Solve 14/3div31/2=quad2/3div2/5=

$$\frac { 14 } { 3 } \div 3 \frac { 1 } { 2 } = \quad \frac { 2 } { 3 } \div \frac { 2 } { 5 } =$$

Verify

Solution Steps

Divide \frac{14}{3} by \frac{3\times 2+1}{2} by multiplying \frac{14}{3} by the reciprocal of \frac{3\times 2+1}{2}.

$$\frac{14\times 2}{3\left(3\times 2+1\right)}=\frac{\frac{2}{3}}{\frac{2}{5}}$$

Multiply 14 and 2 to get 28.

$$\frac{28}{3\left(3\times 2+1\right)}=\frac{\frac{2}{3}}{\frac{2}{5}}$$

Multiply 3 and 2 to get 6.

$$\frac{28}{3\left(6+1\right)}=\frac{\frac{2}{3}}{\frac{2}{5}}$$

Add 6 and 1 to get 7.

$$\frac{28}{3\times 7}=\frac{\frac{2}{3}}{\frac{2}{5}}$$

Multiply 3 and 7 to get 21.

$$\frac{28}{21}=\frac{\frac{2}{3}}{\frac{2}{5}}$$

Reduce the fraction \frac{28}{21} to lowest terms by extracting and canceling out 7.

$$\frac{4}{3}=\frac{\frac{2}{3}}{\frac{2}{5}}$$

Divide \frac{2}{3} by \frac{2}{5} by multiplying \frac{2}{3} by the reciprocal of \frac{2}{5}.

$$\frac{4}{3}=\frac{2}{3}\times \frac{5}{2}$$

Multiply \frac{2}{3} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{3}=\frac{2\times 5}{3\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{4}{3}=\frac{5}{3}$$

Compare \frac{4}{3} and \frac{5}{3}.

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