Question

32. Which equation is true? a 4/-9= -4/9 b 4/-9 = 2/-3c 4/-9= 4/9 d 4-9= 2/3

Answer 1

Let's analyze each given equation:

a) \( \frac{4}{-9} = \frac{-4}{9} \)

This is false. The left side is negative (\(-\frac{4}{9}\)) and the right side is also negative. So this is actually true.

b) \( \frac{4}{-9} = \frac{2}{-3} \)

To check this, we simplify \( \frac{2}{-3} \). This is equal to \( -\frac{2}{3} \). Now, let's find a common denominator for \( \frac{4}{-9} \):

To compare \( \frac{4}{-9} \) with \( \frac{-2}{3} \), we can convert \( \frac{-2}{3} \) to have a denominator of -9:
\[
-2/3 = -2 \times \frac{3}{3} = -\frac{6}{9}
\]
So \( \frac{4}{-9} \) does not equal \( \frac{2}{-3} \).

So, overall it's false.

c) \( \frac{4}{-9} = \frac{4}{9} \)

This is false. On the left, we have \( -\frac{4}{9} \), and on the right, we have \( \frac{4}{9} \). So they are not equal.

d) \( 4 - 9 = \frac{2}{3} \)

Calculating \( 4 - 9 \):
\[
4 - 9 = -5
\]
And \( \frac{2}{3} \) is positive. So this is also false.

From this analysis, option a is the only true statement among the provided equations.