Problem 14 Multiply \((-12)(-2)(6)(3)(-5)\)... [FREE SOLUTION]

Chapter 2: Problem 14

Multiply \((-12)(-2)(6)(3)(-5)\) A. \(-2,160\) B. 216 C. \(-216\) D. \(2,160\)

Short Answer

Expert verified

The result is -2160.

Step by step solution

Multiply First Two Negative Numbers

Start by multiplying the first two negative numbers: \[(-12) \times (-2) = 24\]. The result is positive because the product of two negative numbers is positive.

Multiply the Result with the Next Positive Number

Now multiply the result from Step 1 with 6: \[24 \times 6 = 144\].This multiplication continues with positive numbers and the result remains positive.

Multiply the Result with Another Positive Number

Multiply the result from Step 2 by 3: \[144 \times 3 = 432\].Again, continue multiplying positive numbers, and the result is positive.

Multiply by the Final Negative Number

Finally, multiply the result from Step 3 by the last negative number, -5:\[432 \times (-5) = -2160\].The result is negative because a positive number multiplied by a negative number yields a negative result.

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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, represented with a minus sign, such as (-1), (-5), and (-12). They are fundamental in a variety of math operations and can represent things like debt or temperature below zero. Understanding how negative numbers interact with other types of numbers is key. When multiplying or dividing two negative numbers, the result is always positive. This concept can be confusing, but just remember that the signs "cancel out" each other in these operations. When negative numbers multiply or divide with positive numbers, however, the result is negative.

Multiplication of Integers

The multiplication of integers follows the general rules of arithmetic, but the signs of the numbers involved affect the result. An integer is a whole number that can be either positive, negative, or zero.
When multiplying two integers:

If both integers have the same sign (both positive or both negative), the product is positive.
If the integers have different signs (one positive, one negative), the product is negative.
The product of any integer and zero is always zero.

In the exercise we considered, the process began by multiplying two negative numbers, resulting in a positive product. This is a demonstration of the rule that multiplying like signs results in a positive number.

Integer Operations

Understanding integer operations is crucial for solving problems that involve whole numbers. Integer operations include addition, subtraction, multiplication, and division.
There are some simple rules to follow:

Adding two positive integers or two negative integers is straightforward: combine their values, and keep the sign. For example, (-2) + (-3) = (-5).
When subtracting, add the opposite of the number instead. This means 5 - (-2) becomes 5 + 2 = 7.
For multiplication and division, consider the signs as explained before: two like signs yield a positive result, while unlike signs yield a negative result.

Integer operations are foundational in building up your algebra skills, and mastering these concepts is crucial to advancing in mathematics.

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91影视

Multiply \((-12)(-2)(6)(3)(-5)\) A. \(-2,160\) B. 216 C. \(-216\) D. \(2,160\)

Short Answer

Step by step solution

Multiply First Two Negative Numbers

Multiply the Result with the Next Positive Number

Multiply the Result with Another Positive Number

Multiply by the Final Negative Number

Key Concepts

Negative Numbers

Multiplication of Integers

Integer Operations

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