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Chapter 3: Problem 243

In the following exercises, simplify each expression. $$-3(-5)(6)$$

Short Answer

Expert verified
90

Step by step solution

01

- Simplify inside the parentheses

First, note that there are no operations to simplify inside the parentheses \(-3(-5)(6)\).
02

- Apply the negative sign to the first factor

Multiply \(-3\) and \(-5\) together. The product of two negative numbers is a positive number.\[-3 \times -5 = 15\].
03

- Perform the remaining multiplication

Now, multiply the resulting positive number by \(6\).\[15 \times 6 = 90\].

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Key Concepts

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

Negative Numbers
Understanding negative numbers is vital when simplifying expressions like \(-3(-5)(6)\).
Negative numbers are less than zero and usually represented by a minus sign (`-`).
When you multiply two negative numbers, their product is a positive number.
This is because a negative times a negative reverses twice, resulting in a positive.
If you multiply a negative number by a positive number, the result is always negative.
For example:
  • \(-2 \times -3 = 6\)
  • \(-4 \times 2 = -8\)
This pattern helps simplify complex expressions.
Parentheses
Parentheses ( ) are used in mathematics to group parts of an expression.
They show which operations should be performed first, according to the order of operations.
In the example \(-3(-5)(6)\), the parentheses just group the numbers but do not change their values.
It's important to look inside the parentheses first but since there's no operation within just numbers, you move to multiplication.
This rule helps to structure the steps to solve any math problem correctly.
Multiplication
Multiplication involves combining numbers to get a product.
This operation is straightforward but can be tricky when negative numbers are involved.
Firstly, identify if the numbers to be multiplied are, positive or negative.
Multiplying same-sign numbers (both positive or both negative) gives a positive product.
Multiplying different-sign numbers (one positive, one negative) gives a negative product.
For instance:
  • \(-3 \times -5 = 15\), both negative makes positive
  • \(-3 \times 6 = -18\), different signs make negative
Consistently applying these rules ensures the accuracy of your results.

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Most popular questions from this chapter

In the following exercises, solve. Early one morning, the temperature in Syracuse was \(-8^{\circ} \mathrm{F}\) . By noon, it had risen \(12^{\circ} .\) What was the temperature at noon?

In the following exercises, simplify. $$ -3 \cdot 8 $$

In the following exercises, translate and solve. The product of \(-6\) and \(y\) is \(-42\)

In the following exercises, divide. $$ 96 \div(-16) $$

In the following exercises, compare the numbers, using \(<\) or \(>\) or=. (a) \(-5\\_|-5|\) (b) \(-|-2|\\_-2\)
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