To use fraction bars to find the quotient of [tex]\(\frac{10}{12} \div \frac{4}{6}\)[/tex], follow these steps:
1. Understand the Problem: We are asked to divide [tex]\(\frac{10}{12}\)[/tex] by [tex]\(\frac{4}{6}\)[/tex]. Dividing by a fraction is equivalent to multiplying by its reciprocal.
2. Visualize the Fractions Using Bars:
- The fraction [tex]\(\frac{10}{12}\)[/tex] can be visualized as a bar divided into 12 equal parts with 10 parts shaded.
- The fraction [tex]\(\frac{4}{6}\)[/tex] can be visualized as a bar divided into 6 equal parts with 4 parts shaded.
3. Find the Reciprocal: The reciprocal of [tex]\(\frac{4}{6}\)[/tex] is [tex]\(\frac{6}{4}\)[/tex].
4. Set up the Multiplication: Instead of dividing by [tex]\(\frac{4}{6}\)[/tex], we can multiply [tex]\(\frac{10}{12}\)[/tex] by [tex]\(\frac{6}{4}\)[/tex].
5. Multiply the Fractions:
- Multiply the numerators: [tex]\(10 \times 6 = 60\)[/tex]
- Multiply the denominators: [tex]\(12 \times 4 = 48\)[/tex]
- So the multiplication gives us [tex]\(\frac{60}{48}\)[/tex].
6. Simplify the Fraction:
- Find the greatest common divisor of 60 and 48, which is 12.
- Divide both the numerator and the denominator by 12: [tex]\(\frac{60 \div 12}{48 \div 12} = \frac{5}{4}\)[/tex].
7. Convert to Decimal (optional): If needed, converting [tex]\(\frac{5}{4}\)[/tex] to a decimal gives us 1.25.
Therefore, the quotient of [tex]\(\frac{10}{12} \div \frac{4}{6}\)[/tex] is [tex]\(\frac{5}{4}\)[/tex] or 1.25.
