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Chapter 10: Problem 44

Multiply. \(-14 \cdot 34 \cdot 12\)

Short Answer

Expert verified
The product is -5712.

Step by step solution

01

- Multiply the first two numbers

First, multiply (-14) by 34. The multiplication of a negative number with a positive number results in a negative number: \[ -14 \times 34 = -476 \]
02

- Multiply the result with the third number

Next, take the result from the previous step, which is -476, and multiply it by 12: \[ -476 \times 12 = -5712 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Negative numbers
Negative numbers are numbers less than zero, and they carry a minus sign (-) in front of them. Understanding how negative numbers interact with positive numbers in operations like multiplication is very important.

When you multiply a negative number by a positive number, the result is always negative. This is because of the rules of integer multiplication. For example, when multiplying -14 by 34, the result is -476 because a negative times a positive equals a negative.
Step-by-step multiplication
Breaking down multiplication into steps makes it more manageable, especially when dealing with multiple numbers. Let's take the given example and break it down:

  • Step 1: Start with the first two numbers in the sequence. Here, we have -14 and 34. Multiply them to get -476.

  • Step 2: Take the result from the first step, -476, and multiply it by the third number, which is 12. The final result is -5712.


This method helps ensure each step is understood before moving on to the next one.
Integer multiplication
Multiplying integers, which include both positive and negative whole numbers, follows a set of basic rules:

  • When two positive numbers are multiplied, the result is positive. For example, 3 times 4 equals 12.

  • When a positive number is multiplied by a negative number, the result is negative. For example, 5 times -7 equals -35.

  • When two negative numbers are multiplied together, the result is positive. For example, -6 times -8 equals 48.


Following these rules for the multiplication of -14, 34, and 12 ensures the correct result: -5712.

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