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Find the quotient. \( \frac{1}{4} \div 1 \frac{1}{2}=\square \)

Ask by Donnelly Byrd. in the United States
Jan 20,2025

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Tutor-Verified Answer

Answer

The quotient is \( \frac{1}{6} \).

Solution

To find the quotient of \( \frac{1}{4} \div 1 \frac{1}{2} \), follow these steps: 1. **Convert the mixed number to an improper fraction:** \[ 1 \frac{1}{2} = \frac{3}{2} \] 2. **Set up the division problem with fractions:** \[ \frac{1}{4} \div \frac{3}{2} \] 3. **Change the division to multiplication by the reciprocal:** \[ \frac{1}{4} \times \frac{2}{3} = \frac{2}{12} \] 4. **Simplify the fraction:** \[ \frac{2}{12} = \frac{1}{6} \] **Final Answer:** \(\boxed{\dfrac{1}{6}}\)

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The Deep Dive

To divide \( \frac{1}{4} \) by \( 1 \frac{1}{2} \), first convert \( 1 \frac{1}{2} \) to an improper fraction. \( 1 \frac{1}{2} = \frac{3}{2} \). Now, we need to rewrite the division as multiplication by the reciprocal: \[ \frac{1}{4} \div \frac{3}{2} = \frac{1}{4} \times \frac{2}{3} = \frac{1 \times 2}{4 \times 3} = \frac{2}{12} = \frac{1}{6}. \] So, the quotient is \( \frac{1}{6} \). But wait! Did you know that fractions can often lead to fun kitchen experiments? You can use this knowledge while baking or cooking! For example, if you're converting recipes, understanding fractions helps you scale ingredients accurately. And speaking of scaling, if you're ever in a pinch, remember to break down fractions to their simplest form to make calculations easier. A common mistake is not recognizing when they can be simplified before you do the actual math, which can lead to confusion down the line!

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