Problem 246 In the following exercises, simp... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 3: Problem 246

In the following exercises, simplify each expression. $$-5 \cdot 3 \cdot 10$$

Short Answer

Expert verified

-150

Step by step solution

Multiply the constants

Begin by multiplying the first two numbers: o$-5 \times 3 = -15$

Multiply the result by the remaining constant

Next, take the result from Step 1 and multiply it by the remaining number: o$-15 \times 10 = -150$

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Key Concepts

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

Multiplication

Multiplication is one of the basic arithmetic operations. Essentially, it is repeated addition. For example, multiplying two numbers means adding one of the numbers repeatedly based on the value of the other number.
In the context of our problem, we are multiplying three numbers: $-5, 3, \text{and} 10$.
Here are some key points to remember when multiplying numbers:

Start by multiplying two numbers at a time.
Always multiply constants first and combine them in steps if there are more than two.
It is essential to keep track of the signs (positive or negative) while multiplying.

In our problem, we begin by multiplying $-5 \text{and} \ 3$: $-5 \times 3 = -15$. Finally, we multiply the result by \10\: $-15 \times 10 = -150$..

Negative Numbers

Negative numbers can sometimes be tricky, especially when multiplying. Here are some vital rules to keep in mind:

Multiplying two negative numbers results in a positive number. For example, $-2 \times -3 = 6$.
Multiplying a negative number and a positive number results in a negative number. For instance, $-4 \times 5 = -20$.

In our exercise, the presence of negative numbers affects the outcome. We first multiply $-5 \text{and} 3$, which gives us $-15$.
Then, we multiply \ (-15 \text{and} 10) lines which still gives us a negative number, $-150$.
Be cautious and always check the resulting sign for each multiplication step.

Order of Operations

The order of operations ensures that expressions are simplified correctly. Following the proper sequence avoids confusion and errors. Here are some rules to follow:

Follow the PEMDAS rule: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
When you have only multiplication and no other operations, proceed from left to right.

In our exercise, the order is straightforward since there are only multiplication operations involved.
We start with the leftmost multiplication: $-5 \times 3 = -15$.
Then, we multiply the result by the next number: $-15 \times 10 = -150$.

It helps keep the process organized and makes complex expressions simpler and accurate.

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91影视

In the following exercises, simplify each expression. $$-5 \cdot 3 \cdot 10$$

Short Answer

Step by step solution

Multiply the constants

Multiply the result by the remaining constant

Key Concepts

Multiplication

Negative Numbers

Order of Operations

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