{425}{56} and \frac{1}{12} to fractions with denominator 168.

$$\frac{1275}{168}+\frac{14}{168}$$

Since \frac{1275}{168} and \frac{14}{168} have the same denominator, add them by adding their numerators.

$$\frac{1275+14}{168}$$

Add 1275 and 14 to get 1289.

$$\frac{1289}{168}$$

Factor

$$\frac{1289}{3 \cdot 7 \cdot 2 ^ {3}} = 7\frac{113}{168} = 7.6726190476190474$$