Questions: Find the quotient. 7 ÷ 2 3/4 Write your answer as a mixed number.

Transcript text: Find the quotient. \[ 7 \div 2 \frac{3}{4} \] Write your answer as a mixed number.

Solution

Solution Steps

To find the quotient of \(7 \div 2 \frac{3}{4}\), first convert the mixed number \(2 \frac{3}{4}\) into an improper fraction. Then, perform the division by multiplying 7 by the reciprocal of the improper fraction. Finally, convert the resulting improper fraction back into a mixed number.

Step 1: Convert the Mixed Number to an Improper Fraction

The mixed number \(2 \frac{3}{4}\) can be converted to an improper fraction. Multiply the whole number 2 by the denominator 4 and add the numerator 3: \[ 2 \times 4 + 3 = 8 + 3 = 11 \] Thus, the improper fraction is \(\frac{11}{4}\).

Step 2: Divide by Multiplying with the Reciprocal

To find the quotient of \(7 \div 2 \frac{3}{4}\), multiply 7 by the reciprocal of \(\frac{11}{4}\): \[ 7 \times \frac{4}{11} = \frac{28}{11} \]

Step 3: Convert the Result to a Mixed Number

Convert the improper fraction \(\frac{28}{11}\) to a mixed number. Divide the numerator by the denominator: \[ 28 \div 11 = 2 \quad \text{remainder} \quad 6 \] Thus, the mixed number is \(2 \frac{6}{11}\).

Final Answer

\(\boxed{2 \frac{6}{11}}\)

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