Solve 49/69*8/9+11/92*8/9-frac{3}{92}*frac{8}{9}+frac{3}{64}*frac{8}{9}

$$\frac { 49 } { 69 } \cdot \frac { 8 } { 9 } + \frac { 11 } { 92 } \cdot \frac { 8 } { 9 } - \frac { 3 } { 92 } \cdot \frac { 8 } { 9 } + \frac { 3 } { 64 } \cdot \frac { 8 } { 9 }$$

Evaluate

$$\frac{3727}{4968}\approx 0.750201288$$

Solution Steps

Multiply \frac{49}{69} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 8}{69\times 9}+\frac{11}{92}\times \frac{8}{9}-\frac{3}{92}\times \frac{8}{9}+\frac{3}{64}\times \frac{8}{9}$$

Do the multiplications in the fraction \frac{49\times 8}{69\times 9}.

$$\frac{392}{621}+\frac{11}{92}\times \frac{8}{9}-\frac{3}{92}\times \frac{8}{9}+\frac{3}{64}\times \frac{8}{9}$$

Multiply \frac{11}{92} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{392}{621}+\frac{11\times 8}{92\times 9}-\frac{3}{92}\times \frac{8}{9}+\frac{3}{64}\times \frac{8}{9}$$

Do the multiplications in the fraction \frac{11\times 8}{92\times 9}.

$$\frac{392}{621}+\frac{88}{828}-\frac{3}{92}\times \frac{8}{9}+\frac{3}{64}\times \frac{8}{9}$$

Reduce the fraction \frac{88}{828} to lowest terms by extracting and canceling out 4.

$$\frac{392}{621}+\frac{22}{207}-\frac{3}{92}\times \frac{8}{9}+\frac{3}{64}\times \frac{8}{9}$$

Least common multiple of 621 and 207 is 621. Convert \frac{392}{621} and \frac{22}{207} to fractions with denominator 621.

$$\frac{392}{621}+\frac{66}{621}-\frac{3}{92}\times \frac{8}{9}+\frac{3}{64}\times \frac{8}{9}$$

Since \frac{392}{621} and \frac{66}{621} have the same denominator, add them by adding their numerators.

$$\frac{392+66}{621}-\frac{3}{92}\times \frac{8}{9}+\frac{3}{64}\times \frac{8}{9}$$

Add 392 and 66 to get 458.

$$\frac{458}{621}-\frac{3}{92}\times \frac{8}{9}+\frac{3}{64}\times \frac{8}{9}$$

Multiply \frac{3}{92} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{458}{621}-\frac{3\times 8}{92\times 9}+\frac{3}{64}\times \frac{8}{9}$$

Do the multiplications in the fraction \frac{3\times 8}{92\times 9}.

$$\frac{458}{621}-\frac{24}{828}+\frac{3}{64}\times \frac{8}{9}$$

Reduce the fraction \frac{24}{828} to lowest terms by extracting and canceling out 12.

$$\frac{458}{621}-\frac{2}{69}+\frac{3}{64}\times \frac{8}{9}$$

Least common multiple of 621 and 69 is 621. Convert \frac{458}{621} and \frac{2}{69} to fractions with denominator 621.

$$\frac{458}{621}-\frac{18}{621}+\frac{3}{64}\times \frac{8}{9}$$

Since \frac{458}{621} and \frac{18}{621} have the same denominator, subtract them by subtracting their numerators.

$$\frac{458-18}{621}+\frac{3}{64}\times \frac{8}{9}$$

Subtract 18 from 458 to get 440.

$$\frac{440}{621}+\frac{3}{64}\times \frac{8}{9}$$

Multiply \frac{3}{64} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{440}{621}+\frac{3\times 8}{64\times 9}$$

Do the multiplications in the fraction \frac{3\times 8}{64\times 9}.

$$\frac{440}{621}+\frac{24}{576}$$

Reduce the fraction \frac{24}{576} to lowest terms by extracting and canceling out 24.

$$\frac{440}{621}+\frac{1}{24}$$

Least common multiple of 621 and 24 is 4968. Convert \frac{440}{621} and \frac{1}{24} to fractions with denominator 4968.

$$\frac{3520}{4968}+\frac{207}{4968}$$

Since \frac{3520}{4968} and \frac{207}{4968} have the same denominator, add them by adding their numerators.

$$\frac{3520+207}{4968}$$

Add 3520 and 207 to get 3727.

$$\frac{3727}{4968}$$

Factor

$$\frac{3727}{2 ^ {3} \cdot 3 ^ {3} \cdot 23} = 0.7502012882447665$$