Solve ((11/7-23/49):22/147-(0.6:33/4)2frac{1}{2}+3.75:1frac{1}{2}):2.2

$$( ( 1 \frac { 1 } { 7 } - \frac { 23 } { 49 } ) : \frac { 22 } { 147 } - ( 0.6 : 3 \frac { 3 } { 4 } ) 2 \frac { 1 } { 2 } + 3.75 : 1 \frac { 1 } { 2 } ) : 2.2$$

Evaluate

$$3$$

Solution Steps

Multiply 1 and 7 to get 7.

$$\frac{\frac{\frac{7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Add 7 and 1 to get 8.

$$\frac{\frac{\frac{8}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Least common multiple of 7 and 49 is 49. Convert \frac{8}{7} and \frac{23}{49} to fractions with denominator 49.

$$\frac{\frac{\frac{56}{49}-\frac{23}{49}}{\frac{22}{147}}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Since \frac{56}{49} and \frac{23}{49} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{56-23}{49}}{\frac{22}{147}}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Subtract 23 from 56 to get 33.

$$\frac{\frac{\frac{33}{49}}{\frac{22}{147}}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Divide \frac{33}{49} by \frac{22}{147} by multiplying \frac{33}{49} by the reciprocal of \frac{22}{147}.

$$\frac{\frac{33}{49}\times \frac{147}{22}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Multiply \frac{33}{49} times \frac{147}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{33\times 147}{49\times 22}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Do the multiplications in the fraction \frac{33\times 147}{49\times 22}.

$$\frac{\frac{4851}{1078}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Reduce the fraction \frac{4851}{1078} to lowest terms by extracting and canceling out 539.

$$\frac{\frac{9}{2}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Divide 0.6 by \frac{3\times 4+3}{4} by multiplying 0.6 by the reciprocal of \frac{3\times 4+3}{4}.

$$\frac{\frac{9}{2}-\frac{0.6\times 4}{3\times 4+3}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Multiply 0.6 and 4 to get 2.4.

$$\frac{\frac{9}{2}-\frac{2.4}{3\times 4+3}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{9}{2}-\frac{2.4}{12+3}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Add 12 and 3 to get 15.

$$\frac{\frac{9}{2}-\frac{2.4}{15}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Expand \frac{2.4}{15} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{9}{2}-\frac{24}{150}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Reduce the fraction \frac{24}{150} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{9}{2}-\frac{4}{25}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{9}{2}-\frac{4}{25}\times \frac{4+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Add 4 and 1 to get 5.

$$\frac{\frac{9}{2}-\frac{4}{25}\times \frac{5}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Multiply \frac{4}{25} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9}{2}-\frac{4\times 5}{25\times 2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Do the multiplications in the fraction \frac{4\times 5}{25\times 2}.

$$\frac{\frac{9}{2}-\frac{20}{50}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Reduce the fraction \frac{20}{50} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{9}{2}-\frac{2}{5}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Least common multiple of 2 and 5 is 10. Convert \frac{9}{2} and \frac{2}{5} to fractions with denominator 10.

$$\frac{\frac{45}{10}-\frac{4}{10}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Since \frac{45}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{45-4}{10}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Subtract 4 from 45 to get 41.

$$\frac{\frac{41}{10}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Divide 3.75 by \frac{1\times 2+1}{2} by multiplying 3.75 by the reciprocal of \frac{1\times 2+1}{2}.

$$\frac{\frac{41}{10}+\frac{3.75\times 2}{1\times 2+1}}{2.2}$$

Multiply 3.75 and 2 to get 7.5.

$$\frac{\frac{41}{10}+\frac{7.5}{1\times 2+1}}{2.2}$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{41}{10}+\frac{7.5}{2+1}}{2.2}$$

Add 2 and 1 to get 3.

$$\frac{\frac{41}{10}+\frac{7.5}{3}}{2.2}$$

Expand \frac{7.5}{3} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{41}{10}+\frac{75}{30}}{2.2}$$

Reduce the fraction \frac{75}{30} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{41}{10}+\frac{5}{2}}{2.2}$$

Least common multiple of 10 and 2 is 10. Convert \frac{41}{10} and \frac{5}{2} to fractions with denominator 10.

$$\frac{\frac{41}{10}+\frac{25}{10}}{2.2}$$

Since \frac{41}{10} and \frac{25}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{41+25}{10}}{2.2}$$

Add 41 and 25 to get 66.

$$\frac{\frac{66}{10}}{2.2}$$

Reduce the fraction \frac{66}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{33}{5}}{2.2}$$

Express \frac{\frac{33}{5}}{2.2} as a single fraction.

$$\frac{33}{5\times 2.2}$$

Multiply 5 and 2.2 to get 11.

$$\frac{33}{11}$$

Divide 33 by 11 to get 3.

$$3$$

Factor

$$3$$