Question

Explain how you would use fraction bars to find the quotient of StartFraction 10 Over 12 EndFraction divided by StartFraction 4 Over 6 EndFraction. What is the quotient?

Answer 1

To find the quotient of \( \frac{10}{12} \div \frac{4}{6} \) using fraction bars, you can follow these steps:

1. **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:
\[
\frac{10}{12} \div \frac{4}{6} = \frac{10}{12} \times \frac{6}{4}
\]

2. **Use Fraction Bars to Represent the Fractions**:
You can draw two fraction bars: one for \( \frac{10}{12} \) and one for \( \frac{6}{4} \).

3. **Multiply the Fraction Bars**:
When you multiply two fractions, you multiply the numerators and the denominators:
\[
\frac{10 \times 6}{12 \times 4}
\]

4. **Calculate the Numerator and Denominator**:
- Calculate the numerator:
\[
10 \times 6 = 60
\]
- Calculate the denominator:
\[
12 \times 4 = 48
\]

Therefore, the expression becomes:
\[
\frac{60}{48}
\]

5. **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:
\[
\frac{60 \div 12}{48 \div 12} = \frac{5}{4}
\]

6. **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.