Multiplication and Division of Rational Numbers - Steps ... - Free Printable

To solve the problem, we need to evaluate each expression and determine which ones equal \(-8\). Let's go through each expression step by step.

Expression 1: \( 16 \cdot -\frac{1}{2} \)

\[
16 \cdot -\frac{1}{2} = 16 \cdot -0.5 = -8
\]
This expression equals \(-8\).

Expression 2: \( -\frac{16}{3} \cdot \frac{1}{2} \)

\[
-\frac{16}{3} \cdot \frac{1}{2} = -\frac{16 \cdot 1}{3 \cdot 2} = -\frac{16}{6} = -\frac{8}{3}
\]
This expression does not equal \(-8\).

Expression 3: \( -1.25 \times 6.4 \)

\[
-1.25 \times 6.4 = -8
\]
This expression equals \(-8\).

Expression 4: \( -2 \cdot 4 \)

\[
-2 \cdot 4 = -8
\]
This expression equals \(-8\).

Expression 5: \( 12 \times -\frac{2}{3} \)

\[
12 \times -\frac{2}{3} = -\frac{12 \cdot 2}{3} = -\frac{24}{3} = -8
\]
This expression equals \(-8\).

Expression 6: \( -1(-8) \)

\[
-1(-8) = 8
\]
This expression does not equal \(-8\).

Expression 7: \( -32 \left( -\frac{1}{4} \right) \)

\[
-32 \left( -\frac{1}{4} \right) = 32 \cdot \frac{1}{4} = 8
\]
This expression does not equal \(-8\).

Expression 8: \( -18 \cdot \frac{1}{2} \)

\[
-18 \cdot \frac{1}{2} = -\frac{18}{2} = -9
\]
This expression does not equal \(-8\).

Expression 9: \( -24 \times \frac{1}{3} \)

\[
-24 \times \frac{1}{3} = -\frac{24}{3} = -8
\]
This expression equals \(-8\).

Expression 10: \( -1.75 \cdot 4.6 \)

\[
-1.75 \cdot 4.6 = -8.05
\]
This expression does not equal \(-8\).

Expression 11: \( -2 \cdot -4 \)

\[
-2 \cdot -4 = 8
\]
This expression does not equal \(-8\).

Expression 12: \( 12 \times -\frac{1}{3} \)

\[
12 \times -\frac{1}{3} = -\frac{12}{3} = -4
\]
This expression does not equal \(-8\).

Expression 13: \( -32 \left( \frac{1}{4} \right) \)

\[
-32 \left( \frac{1}{4} \right) = -\frac{32}{4} = -8
\]
This expression equals \(-8\).

Expression 14: \( 1.6 \cdot -5 \)

\[
1.6 \cdot -5 = -8
\]
This expression equals \(-8\).

Expression 15: \( 1.5 \cdot -6 \)

\[
1.5 \cdot -6 = -9
\]
This expression does not equal \(-8\).

Final Answer:

The expressions that equal \(-8\) are:
1. \( 16 \cdot -\frac{1}{2} \)
2. \( -1.25 \times 6.4 \)
3. \( -2 \cdot 4 \)
4. \( 12 \times -\frac{2}{3} \)
5. \( -24 \times \frac{1}{3} \)
6. \( -32 \left( \frac{1}{4} \right) \)
7. \( 1.6 \cdot -5 \)

Thus, the final answer is:
\[
\boxed{1, 3, 4, 5, 6, 7, 14}
\]