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Chapter 2: Problem 14

Multiply \((-8)(-3)(+4)(-2)(5)\) (a) \(-720\) (b) \(-960\) (c) 540 (d) 400

Short Answer

Expert verified
The correct answer is (b) \(-960\).

Step by step solution

01

Multiply the first two numbers

First, multiply the first two numbers: \((-8) \times (-3) = 24\).Two negative numbers multiplied together result in a positive number.
02

Multiply the result by the third number

Next, multiply the result from Step 1 by the third number: \(24 \times (+4) = 96\).A positive number multiplied by a positive number results in a positive number.
03

Multiply the result by the fourth number

Now, take the result from Step 2 and multiply it by the next number: \(96 \times (-2) = -192\).A positive number multiplied by a negative number results in a negative number.
04

Multiply by the final number

Finally, multiply the result from Step 3 by the last given number: \(-192 \times 5 = -960\).A negative number multiplied by a positive number results in a negative number.

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are those less than zero and are typically used to describe loss, debt, or direction. In multiplication, two negative numbers multiplied together become positive because a negative times a negative reverses direction twice. For example:
  • When you have \((-3) \times (-4)\) , it equals \(12\) .
  • Similarly, \((-5) \times (-6)\) results in \(30\) .
Remember, multiplying a negative number by a positive number yields a negative result because it only reverses direction once. It鈥檚 crucial in mathematical operations involving signed numbers to carry over signs correctly for accurate results.
Grasping Positive Numbers
Positive numbers are greater than zero and stand as the standard form for counting and measuring. They are straightforward in arithmetic operations:
  • Multiplying two positive numbers yields another positive number.
  • For example, \(+4 \times +5 = 20\).
In our exercise, you'll notice positive numbers maintain their nature unless intermixed with negative numbers.
In a product with negative numbers, the presence of a positive number will not alter the result from being positive if multiplied by another positive.
However, if multiplied with a negative, the overall result becomes negative, as was in Step 3 of the solution.
Step-by-Step Solution Clarity
Breaking the multiplication process into smaller, manageable steps can clarify the complex interactions between negative and positive numbers. Here鈥檚 how we apply this step-by-step method:
  • **Step 1:** Calculating \((-8) \times (-3)\) is simplified by recognizing the pair of negatives, resulting in \(24\).
  • **Step 2:** Then, multiply \(24 \times (+4)\) that follows the simple rule of positive multiplication.
  • **Step 3:** Transition to \(96 \times (-2)\) requires understanding that now the product becomes negative.
  • **Step 4:** When multiplying \(-192\) with \(5\) , the result remains negative, leading us to \(-960\).
Each step ensures that signs are correctly applied, optimizing comprehension of signed number multiplication. This meticulous method helps prevent mistakes often made in calculations involving both negative and positive elements.

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Most popular questions from this chapter

Divide \((-48) \div(+6)\) (a) 8 (b) \(-8\) (c) 9 1 (d) \(-5\)

Subtract \(-12-3\) (a) \(-9\) (b) \(-15\) (c) 9 (d) 15

Divide \((-22) \div(-11)\) (a) \(-2\) (b) 11 (c) \(-11\) (d) 2

Simplify \(8-3+2-7-5\) (a) 25 (b) \(-19\) (c) \(-5\) (d) \(+5\)

Simplify \(5 \times 2^{2}+4-3\) (a) 101 (b) 0 (c) 19 (d) 21
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