Question

Which inequality is true?
StartFraction 8 Over 5 EndFraction less-than StartFraction 9 Over 10 EndFraction
1 greater-than StartFraction 6 Over 5 EndFraction
Five-halves less-than 2 and one-half
StartFraction 8 Over 4 EndFraction less-than five-halves

Answer 1

Let's evaluate each inequality one by one.

1. \( \frac{8}{5} < \frac{9}{10} \)

To compare these fractions, we can convert them to decimals or find a common denominator.

- \( \frac{8}{5} = 1.6 \)
- \( \frac{9}{10} = 0.9 \)

So, \( 1.6 < 0.9 \) is false.

2. \( 1 > \frac{6}{5} \)

This can be computed as:

- \( \frac{6}{5} = 1.2 \)

Thus, \( 1 > 1.2 \) is false.

3. \( \frac{5}{2} < 2 \frac{1}{2} \)

First, convert \( 2 \frac{1}{2} \) to an improper fraction:

- \( 2 \frac{1}{2} = \frac{5}{2} \)

Then, \( \frac{5}{2} < \frac{5}{2} \) is false because they are equal.

4. \( \frac{8}{4} < \frac{5}{2} \)

Simplify \( \frac{8}{4} \):

- \( \frac{8}{4} = 2 \)

Now compare:

- \( 2 < \frac{5}{2} = 2.5 \)

This is true.

Thus, the only true inequality is:

**\( \frac{8}{4} < \frac{5}{2} \)**