Question
(4) Find the quotient. \( 3 \frac{5}{7} \div 4=\square \)
Ask by Wright Phillips. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The quotient is \( \frac{13}{14} \).
Solution
To find the quotient of \( 3 \frac{5}{7} \div 4 \), follow these steps:
1. **Convert the Mixed Number to an Improper Fraction:**
\( 3 \frac{5}{7} = \frac{3 \times 7 + 5}{7} = \frac{21 + 5}{7} = \frac{26}{7} \)
2. **Divide by 4:**
Dividing by 4 is the same as multiplying by \( \frac{1}{4} \):
\( \frac{26}{7} \div 4 = \frac{26}{7} \times \frac{1}{4} = \frac{26}{28} \)
3. **Simplify the Fraction:**
Both numerator and denominator can be divided by 2:
\( \frac{26 \div 2}{28 \div 2} = \frac{13}{14} \)
**Quotient:** \( \frac{13}{14} \)
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Simplify this solution Bonus Knowledge
To solve \( 3 \frac{5}{7} \div 4 \), first convert the mixed number to an improper fraction. Multiply the whole number (3) by the denominator (7) and add the numerator (5) to get \( 3 \frac{5}{7} = \frac{26}{7} \). Now, divide by 4, which is the same as multiplying by its reciprocal, \( \frac{1}{4} \): \[ \frac{26}{7} \div 4 = \frac{26}{7} \times \frac{1}{4} = \frac{26 \times 1}{7 \times 4} = \frac{26}{28}. \] Now simplify \( \frac{26}{28} \) by dividing the numerator and the denominator by their greatest common divisor, which is 2: \[ \frac{26 \div 2}{28 \div 2} = \frac{13}{14}. \] So, the final quotient is \( \frac{13}{14} \).
