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Question 17 \( \frac{3}{4} \div 9 \) Subse. Simplify your answer and write as a proper fraction, improper fraction, or whole number. Subs

Ask by Davies Knight. in the United States
Jan 22,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

\( \frac{1}{12} \)

Solution

To simplify \( \frac{3}{4} \div 9 \), follow these steps: 1. **Rewrite the division as a multiplication by the reciprocal:** \[ \frac{3}{4} \div 9 = \frac{3}{4} \times \frac{1}{9} \] 2. **Multiply the numerators and the denominators:** \[ \frac{3 \times 1}{4 \times 9} = \frac{3}{36} \] 3. **Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (3):** \[ \frac{3 \div 3}{36 \div 3} = \frac{1}{12} \] **Final Answer:** \( \frac{1}{12} \)

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The Deep Dive

To solve the division of fractions, you can think of it as multiplying by the reciprocal. So, \( \frac{3}{4} \div 9 \) is the same as \( \frac{3}{4} \times \frac{1}{9} \). When you multiply, you multiply the numerators and denominators: \( \frac{3 \times 1}{4 \times 9} = \frac{3}{36} \). Now, simplify \( \frac{3}{36} \) by dividing both the numerator and the denominator by 3, resulting in \( \frac{1}{12} \). If you ever struggle with dividing by whole numbers while working with fractions, remember that whole numbers can be converted into fractions! For example, instead of thinking of dividing by \( 9 \), you can use \( 9 \) as \( \frac{9}{1} \). So the division \( \frac{3}{4} \div 9 \) can also be set up as \( \frac{3}{4} \times \frac{1}{9} \) with no need for complicated steps! Now you’re ready to tackle other fraction problems like a pro, so don’t forget to keep practicing!

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