Solve {l}{2/3=(5/6)(8/3)(5/81)}{3=2}

$$\left. \begin{array} { l } { \frac { 2 } { 3 } = ( \frac { 5 } { 6 } ) ( \frac { 8 } { 3 } ) ( \frac { 5 } { 81 } ) } \\ { 3 = 2 } \end{array} \right.$$

Verify

Solution Steps

Multiply \frac{5}{6} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}=\frac{5\times 8}{6\times 3}\times \frac{5}{81}\text{ and }3=2$$

Do the multiplications in the fraction \frac{5\times 8}{6\times 3}.

$$\frac{2}{3}=\frac{40}{18}\times \frac{5}{81}\text{ and }3=2$$

Reduce the fraction \frac{40}{18} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}=\frac{20}{9}\times \frac{5}{81}\text{ and }3=2$$

Multiply \frac{20}{9} times \frac{5}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}=\frac{20\times 5}{9\times 81}\text{ and }3=2$$

Do the multiplications in the fraction \frac{20\times 5}{9\times 81}.

$$\frac{2}{3}=\frac{100}{729}\text{ and }3=2$$

Least common multiple of 3 and 729 is 729. Convert \frac{2}{3} and \frac{100}{729} to fractions with denominator 729.

$$\frac{486}{729}=\frac{100}{729}\text{ and }3=2$$

Compare \frac{486}{729} and \frac{100}{729}.

$$\text{false}\text{ and }3=2$$

Compare 3 and 2.

$$\text{false}\text{ and }\text{false}$$

The conjunction of \text{false} and \text{false} is \text{false}.

$$\text{false}$$