Question

5/6,11/9,3/4 increasing order by common denominator

Answer 1

To compare the fractions \( \frac{5}{6} \), \( \frac{11}{9} \), and \( \frac{3}{4} \) and arrange them in increasing order using a common denominator, we first need to find the least common multiple (LCM) of the denominators (6, 9, and 4).

1. **Finding the LCM:**
- The prime factorization of the numbers is:
- \( 6 = 2 \times 3 \)
- \( 9 = 3^2 \)
- \( 4 = 2^2 \)

- The LCM is found by taking the highest power of each prime:
- \( 2^2 \) from 4
- \( 3^2 \) from 9

- Therefore, the LCM is:
- \( 4 \times 9 = 36 \)

2. **Convert each fraction to have a denominator of 36:**
- Convert \( \frac{5}{6} \):
\[
\frac{5}{6} = \frac{5 \times 6}{6 \times 6} = \frac{30}{36}
\]

- Convert \( \frac{11}{9} \):
\[
\frac{11}{9} = \frac{11 \times 4}{9 \times 4} = \frac{44}{36}
\]

- Convert \( \frac{3}{4} \):
\[
\frac{3}{4} = \frac{3 \times 9}{4 \times 9} = \frac{27}{36}
\]

3. **Now, we have the fractions:**
- \( \frac{5}{6} = \frac{30}{36} \)
- \( \frac{3}{4} = \frac{27}{36} \)
- \( \frac{11}{9} = \frac{44}{36} \)

4. **Arranging in increasing order:**
- \( \frac{27}{36} < \frac{30}{36} < \frac{44}{36} \)

Thus, in increasing order, the fractions are:
\[
\frac{3}{4}, \frac{5}{6}, \frac{11}{9}
\]