Question

Which expression(s), when simplified, give positive values?

Select ALL that apply.

A. -1/2 x 1/3
B. 1/2 x -1/3
C. -1/2 x -1/3
D. -1/2 / -1/3
E. 1/2 / -1/3

Answer 1

Let's simplify each expression step by step to determine if they give positive values.

A. \(-\frac{1}{2} \times \frac{1}{3}\)
\[ = -\frac{1}{6} \]
This is negative.

B. \(\frac{1}{2} \times -\frac{1}{3}\)
\[ = -\frac{1}{6} \]
This is negative.

C. \(-\frac{1}{2} \times -\frac{1}{3}\)
\[ = \frac{1}{6} \]
This is positive.

D. \(-\frac{1}{2} \div -\frac{1}{3}\)
To divide by a fraction, we can multiply by its reciprocal:
\[ = -\frac{1}{2} \times -\frac{3}{1} = \frac{3}{2} \]
This is positive.

E. \(\frac{1}{2} \div -\frac{1}{3}\)
\[ = \frac{1}{2} \times -\frac{3}{1} = -\frac{3}{2} \]
This is negative.

So, the expressions that give positive values when simplified are:

**C and D.**