Solve 4(16/3+3)-5(32/3-6)=2(64/3-3)+16/3

$$4( \frac{ 16 }{ 3 } +3)-5( \frac{ 32 }{ 3 } -6)=2( \frac{ 64 }{ 3 } -3)+ \frac{ 16 }{ 3 }$$

Verify

Solution Steps

Convert 3 to fraction \frac{9}{3}.

$$4\left(\frac{16}{3}+\frac{9}{3}\right)-5\left(\frac{32}{3}-6\right)=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Since \frac{16}{3} and \frac{9}{3} have the same denominator, add them by adding their numerators.

$$4\times \frac{16+9}{3}-5\left(\frac{32}{3}-6\right)=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Add 16 and 9 to get 25.

$$4\times \frac{25}{3}-5\left(\frac{32}{3}-6\right)=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Express 4\times \frac{25}{3} as a single fraction.

$$\frac{4\times 25}{3}-5\left(\frac{32}{3}-6\right)=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Multiply 4 and 25 to get 100.

$$\frac{100}{3}-5\left(\frac{32}{3}-6\right)=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Convert 6 to fraction \frac{18}{3}.

$$\frac{100}{3}-5\left(\frac{32}{3}-\frac{18}{3}\right)=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Since \frac{32}{3} and \frac{18}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{100}{3}-5\times \frac{32-18}{3}=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Subtract 18 from 32 to get 14.

$$\frac{100}{3}-5\times \frac{14}{3}=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Express 5\times \frac{14}{3} as a single fraction.

$$\frac{100}{3}-\frac{5\times 14}{3}=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Multiply 5 and 14 to get 70.

$$\frac{100}{3}-\frac{70}{3}=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Since \frac{100}{3} and \frac{70}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{100-70}{3}=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Subtract 70 from 100 to get 30.

$$\frac{30}{3}=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Divide 30 by 3 to get 10.

$$10=2\left(\frac{64}{3}-3\right)+\frac{16}{3}$$

Convert 3 to fraction \frac{9}{3}.

$$10=2\left(\frac{64}{3}-\frac{9}{3}\right)+\frac{16}{3}$$

Since \frac{64}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$10=2\times \frac{64-9}{3}+\frac{16}{3}$$

Subtract 9 from 64 to get 55.

$$10=2\times \frac{55}{3}+\frac{16}{3}$$

Express 2\times \frac{55}{3} as a single fraction.

$$10=\frac{2\times 55}{3}+\frac{16}{3}$$

Multiply 2 and 55 to get 110.

$$10=\frac{110}{3}+\frac{16}{3}$$

Since \frac{110}{3} and \frac{16}{3} have the same denominator, add them by adding their numerators.

$$10=\frac{110+16}{3}$$

Add 110 and 16 to get 126.

$$10=\frac{126}{3}$$

Divide 126 by 3 to get 42.

$$10=42$$

Compare 10 and 42.

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