To find the quotient of \(\frac{10}{12}\) divided by \(\frac{4}{6}\) using fraction bars, you can follow these steps:
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Set Up Fraction Bars: Draw two fraction bars, one for \(\frac{10}{12}\) and one for \(\frac{4}{6}\).
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Represent Each Fraction:
- For \(\frac{10}{12}\), divide the first bar into 12 equal parts and shade 10 of those parts. Each part represents \(\frac{1}{12}\).
- For \(\frac{4}{6}\), divide the second bar into 6 equal parts and shade 4 of those parts. Each part represents \(\frac{1}{6}\).
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Find Equivalent Fractions: To facilitate the division, convert \(\frac{4}{6}\) into an equivalent fraction with a denominator of 12 (to match the first fraction). Since \(\frac{4}{6}\) is equal to \(\frac{8}{12}\), rewrite it as so.
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Set Up Division of Fractions: Now, you need to divide \(\frac{10}{12}\) by \(\frac{8}{12}\). When dividing fractions, you can multiply by the reciprocal of the second fraction: \[ \frac{10}{12} \div \frac{8}{12} = \frac{10}{12} \times \frac{12}{8} \]
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Multiply and Simplify:
- Multiply the numerators: \(10 \times 12 = 120\)
- Multiply the denominators: \(12 \times 8 = 96\)
- This results in \(\frac{120}{96}\).
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Simplify the Result:
- To simplify \(\frac{120}{96}\), find the greatest common divisor (GCD) of 120 and 96, which is 24.
- Divide both the numerator and the denominator by 24: \[ \frac{120 \div 24}{96 \div 24} = \frac{5}{4} \]
Thus, the quotient of \(\frac{10}{12}\) divided by \(\frac{4}{6}\) is \(\frac{5}{4}\) or \(1 \frac{1}{4}\) in mixed number form.
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