Question

Use the properties of operations and rules for multiplying and dividing signed numbers to solve:

(−3)×( 4/3)÷(− 2/5)×( 1/6)

2

1 2/3

-2

1 3/4
​

Answer 1

Let's solve the expression step by step, applying the properties of operations with signed numbers.

The original expression is:
\[
(-3) \times \left(\frac{4}{3}\right) \div \left(-\frac{2}{5}\right) \times \left(\frac{1}{6}\right)
\]

1. **Multiplication and Division of Signed Numbers**:
- Multiply first:
\[
(-3) \times \left(\frac{4}{3}\right) = -\frac{12}{3} = -4
\]

2. **Next, divide**:
- Now we have:
\[
-4 \div \left(-\frac{2}{5}\right)
\]
- Dividing by a negative number involves changing signs:
\[
-4 \div \left(-\frac{2}{5}\right) = -4 \times \left(-\frac{5}{2}\right) = 4 \times \frac{5}{2} = \frac{20}{2} = 10
\]

3. **Finally, multiply**:
- Now, we will multiply by \(\frac{1}{6}\):
\[
10 \times \left(\frac{1}{6}\right) = \frac{10}{6} = \frac{5}{3}
\]

At this point, \(\frac{5}{3}\) can be expressed as a mixed number:
\[
\frac{5}{3} = 1 \frac{2}{3}
\]

Therefore, the final result of the expression is:
\[
\boxed{1 \frac{2}{3}}
\]