Solve (91/4-82/3)+5/4+(42/9-2frac{5}{6}):1frac{1}{9}=2frac{1}{4}

$$( 9 \frac { 1 } { 4 } - 8 \frac { 2 } { 3 } ) + \frac { 5 } { 4 } + ( 4 \frac { 2 } { 9 } - 2 \frac { 5 } { 6 } ) : 1 \frac { 1 } { 9 } = 2 \frac { 1 } { 4 }$$

Verify

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3.

$$3\left(9\times 4+1\right)-4\left(8\times 3+2\right)+15+\frac{54}{5}\left(\frac{4\times 9+2}{9}-\frac{2\times 6+5}{6}\right)=3\left(2\times 4+1\right)$$

Multiply 9 and 4 to get 36.

$$3\left(36+1\right)-4\left(8\times 3+2\right)+15+\frac{54}{5}\left(\frac{4\times 9+2}{9}-\frac{2\times 6+5}{6}\right)=3\left(2\times 4+1\right)$$

Add 36 and 1 to get 37.

$$3\times 37-4\left(8\times 3+2\right)+15+\frac{54}{5}\left(\frac{4\times 9+2}{9}-\frac{2\times 6+5}{6}\right)=3\left(2\times 4+1\right)$$

Multiply 3 and 37 to get 111.

$$111-4\left(8\times 3+2\right)+15+\frac{54}{5}\left(\frac{4\times 9+2}{9}-\frac{2\times 6+5}{6}\right)=3\left(2\times 4+1\right)$$

Multiply 8 and 3 to get 24.

$$111-4\left(24+2\right)+15+\frac{54}{5}\left(\frac{4\times 9+2}{9}-\frac{2\times 6+5}{6}\right)=3\left(2\times 4+1\right)$$

Add 24 and 2 to get 26.

$$111-4\times 26+15+\frac{54}{5}\left(\frac{4\times 9+2}{9}-\frac{2\times 6+5}{6}\right)=3\left(2\times 4+1\right)$$

Multiply -4 and 26 to get -104.

$$111-104+15+\frac{54}{5}\left(\frac{4\times 9+2}{9}-\frac{2\times 6+5}{6}\right)=3\left(2\times 4+1\right)$$

Subtract 104 from 111 to get 7.

$$7+15+\frac{54}{5}\left(\frac{4\times 9+2}{9}-\frac{2\times 6+5}{6}\right)=3\left(2\times 4+1\right)$$

Add 7 and 15 to get 22.

$$22+\frac{54}{5}\left(\frac{4\times 9+2}{9}-\frac{2\times 6+5}{6}\right)=3\left(2\times 4+1\right)$$

Multiply 4 and 9 to get 36.

$$22+\frac{54}{5}\left(\frac{36+2}{9}-\frac{2\times 6+5}{6}\right)=3\left(2\times 4+1\right)$$

Add 36 and 2 to get 38.

$$22+\frac{54}{5}\left(\frac{38}{9}-\frac{2\times 6+5}{6}\right)=3\left(2\times 4+1\right)$$

Multiply 2 and 6 to get 12.

$$22+\frac{54}{5}\left(\frac{38}{9}-\frac{12+5}{6}\right)=3\left(2\times 4+1\right)$$

Add 12 and 5 to get 17.

$$22+\frac{54}{5}\left(\frac{38}{9}-\frac{17}{6}\right)=3\left(2\times 4+1\right)$$

Least common multiple of 9 and 6 is 18. Convert \frac{38}{9} and \frac{17}{6} to fractions with denominator 18.

$$22+\frac{54}{5}\left(\frac{76}{18}-\frac{51}{18}\right)=3\left(2\times 4+1\right)$$

Since \frac{76}{18} and \frac{51}{18} have the same denominator, subtract them by subtracting their numerators.

$$22+\frac{54}{5}\times \frac{76-51}{18}=3\left(2\times 4+1\right)$$

Subtract 51 from 76 to get 25.

$$22+\frac{54}{5}\times \frac{25}{18}=3\left(2\times 4+1\right)$$

Multiply \frac{54}{5} times \frac{25}{18} by multiplying numerator times numerator and denominator times denominator.

$$22+\frac{54\times 25}{5\times 18}=3\left(2\times 4+1\right)$$

Do the multiplications in the fraction \frac{54\times 25}{5\times 18}.

$$22+\frac{1350}{90}=3\left(2\times 4+1\right)$$

Divide 1350 by 90 to get 15.

$$22+15=3\left(2\times 4+1\right)$$

Add 22 and 15 to get 37.

$$37=3\left(2\times 4+1\right)$$

Multiply 2 and 4 to get 8.

$$37=3\left(8+1\right)$$

Add 8 and 1 to get 9.

$$37=3\times 9$$

Multiply 3 and 9 to get 27.

$$37=27$$

Compare 37 and 27.

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