To find the quotient of \( \frac{10}{12} \div \frac{4}{6} \) using fraction bars, you can follow these steps:
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Rewrite the Division as Multiplication by the Reciprocal: Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the expression as: \[ \frac{10}{12} \div \frac{4}{6} = \frac{10}{12} \times \frac{6}{4} \]
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Use Fraction Bars to Represent the Fractions: You can draw two fraction bars: one for \( \frac{10}{12} \) and one for \( \frac{6}{4} \).
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Multiply the Fraction Bars: When you multiply two fractions, you multiply the numerators and the denominators: \[ \frac{10 \times 6}{12 \times 4} \]
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Calculate the Numerator and Denominator:
- Calculate the numerator: \[ 10 \times 6 = 60 \]
- Calculate the denominator: \[ 12 \times 4 = 48 \]
Therefore, the expression becomes: \[ \frac{60}{48} \]
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Simplify the Fraction: Now, we need to simplify \( \frac{60}{48} \). We can find the greatest common divisor (GCD) of 60 and 48. The GCD is 12.
Divide both the numerator and the denominator by 12: \[ \frac{60 \div 12}{48 \div 12} = \frac{5}{4} \]
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Final Result: The quotient of \( \frac{10}{12} \div \frac{4}{6} \) is: \[ \frac{5}{4} \]
So, the final answer is \( \frac{5}{4} \) or \( 1 \frac{1}{4} \) in mixed number form.
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