Question

Multiply \(2(-4)(-1)\) A. -8 B. 8 C. 7 D. -3

Short answer

B. 8

Step-by-step solution

- Understand Multiplication of Integers

To solve this exercise, it is essential to understand how to multiply integers, especially when negative numbers are involved. Recall that the product of two negative numbers is a positive number.

- Multiply the First Two Numbers

Start by multiplying the first two numbers: a. Multiply 2 by -4: \( 2 \times (-4) = -8 \) b. The result is -8.

- Multiply the Result with the Third Number

Next, multiply the result from step 2 (-8) by the third number (-1): a. Multiply -8 by -1: \( -8 \times (-1) = 8 \) b. The result is 8.

- Select the Correct Answer

Based on the calculations, the final answer is 8. Thus, the correct option is B.

Key concepts

multiplying integers

When multiplying integers, knowing the rules can make the process simpler. Integers are whole numbers that can be either positive or negative. When you multiply any two integers, the product can be positive or negative, depending on the signs of the integers involved.
Here’s a quick guide:

• Multiplying two positive integers results in a positive product.
• Multiplying two negative integers also gives a positive product.
• Multiplying a positive integer by a negative integer yields a negative product.

Knowing these rules can greatly help in solving multiplication problems involving integers.

negative numbers

Negative numbers are numbers less than zero, represented with a minus sign (-). Understanding how to handle negative numbers is crucial when performing operations like multiplication. For example:

• If you multiply a negative number by another negative number, the negatives cancel out, and the product is positive.
• When you multiply a negative number by a positive number, the product remains negative because the two different signs do not cancel each other out.

It’s important to be vigilant and not confuse the cancellation rule for addition and subtraction with multiplication.

product of integers

The product of integers refers to the result you get when you multiply two or more integers together. Consider the problem: Multiply 2, -4, and -1.

Let’s walk through it:

• First, multiply 2 by -4. The positive multiplied by the negative results in -8. Hence, 2 × (-4) = -8.
• Next, take the result (-8) and multiply it by -1. Since we’re multiplying two negative numbers, the result is a positive number. Thus, -8 × (-1) = 8.

Hence, the product of these integers (2, -4, and -1) is 8. Always apply the rules of integer multiplication to determine the correct sign and final product.