Solve (1999*1/24+1)*13/5-33/11*32/3=127

$$( 1999 \times \frac { 1 } { 24 } + 1 ) \times 1 \frac { 3 } { 5 } - 3 \frac { 3 } { 11 } \times 3 \frac { 2 } { 3 } = 127$$

Verify

Solution Steps

Multiply both sides of the equation by 1320, the least common multiple of 24,5,11,3.

$$264\left(1999\times \frac{1}{24}+1\right)\left(1\times 5+3\right)-40\left(3\times 11+3\right)\left(3\times 3+2\right)=167640$$

Multiply 1999 and \frac{1}{24} to get \frac{1999}{24}.

$$264\left(\frac{1999}{24}+1\right)\left(1\times 5+3\right)-40\left(3\times 11+3\right)\left(3\times 3+2\right)=167640$$

Convert 1 to fraction \frac{24}{24}.

$$264\left(\frac{1999}{24}+\frac{24}{24}\right)\left(1\times 5+3\right)-40\left(3\times 11+3\right)\left(3\times 3+2\right)=167640$$

Since \frac{1999}{24} and \frac{24}{24} have the same denominator, add them by adding their numerators.

$$264\times \frac{1999+24}{24}\left(1\times 5+3\right)-40\left(3\times 11+3\right)\left(3\times 3+2\right)=167640$$

Add 1999 and 24 to get 2023.

$$264\times \frac{2023}{24}\left(1\times 5+3\right)-40\left(3\times 11+3\right)\left(3\times 3+2\right)=167640$$

Express 264\times \frac{2023}{24} as a single fraction.

$$\frac{264\times 2023}{24}\left(1\times 5+3\right)-40\left(3\times 11+3\right)\left(3\times 3+2\right)=167640$$

Multiply 264 and 2023 to get 534072.

$$\frac{534072}{24}\left(1\times 5+3\right)-40\left(3\times 11+3\right)\left(3\times 3+2\right)=167640$$

Divide 534072 by 24 to get 22253.

$$22253\left(1\times 5+3\right)-40\left(3\times 11+3\right)\left(3\times 3+2\right)=167640$$

Multiply 1 and 5 to get 5.

$$22253\left(5+3\right)-40\left(3\times 11+3\right)\left(3\times 3+2\right)=167640$$

Add 5 and 3 to get 8.

$$22253\times 8-40\left(3\times 11+3\right)\left(3\times 3+2\right)=167640$$

Multiply 22253 and 8 to get 178024.

$$178024-40\left(3\times 11+3\right)\left(3\times 3+2\right)=167640$$

Multiply 3 and 11 to get 33.

$$178024-40\left(33+3\right)\left(3\times 3+2\right)=167640$$

Add 33 and 3 to get 36.

$$178024-40\times 36\left(3\times 3+2\right)=167640$$

Multiply 40 and 36 to get 1440.

$$178024-1440\left(3\times 3+2\right)=167640$$

Multiply 3 and 3 to get 9.

$$178024-1440\left(9+2\right)=167640$$

Add 9 and 2 to get 11.

$$178024-1440\times 11=167640$$

Multiply 1440 and 11 to get 15840.

$$178024-15840=167640$$

Subtract 15840 from 178024 to get 162184.

$$162184=167640$$

Compare 162184 and 167640.

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