Solve 5div31/3=3div10/3=?

$$5 \div 3 \frac { 1 } { 3 } = 3 \div \frac { 10 } { 3 } = ?$$

Verify

Solution Steps

Divide 5 by \frac{3\times 3+1}{3} by multiplying 5 by the reciprocal of \frac{3\times 3+1}{3}.

$$\frac{5\times 3}{3\times 3+1}=\frac{3}{\frac{10}{3}}$$

Multiply 5 and 3 to get 15.

$$\frac{15}{3\times 3+1}=\frac{3}{\frac{10}{3}}$$

Multiply 3 and 3 to get 9.

$$\frac{15}{9+1}=\frac{3}{\frac{10}{3}}$$

Add 9 and 1 to get 10.

$$\frac{15}{10}=\frac{3}{\frac{10}{3}}$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{3}{2}=\frac{3}{\frac{10}{3}}$$

Divide 3 by \frac{10}{3} by multiplying 3 by the reciprocal of \frac{10}{3}.

$$\frac{3}{2}=3\times \frac{3}{10}$$

Express 3\times \frac{3}{10} as a single fraction.

$$\frac{3}{2}=\frac{3\times 3}{10}$$

Multiply 3 and 3 to get 9.

$$\frac{3}{2}=\frac{9}{10}$$

Least common multiple of 2 and 10 is 10. Convert \frac{3}{2} and \frac{9}{10} to fractions with denominator 10.

$$\frac{15}{10}=\frac{9}{10}$$

Compare \frac{15}{10} and \frac{9}{10}.

$$\text{false}$$