To find the quotient of [tex]\(\frac{10}{12} \div \frac{4}{6}\)[/tex] using fraction bars, let's break down the process into clear, understandable steps.
1. Understanding Division of Fractions:
- Division of fractions is equivalent to multiplying the first fraction by the reciprocal of the second fraction.
- The reciprocal of a fraction is obtained by flipping its numerator and denominator. Thus, the reciprocal of [tex]\(\frac{4}{6}\)[/tex] is [tex]\(\frac{6}{4}\)[/tex].
2. Setting Up the Problem:
- We start with the original division problem: [tex]\(\frac{10}{12} \div \frac{4}{6}\)[/tex].
3. Convert the Problem to Multiplication:
- Instead of dividing by [tex]\(\frac{4}{6}\)[/tex], we multiply by its reciprocal:
[tex]\[
\frac{10}{12} \times \frac{6}{4}
\][/tex]
4. Multiplying the Fractions:
- To multiply fractions, multiply the numerators together and the denominators together:
[tex]\[
\left( \frac{10 \times 6}{12 \times 4} \right)
\][/tex]
5. Calculate the Result:
- Numerator: [tex]\(10 \times 6 = 60\)[/tex]
- Denominator: [tex]\(12 \times 4 = 48\)[/tex]
- So, the fraction resulting from the multiplication is:
[tex]\[
\frac{60}{48}
\][/tex]
6. Simplify the Fraction:
- Divide both the numerator and the denominator by their greatest common divisor (GCD). For [tex]\(60\)[/tex] and [tex]\(48\)[/tex], the GCD is [tex]\(12\)[/tex].
- Simplifying [tex]\( \frac{60}{48} \)[/tex]:
[tex]\[
\frac{60 \div 12}{48 \div 12} = \frac{5}{4}
\][/tex]
7. Converting the Simplified Fraction to Decimal (Optional):
- [tex]\(\frac{5}{4}\)[/tex] is equivalent to [tex]\(5 \div 4 = 1.25\)[/tex].
Thus, the quotient of [tex]\(\frac{10}{12} \div \frac{4}{6}\)[/tex] is [tex]\(\frac{5}{4}\)[/tex], which is [tex]\(1.25\)[/tex] in decimal form.
