Questions: Write the ratio 6 2/3 to 3 1/7 as a simplified fraction.

Solution Steps

To write the given ratio as a simplified fraction, first convert the mixed numbers to improper fractions. Then, divide the first fraction by the second fraction, which is equivalent to multiplying the first fraction by the reciprocal of the second fraction. Finally, simplify the resulting fraction.

The mixed number \(6 \frac{2}{3}\) can be converted to an improper fraction as follows: \[ 6 \frac{2}{3} = 6 + \frac{2}{3} = \frac{18}{3} + \frac{2}{3} = \frac{20}{3} \]

Similarly, the mixed number \(3 \frac{1}{7}\) is converted: \[ 3 \frac{1}{7} = 3 + \frac{1}{7} = \frac{21}{7} + \frac{1}{7} = \frac{22}{7} \]

The ratio of \(6 \frac{2}{3}\) to \(3 \frac{1}{7}\) can be expressed as: \[ \text{Ratio} = \frac{20/3}{22/7} \]

This can be simplified by multiplying by the reciprocal of the second fraction: \[ \text{Ratio} = \frac{20}{3} \times \frac{7}{22} = \frac{20 \times 7}{3 \times 22} = \frac{140}{66} \]

To simplify \(\frac{140}{66}\), we find the greatest common divisor (GCD) of 140 and 66, which is 2: \[ \frac{140 \div 2}{66 \div 2} = \frac{70}{33} \]

Final Answer