Evaluate the following.
$\begin{array}{r}
-10 \div 5= \\
-4 \times(-6)=
\end{array}$
Answer (1)
Divide -10 by 5, resulting in -2.
Multiply -4 by -6, resulting in 24.
The evaluated expressions are − 10 ÷ 5 = − 2 and − 4 × ( − 6 ) = 24 .
The final answers are − 2 and 24 .
Explanation
Problem Analysis We are asked to evaluate two simple arithmetic expressions: a division and a multiplication involving negative numbers. Let's tackle them one at a time!
Evaluating the Division First, we need to evaluate − 10 ÷ 5 . This is a division operation. When we divide a negative number by a positive number, the result is negative. So, we have: − 10 ÷ 5 = − 2
Evaluating the Multiplication Next, we need to evaluate − 4 × ( − 6 ) . This is a multiplication operation. When we multiply two negative numbers, the result is positive. So, we have: − 4 × ( − 6 ) = 24
Final Answer Therefore, the results of the two expressions are -2 and 24, respectively.
Examples
Understanding how to perform arithmetic operations with negative numbers is crucial in many real-world scenarios. For example, if you have a debt of $10 and you split it equally among 5 friends, each friend owes you 2 ( -10 \div 5 = -2$). Similarly, if you lose $4 each day for 6 days, your total loss is 24 ( -4 \times 6 = -24$), but if you reduce your losses by $4 each day for 6 days, the total reduction in losses is 24 ( -4 \times -6 = 24$). These basic operations are fundamental in personal finance, accounting, and many other fields.
