Solve 4(14/3)+17-8(14/3)+15(14/3)=3-5(14/3)+19(frac{14}{3})

$$4( \frac{ 14 }{ 3 } )+17-8( \frac{ 14 }{ 3 } )+15( \frac{ 14 }{ 3 } ) = 3-5( \frac{ 14 }{ 3 } )+19( \frac{ 14 }{ 3 } )$$

Verify

Solution Steps

Express 4\times \frac{14}{3} as a single fraction.

$$\frac{4\times 14}{3}+17-8\times \frac{14}{3}+15\times \frac{14}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

Multiply 4 and 14 to get 56.

$$\frac{56}{3}+17-8\times \frac{14}{3}+15\times \frac{14}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

Convert 17 to fraction \frac{51}{3}.

$$\frac{56}{3}+\frac{51}{3}-8\times \frac{14}{3}+15\times \frac{14}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

Since \frac{56}{3} and \frac{51}{3} have the same denominator, add them by adding their numerators.

$$\frac{56+51}{3}-8\times \frac{14}{3}+15\times \frac{14}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

Add 56 and 51 to get 107.

$$\frac{107}{3}-8\times \frac{14}{3}+15\times \frac{14}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

Express 8\times \frac{14}{3} as a single fraction.

$$\frac{107}{3}-\frac{8\times 14}{3}+15\times \frac{14}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

Multiply 8 and 14 to get 112.

$$\frac{107}{3}-\frac{112}{3}+15\times \frac{14}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

Since \frac{107}{3} and \frac{112}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{107-112}{3}+15\times \frac{14}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

Subtract 112 from 107 to get -5.

$$-\frac{5}{3}+15\times \frac{14}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

Express 15\times \frac{14}{3} as a single fraction.

$$-\frac{5}{3}+\frac{15\times 14}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

Multiply 15 and 14 to get 210.

$$-\frac{5}{3}+\frac{210}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

Since -\frac{5}{3} and \frac{210}{3} have the same denominator, add them by adding their numerators.

$$\frac{-5+210}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

Add -5 and 210 to get 205.

$$\frac{205}{3}=3-5\times \frac{14}{3}+19\times \frac{14}{3}$$

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

$$\frac{205}{3}=3-\frac{5\times 14}{3}+19\times \frac{14}{3}$$

Multiply 5 and 14 to get 70.

$$\frac{205}{3}=3-\frac{70}{3}+19\times \frac{14}{3}$$

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

$$\frac{205}{3}=\frac{9}{3}-\frac{70}{3}+19\times \frac{14}{3}$$

Since \frac{9}{3} and \frac{70}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{205}{3}=\frac{9-70}{3}+19\times \frac{14}{3}$$

Subtract 70 from 9 to get -61.

$$\frac{205}{3}=-\frac{61}{3}+19\times \frac{14}{3}$$

Express 19\times \frac{14}{3} as a single fraction.

$$\frac{205}{3}=-\frac{61}{3}+\frac{19\times 14}{3}$$

Multiply 19 and 14 to get 266.

$$\frac{205}{3}=-\frac{61}{3}+\frac{266}{3}$$

Since -\frac{61}{3} and \frac{266}{3} have the same denominator, add them by adding their numerators.

$$\frac{205}{3}=\frac{-61+266}{3}$$

Add -61 and 266 to get 205.

$$\frac{205}{3}=\frac{205}{3}$$

Compare \frac{205}{3} and \frac{205}{3}.

$$\text{true}$$