Solve 63/11/1frac{5{7}1.48}2.96-21/116/7

$$\frac{ 6 \frac{ 3 }{ 11 } }{ 1 \frac{ 5 }{ 7 } 1.48 } 2.96-2 \frac{ 1 }{ 11 } \frac{ 6 }{ 7 }$$

Evaluate

$$\frac{851}{154}\approx 5.525974026$$

Solution Steps

Multiply 6 and 11 to get 66.

$$\frac{\frac{66+3}{11}}{\frac{1\times 7+5}{7}\times 1.48}\times 2.96-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Add 66 and 3 to get 69.

$$\frac{\frac{69}{11}}{\frac{1\times 7+5}{7}\times 1.48}\times 2.96-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Multiply 1 and 7 to get 7.

$$\frac{\frac{69}{11}}{\frac{7+5}{7}\times 1.48}\times 2.96-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Add 7 and 5 to get 12.

$$\frac{\frac{69}{11}}{\frac{12}{7}\times 1.48}\times 2.96-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Convert decimal number 1.48 to fraction \frac{148}{100}. Reduce the fraction \frac{148}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{69}{11}}{\frac{12}{7}\times \frac{37}{25}}\times 2.96-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Multiply \frac{12}{7} times \frac{37}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{69}{11}}{\frac{12\times 37}{7\times 25}}\times 2.96-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Do the multiplications in the fraction \frac{12\times 37}{7\times 25}.

$$\frac{\frac{69}{11}}{\frac{444}{175}}\times 2.96-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Divide \frac{69}{11} by \frac{444}{175} by multiplying \frac{69}{11} by the reciprocal of \frac{444}{175}.

$$\frac{69}{11}\times \frac{175}{444}\times 2.96-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Multiply \frac{69}{11} times \frac{175}{444} by multiplying numerator times numerator and denominator times denominator.

$$\frac{69\times 175}{11\times 444}\times 2.96-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Do the multiplications in the fraction \frac{69\times 175}{11\times 444}.

$$\frac{12075}{4884}\times 2.96-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Reduce the fraction \frac{12075}{4884} to lowest terms by extracting and canceling out 3.

$$\frac{4025}{1628}\times 2.96-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Convert decimal number 2.96 to fraction \frac{296}{100}. Reduce the fraction \frac{296}{100} to lowest terms by extracting and canceling out 4.

$$\frac{4025}{1628}\times \frac{74}{25}-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Multiply \frac{4025}{1628} times \frac{74}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4025\times 74}{1628\times 25}-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Do the multiplications in the fraction \frac{4025\times 74}{1628\times 25}.

$$\frac{297850}{40700}-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Reduce the fraction \frac{297850}{40700} to lowest terms by extracting and canceling out 1850.

$$\frac{161}{22}-\frac{2\times 11+1}{11}\times \frac{6}{7}$$

Multiply 2 and 11 to get 22.

$$\frac{161}{22}-\frac{22+1}{11}\times \frac{6}{7}$$

Add 22 and 1 to get 23.

$$\frac{161}{22}-\frac{23}{11}\times \frac{6}{7}$$

Multiply \frac{23}{11} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{161}{22}-\frac{23\times 6}{11\times 7}$$

Do the multiplications in the fraction \frac{23\times 6}{11\times 7}.

$$\frac{161}{22}-\frac{138}{77}$$

Least common multiple of 22 and 77 is 154. Convert \frac{161}{22} and \frac{138}{77} to fractions with denominator 154.

$$\frac{1127}{154}-\frac{276}{154}$$

Since \frac{1127}{154} and \frac{276}{154} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1127-276}{154}$$

Subtract 276 from 1127 to get 851.

$$\frac{851}{154}$$

Factor

$$\frac{23 \cdot 37}{2 \cdot 7 \cdot 11} = 5\frac{81}{154} = 5.525974025974026$$