Question

7/4,9/5,11/8 increasing order by common denominator

Answer 1

To compare the fractions \( \frac{7}{4} \), \( \frac{9}{5} \), and \( \frac{11}{8} \) using a common denominator, we first need to find the least common multiple (LCM) of the denominators 4, 5, and 8.

The denominators are:
- \( 4 = 2^2 \)
- \( 5 = 5^1 \)
- \( 8 = 2^3 \)

The LCM is obtained by taking the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \) (from 8).
- For \( 5 \): The highest power is \( 5^1 \) (from 5).

Thus, the LCM is \( 2^3 \times 5^1 = 8 \times 5 = 40 \).

Next, we convert each fraction to have the common denominator of 40.

1. For \( \frac{7}{4} \):
\[
\frac{7}{4} = \frac{7 \times 10}{4 \times 10} = \frac{70}{40}
\]

2. For \( \frac{9}{5} \):
\[
\frac{9}{5} = \frac{9 \times 8}{5 \times 8} = \frac{72}{40}
\]

3. For \( \frac{11}{8} \):
\[
\frac{11}{8} = \frac{11 \times 5}{8 \times 5} = \frac{55}{40}
\]

Now we can compare these fractions:
- \( \frac{55}{40} \)
- \( \frac{70}{40} \)
- \( \frac{72}{40} \)

Ordering them from smallest to largest, we get:
\[
\frac{11}{8}, \frac{7}{4}, \frac{9}{5}
\]

Thus, the fractions in increasing order are:
\[
\frac{11}{8}, \frac{7}{4}, \frac{9}{5}
\]