Questions: Estimate. Then enter the quotient as a fraction greater than 1 and in mixed number form. 3 1/2 ÷ 2/3 Estimate: +1= 3 1/2+2/3= or 7

Solution Steps

To solve the division of mixed numbers and fractions, first convert the mixed number into an improper fraction. Then, divide by the fraction by multiplying by its reciprocal. Simplify the resulting fraction if possible. Finally, convert the improper fraction back into a mixed number.

The mixed number \(3 \frac{1}{2}\) can be converted to an improper fraction as follows: \[ 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2} \]

Next, we need to divide the improper fraction by \(\frac{2}{3}\). This is done by multiplying by the reciprocal: \[ \frac{7}{2} \div \frac{2}{3} = \frac{7}{2} \times \frac{3}{2} = \frac{21}{4} \]

The result \(\frac{21}{4}\) can be converted back to a mixed number: \[ 21 \div 4 = 5 \quad \text{(whole number)} \] \[ 21 \mod 4 = 1 \quad \text{(remainder)} \] Thus, the mixed number is: \[ 5 \frac{1}{4} \]

Final Answer